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Report Overview
Summary of Alignment & Usability: Open Up Resources 6-8 Mathematics | Math
Math 6-8
The materials reviewed for Open Up Resources 6-8 Math meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for usability including teacher supports, assessment, and student supports.
6th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
7th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
8th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 7th Grade
Alignment Summary
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and meet expectations for practice-content connections.
7th Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.
Gateway 1
v1.5
Criterion 1.1: Focus
Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.
Indicator 1A
Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for Open Up Resources Grade 7 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.
Program assessments include Pre-Unit Diagnostic Assessments, Cool Downs, Mid-Unit Assessments, Performance Tasks, and End-of-Unit Assessments which are summative. According to the Course Guide, “At the end of each unit is the end-of-unit assessment. These assessments have a specific length and breadth, with problem types that are intended to gauge students’ understanding of the key concepts of the unit while also preparing students for new-generation standardized exams. Problem types include multiple-choice, multiple-response, short answer, restricted constructed response, and extended response. Problems vary in difficulty and depth of knowledge.” Examples of summative End-of-Unit Assessment problems that assess grade-level standards include:
Unit 2: Introducing Proportional Relationships, End-of-Unit Assessment: Version B, Problem 3, “Kiran walked at a constant speed. He walked 1 mile in 15 minutes. Which of these equations represents the distance d (in miles) that Kiran walks in t minutes. A. d = t + 14 B. d = t - 14 C. d = 15t D. d = 115t.” (7.RP.2c)
Unit 5: Rational Number Arithmetic, End-of-Unit Assessment: Version A, Problem 7, “Jada walks up to a tank of water that can hold up to 10 gallons. When it is active, a drain empties water from the tank at a constant rate. When Jada first sees the tank, it contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water. 1. At what rate is the amount of water in the tank changing? Use a signed number, and include the unit of measurement in your answer. 2. How many more minutes will it take for the tank to drain completely? Explain or show your reasoning. 3. How many minutes before Jada arrived was the water tank completely full? Explain or show your reasoning.” (7.NS.2 and 7.NS.3)
Unit 6: Expressions, Equations, and Inequalities, End-of-Unit Assessment: Version A, Problem 3, “Select all expressions that are equivalent to 6x + 1 - (3x - 1). A. 6x + 1 - 3x - 1 B. 6x + (-3x) + 1 + 1 C. 3x + 2 D. 6x - 3x + 1 - 1 E. 6x + 1 + (-3x) - (-1).” (7.EE.1)
Unit 7: Angles, Triangles, and Prisms, End-of-Unit Assessment: Version B, Problem 5, “Draw as many different triangles as possible that have a side length of 5 units, a 45° angle, and a 90° angle. Clearly mark the side lengths and angles given.” (7.G.2)
Unit 8: Probability and Sampling, End-of-Unit Assessment: Version B, Problem 4, “A school plans to start selling snacks at their basketball games. They want to know which snacks would be most popular. 1. What is the population for the school’s question? 2. Give an example of a sample the school could use to help answer their question.” (7.SP.1)
Indicator 1B
Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Open Up Resources Grade 7 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.
Each lesson is structured into four phases: Warm Up, Instructional Activities, Lesson Synthesis, and Cool Down. This structure ensures thorough engagement with grade-level problems and alignment with educational standards.
The Warm Up phase starts each lesson, helping students prepare for the day’s content and enhancing their number sense or procedural fluency. Following the Warm Up, students participate in one to three instructional activities that focus on the learning standards. These activities, described in the Activity Narrative, form the lesson's core.
After completing the activities, students synthesize their learning, integrating new knowledge with prior understanding. The lesson concludes with a Cool Down phase, a formative assessment to measure student understanding. Additionally, each lesson includes Independent Practice Problems to reinforce the concepts.
Instructional materials engage all students in extensive work with grade-level problems. Examples include:
Unit 4: Proportional Relationships and Percentages, Section B: Percent Increase and Decrease, Lesson 6: Increasing and Decreasing, students use proportional reasoning and percentages to describe and solve problems involving increases and decreases. Activity 1: More Cereal and a Discounted Shirt, Problem 1, “A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much cereal does the box come with now?” Activity 2: Using Tape Diagrams, Problem 1, “Match each situation to a diagram. Be prepared to explain your reasoning (two tape diagrams with 25% shaded are shown, one diagram is longer on the bottom, the second has equal parts on top and bottom). a. Compared with last year’s strawberry harvest, this year’s strawberry harvest is a 25% increase. b. This year’s blueberry harvest is 75% of last year’s. c. Compared with last year, this year’s peach harvest decreased 25%. d. This year’s plum harvest is 125% of last year’s plum harvest.” Practice Problems, Problem 3, “Write each percent increase or decrease as a percentage of the initial amount. The first one is done for you. a. This year, there was 40% more snow than last year. The amount of snow this year is 140% of the amount of snow last year. b. This year, there were 25% fewer sunny days than last year. c. Compared to last month, there was a 50% increase in the number of houses sold this month. d. The runner’s time to complete the marathon was 10% less than the time to complete the last marathon.” Materials present students with extensive work with grade-level problems of 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems.)
Unit 5: Rational Number Arithmetic, Section B: Adding and Subtracting Rational Numbers, Lesson 7: Adding and Subtracting to Solve Problems, students add and subtract rational numbers to solve problems in unfamiliar contexts. Warm-Up: Positive or Negative, Problem a. “Without computing: is the solution to -2.7 + x = -3.5 positive or negative?” Activity 1: Phone Inventory, “A store tracks the number of cell phones it has in stock and how many phones it sells. The table shows the inventory for one phone model at the beginning of each day last week. The inventory changes when they sell phones or get shipments of phones into the store. a. What do you think it means when the change is positive? Negative? b. What do you think it means when the inventory is positive? Negative? c. Based on the information in the table, what do you think the inventory will be at on Saturday morning? Explain your reasoning. d. What is the difference between the greatest inventory and the least inventory?” Students are given a table of data that shows the daily inventory and change for Monday through Friday. Practice Problems, Problem 3, “a. How much higher is 500 than 400 m? b. How much higher is 500 than -400 m? c. What is the change in elevation from 8,500 m to 3,400 m? d. What is the change in elevation between 8,500 m and -300 m? e. How much higher is -200 m than 450 m?” Materials present students with extensive work with grade-level problems of 7.NS.3 (Solve real-world and mathematical problems involving the four operations with rational numbers.)
Unit 6: Expressions, Equations, and Inequalities, Section D: Writing Equivalent Expressions, Lesson 19: Expanding and Factoring, students use the distributive property to write equivalent expressions. Activity 1: Factoring and Expanding with Negative Numbers, “In each row, write the equivalent expression. If you get stuck, use a diagram to organize your work. The first row is provided as an example. Diagrams are provided for the first three rows.” Students complete missing information in the table of factored and expanded expressions. Cool Down: Equivalent Expressions, “If you get stuck, use a diagram to organize your work. a. Expand to write an equivalent expression: (-2x + 4y) b. Factor to write an equivalent expression: 26a - 10.” Practice Problems, Problem 1, “a. Expand to write an equivalent expression: (-8x + 12y) b. Factor to write an equivalent expression: 36a - 16.” Materials present students with extensive work with grade-level problems of 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients).
Instructional materials provide opportunities for all students to engage with the full intent of grade-level standards. Examples include:
Unit 2: Introducing Proportional Relationships, Section C: Comparing Proportional and Nonproportional Relationships, Lesson 8: Comparing Relationships with Equations, students determine whether relationships are proportional. Activity 3: All Kinds of Equations, “Here are 6 different equations. y = 4 + x, y = , y = 4x, y = , y = , y = . a. Predict which of these equations represent a proportional relationship. b. Complete each table using the equation that represents the relationship. c. Do these results change your answer to the first question? Explain your reasoning. d. What do the equations of the proportional relationships have in common?” Cool Down: Tables and Chairs, “Andre is setting up rectangular tables for a party. He can fit 6 chairs around a single table. Andre lines up 10 tables end-to-end and tries to fit 60 chairs around them, but he is surprised when he cannot fit them all. a. Write an equation for the relationship between the number of chairs and the number of tables when: 1. the tables are apart from each other: 2. the tables are placed end-to-end: b. Is the first relationship proportional? Explain how you know. c. Is the second relationship proportional? Explain how you know.” Practice Problems, Problem 2, “Decide whether or not each equation represents a proportional relationship. a. The remaining length (L) of a 120-inch rope after x inches have been cut off: 120 - x = L b. The total cost (t) after 8% sales tax is added to an item’s price (p): 1.08p = tc. The number of marbles each sister gets (x) when m marbles are shared equally among four sisters: x = d. The volume (V) of a rectangular prism whose height is 12 cm and base is a square with side lengths s cm: V = 12”. The materials meet the full intent of 7.RP.2 (Recognize and represent proportional relationships between quantities.)
Unit 7: Angles, Triangles, and Prisms, Section A: Angle Relations, Lesson 1: Relationships of Angles, students use reasoning about adjacent angles to determine angle measures. Activity 2: More Pattern Block Angles, “Use pattern blocks to determine the measure of each of these angles.” Students measure an obtuse, exterior, and straight angle (which are pictured). Activity 3: Measuring Like This or Like That, “Tyler and Priya were both measuring angle TUS. Priya thinks the angle measures 40 degrees. Tyler thinks the angle measures 140 degrees. Do you agree with either of them? Explain your reasoning.” Pictured is an acute angle on a protractor. “Cool Down: Identical Isosceles Triangle, “Here are two different patterns made out of the same five identical isosceles triangles. Without using a protractor, determine the measure of ∠x and ∠y. Explain or show your reasoning.” Practice Problems, Problem 3, “Here is a square and some regular octagons. In this pattern, all of the angles inside the octagons have the same measure. The shape in the center is a square. Find the measure of one of the angles inside one of the octagons.” The materials meet the full intent of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.)
Unit 8: Probability and Sampling, Section B: Probability of Multi-step Events, Lesson 8: Keeping Track of All Possible Events, students determine the total possible outcomes of a compound event. Warm-Up: How Many Different Meals?, “How many different meals are possible if each meal includes one main course, one side dish, and one drink?” A table is shown with main courses (grilled chicken, turkey sandwich, pasta salad), side dishes (salad, applesauce), and drinks (milk, juice, water). Activity 2: How Many Sandwiches?, Problem 1, “A submarine sandwich shop makes sandwiches with one kind of bread, one protein, one choice of cheese, and two vegetables. How many different sandwiches are possible? Explain your reasoning. You do not need to write out the sample space. Breads: Italian, white, wheat, Proteins: Tuna, ham, turkey, beans, Cheese: Provolone, Swiss, American, none, and Vegetables: Lettuce, tomatoes, peppers, onions, pickles.” Cool Down: Random Points, “Andre is reviewing proportional relationships. He wants to practice using a graph that goes through a point so that each coordinate is between 1 and 10. a. For the point, how many outcomes are in the sample space? b. For how many outcomes are the x-coordinate and the y-coordinate the same number?” The materials meet the full intent of 7.SP.8b (Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams…)
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, and make connections between clusters and domains. The materials make explicit connections from grade-level work to knowledge from earlier grades and connections from grade-level work to future grades.
Indicator 1C
When implemented as designed, the majority of the materials address the major clusters of each grade.
The materials reviewed for Open Up Resources Grade 7 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.
When implemented as designed, the majority (at least 65%) of the materials, when implemented as designed, address the major clusters of the grade. For example:
The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 5 out of 8, approximately 63%.
The number of lessons devoted to major work of the grade, including supporting work connected to major work is 76 out of 110, approximately 69%.
The number of instructional days devoted to major work of the grade and supporting work connected to major work (includes required lessons and assessments) is 81 out of 118, approximately 69%.
An instructional day analysis is most representative of the materials, including the required lessons and End-of-Unit Assessments from the required Units. As a result, approximately 69% of materials focus on major work of the grade.
Indicator 1D
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials reviewed for Open Up Resources Grade 7 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Each lesson contains Learning Targets that provide descriptions of what students should be able to do after completing the lesson. Standards being addressed are identified and defined. Materials connect learning of supporting and major work to enhance focus on major work. Examples include:
Unit 2: Introducing Proportional Relationships, Section C: Comparing Proportional and Nonproportional Relationships, Lesson 8: Comparing Relationships with Equations, Activity 2: Total Edge Length, Surface Area, and Volume, Problems 1-3, connects the supporting work of 7.G.6 (Solve real-world and mathematical problems involving area, volume and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms) to the major work of 7.RP.1 (Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measure in like or different units) and 7.RP.2 (Recognize and represent proportional relationships between quantities). Students determine whether or not relationships between the quantities are proportional as they reinforce their understanding of edge length, surface area, and volume.) “Here are some cubes with different side lengths. Complete each table. Be prepared to explain your reasoning. a. How long is the total edge length of each cube? b. What is the surface area of each cube? c. What is the volume of each cube?” Problem 2, “Which of these relationships is proportional? Explain how you know.” Problem 3, “Write equations for the total edge length E, total surface area A, and volume V of a cube with side length s.” Students are shown pictures of cubes with side lengths 3, 5, and 7.
Unit 3: Measuring Circles, SectionC: Let’s Put It to Work, Lesson 11: Stained-Glass Windows, Activity 2: A Bigger Window, connects the supporting work of 7.G.1 (Solve problems involving scale drawings of geometric figures) and 7.G.4 (Know the formulas for the area and circumference of a circle and use them to solve problems) and major work of 7.EE.3 (Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form using tools strategically). Students use their cost computations from the previous activity to find the cost of an enlarged version of the stained glass window, scaled by a factor of 3, “A local community member sees the school’s stained glass window and really likes the design. They ask the students to create a larger copy of the window using a scale factor of 3. Would $450 be enough to buy the materials for the larger window? Explain or show your reasoning.” Students are given a picture of the stained glass window, which consists of semi-circles and diamond-shaped pieces.
Unit 7: Angles, Triangles, and Prisms, Section B: Drawing Polygons with Given Conditions, Lesson 6: Building Polygons (Part 1), Activity 2: Building Diego’s and Jada’s Shapes, Problem 1, connects the supporting work of 7.G.2 (Draw geometric shapes with given conditions), to the major work of 7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers). Students build polygons given descriptions of side lengths, “Diego built a quadrilateral using side lengths of 4 in, 5 in, 6 in, and 9 in. a. Build such a shape (students use applet in presentation mode). b. Is your shape an identical copy of Diego’s shape? Explain your reasoning.”
Indicator 1E
Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
The materials reviewed for Open Up Resources Grade 7 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
Each lesson contains Learning Targets that describe what the students should be able to do after completing the lesson. Standards being addressed are identified and defined.
Materials connect major work to major work throughout the grade level when appropriate. Examples include.
Unit 4: Proportional Relationships and Percentages, Section A: Proportional Relationships with Fractions, Lesson 5: Say It with Decimals, Activity 1: Repeating Decimals, Problems 1 and 2 connects the major work of 7.NS.A (Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.) to the major work 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems.) Students convert ratios written as fractions to decimals that repeat or terminate, “Use long division to express each fraction as a decimal. a. b. c. What is similar about your answers to the previous question? What is different?”
Unit 5: Rational Number Arithmetic, Section E: Solving Equations When They are Negative Numbers, Lesson 15: Solving Equations with Rational Numbers, Activity 2: Trip to the Mountains, Problem 1, connects the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations.) to the major work 7.NS.A (Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.) Students solve equations using inverse operations with negative values, “The Hiking Club is on a trip to hike up a mountain. The members increased their elevation 290 feet during their hike this morning, Now they are at an elevation of 450 feet. a. Explain how to find their elevation before the hike. b. Han says the equation e + 290 = 450 describes the situation. What does the variable e represent? c. Han says that he can rewrite the equation as e = 450 + (-290) to solve for e. Compare Han’s strategy to your strategy for finding the beginning elevation.”
Unit 6: Expressions, Equations, and Inequalities, Section D: Writing Equivalent Expressions, Lesson 18: Subtraction in Equivalent Expressions, Activity 2: Organizing Work, Problem 2, connects the major work of 7.EE.A (Use properties of operations to generate equivalent expressions.) to the major work of 7.NS.A (Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.) Students use distributive property to write equivalent expressions with negative numbers, “Use the distributive property to write an expression that is equivalent to (8y + -x + -12). The boxes can help you organize your work.” Students are shown a rectangle with a width of and segmented lengths of 8y, -x and -12.
Materials provide connections from supporting work to supporting work throughout the grade-level when appropriate. Examples include:
Unit 7: Angles, Triangles, and Prisms, Section A: Angle Relationships: Lesson 4: Solving for Unknown Angles, Activity 2: What’s the Match? connects the supporting work of 7.G.A (Draw, construct, and describe geometric figures and describe the relationships between them.) to the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.) Students match relationships between angles in a figure with equations that can represent those relationships, “Match each figure to an equation that represents what is seen in the figure. For each match, explain how you know they are a match. 1. g + h = 180 2. g = h 3. 2h + g = 90 4. g + h + 48 = 180 5. g + h + 35 = 180” Students are given five figures to match.
Unit 8: Probability and Sampling, Section D: Using Samples, Lesson 15: Estimating Population Measures of Center, Activity 2: Who’s Watching What? Connects the supporting work of 7.SP.A (Use random sampling to draw inferences about a population.) to the supporting work of 7.SP.B (Draw informal comparative inferences about two populations.) Students compute the means for sample ages to determine what shows might be associated with each sample and assess the accuracy of population estimates, “Here are three more samples of viewer ages collected for these same 3 television shows. Sample 4: 57, 71, 5, 54, 52, 13, 59, 65, 10, 71 Sample 5: 15, 4, 4, 5, 4, 3, 25, 2, 8, 3 Sample 6: 6, 11, 9, 56, 1, 3, 11, 10, 11, 2. a. Calculate the mean for one of these samples. Record all three answers. b. Which show do you think each of these samples represents? Explain your reasoning. c. For each show, estimate the mean age for all the show’s viewers. d. Calculate the mean absolute deviation for one of the shows’ samples. Make sure each person in your group works with a different sample. Record all three answers. e. What do the different values for the MAD tell you about each group? f. An advertiser has a commercial that appeals to 15- to 16-year-olds. Based on these samples, are any of these shows a good fit for this commercial? Explain or show your reasoning.
Indicator 1F
Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The materials reviewed for Open-Up Resources Grade 7 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The Course Guide contains a Scope and Sequence explaining content standard connections. Some Unit Overviews, Lesson Narratives, and Activity Syntheses describe the progression of standards for the concept being taught. Each Lesson contains a Preparation section identifying learning standards (Building on, Addressing, or Building toward). Content from future grades is identified and related to grade-level work. Examples include:
Unit 2: Proportional Relationships, Unit 2 Overview, “In grades 6–8, students write rates without abbreviated units, for example as ‘3 miles per hour’ or ‘3 miles in every 1 hour.’ Use of notation for derived units such as waits for high school—except for the special cases of area and volume. Students have worked with area since grade 3 and volume since grade 5. Before grade 6, they have learned the meanings of such things as sq cm and cu cm. After students learn exponent notation in grade 6, they also use and .”
Unit 4: Proportional Relationships and Percentages, Section C: Applying Percentages, Lesson 15: Error Intervals, Lesson Narrative, “This material gives students a solid foundation for future work in statistics. It is not necessary at this stage to emphasize the idea of a margin of error which defines a range of possible values. It is enough for students to see the values falling into that range, as preparation for future learning.”
Unit 7: Angles, Triangles, and Prisms, Section B: Drawing Polygons with Given Conditions, Lesson 6: Building Polygons (Part 1), Activity 1 Synthesis, “The purpose of this discussion is to establish what is meant when we say two shapes are identical copies. While students don’t use the word congruent until grade 8, they should recognize that two shapes are identical only when they can match perfectly on top of each other by movements that don’t change lengths or angles.”
Materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples include:
Course Guide, Scope and Sequence, Unit 1: Scaled Drawings, “In grade 3, students distinguished between perimeter and area. They connected rectangle area with multiplication, understanding why (for whole-number side lengths) multiplying the side lengths of a rectangle yields the number of unit squares that tile the rectangle. They used area diagrams to represent instances of the distributive property. In grade 4, students applied area and perimeter formulas for rectangles to solve real-world and mathematical problems, and learned to use protractors. In grade 5, students extended the formula for the area of a rectangle to include rectangles with fractional side lengths. In grade 6, students built on their knowledge of geometry and geometric measurement to produce formulas for the areas of parallelograms and triangles, using these formulas to find surface areas of polyhedra.”
Course Guide, Scope and Sequence, Unit 3: Measuring Circles, “In this unit, students extend their knowledge of circles and geometric measurement, applying their knowledge of proportional relationships to the study of circles. They extend their grade 6 work with perimeters of polygons to circumferences of circles, and recognize that the circumference of a circle is proportional to its diameter, with constant of proportionality π. They encounter informal derivations of the relationship between area, circumference, and radius.”
Unit 5: Rational Number Arithmetic, Section A: Interpreting Negative Numbers, Lesson 1: Interpreting Negative Numbers, Lesson Narrative, “In this lesson, students review what they learned about negative numbers in grade 6, including placing them on the number line, comparing and ordering them, and interpreting them in the contexts of temperature and elevation (MP2). The context of temperature helps build students’ intuition about signed numbers because most students know what it means for a temperature to be negative and are familiar with representing temperatures on a number line (a thermometer). The context of elevation may be less familiar to students, but it provides a concrete (as well as cultural) example of one of the most fundamental uses of signed numbers: representing positions along a line relative to a reference point (sea level in this case). The number line is the primary representation for signed numbers in this unit, and the structure of the number line is used to make sense of the rules of signed number arithmetic in later lessons.”
Indicator 1G
In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.
The materials reviewed for Open Up Resources Grade 7 foster coherence between grades and can be completed within a regular school year with little to no modification.
According to the Grade 7 Course Guide, About These Materials, “Each course contains nine units. Each of the first eight are anchored by a few big ideas in grade-level mathematics. Units contain between 11 and 23 lesson plans. Each unit has a diagnostic assessment for the beginning of the unit (Check Your Readiness) and an end-of-unit assessment. Longer units also have a mid-unit assessment. The last unit in each course is structured differently, and contains optional lessons that help students apply and tie together big ideas from the year. The time estimates in these materials refer to instructional time. Each lesson plan is designed to fit within a class period that is at least 45 minutes long. Some lessons contain optional activities that provide additional scaffolding or practice for teachers to use at their discretion.”
According to the Grade 7 Course Guide:
8 end-of-unit assessments
110 days of lessons
35 days of optional lessons
8 days of optional check your readiness assessments
2 days of optional mid-unit assessments throughout the materials
118 days required (lower range) to 163 days required and optional (upper range)
According to the Grade 7 Course Guide, About These Materials, A Typical Lesson, “A typical lesson has four phases: 1. a Warm-up (5-10 minutes) 2. one or more instructional activities (10-25 minutes) 3. the lesson synthesis (5-10 minutes) 4. a Cool-down (about 5 minutes).”
Overview of Gateway 2
Rigor & the Mathematical Practices
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).
Gateway 2
v1.5
Criterion 2.1: Rigor and Balance
Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and spend sufficient time working with engaging applications of mathematics. There is a balance of the three aspects of rigor within the grade.
Indicator 2A
Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
The materials reviewed for Open Up Resources Grade 7 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
According to the Course Guide, About These Materials, Design Principles, “Each unit begins with a pre-assessment that helps teachers gauge what students know about both prerequisite and upcoming concepts and skills, so that teachers can gauge where students are and make adjustments accordingly. The initial lesson in a unit is designed to activate prior knowledge and provide an easy entry to point to new concepts, so that students at different levels of both mathematical and English language proficiency can engage productively in the work. As the unit progresses, students are systematically introduced to representations, contexts, concepts, language and notation. As their learning progresses, they make connections between different representations and strategies, consolidating their conceptual understanding, and see and understand more efficient methods of solving problems, supporting the shift towards procedural fluency. The distributed practice problems give students ongoing practice, which also supports developing procedural proficiency.”
Materials develop conceptual understanding throughout the grade level. Examples include:
Unit 4: Proportional Relationships and Percentages, Section A: Proportional Relationships with Fractions, Lesson 5: Say It with Decimals, Activity 1: Repeating Decimals, Problem 1, students develop conceptual understanding of rational numbers as repeating and terminating decimals. “Use long division to express each fraction as a decimal. a. b. c. .” (7.NS.2)
Unit 8: Probability and Samples, Section A: Probabilities of Single Step Events, Lesson 3: What are Probabilities?, Warm Up: Which Game Would You Choose? students develop conceptual understanding of probability and possible outcome. “Which game would you choose to play? Explain your reasoning. A. Game 1: You flip a coin and win if it lands showing heads. B. Game 2: You roll a standard number cube and win if it lands showing a number that is divisible by 3.” If it does not come out during student instruction, teachers are prompted to explain, “The number of possible outcomes that count as a win and the number of total possible outcomes are both important to determining the likelihood of an event. That is, although there are two ways to win with the standard number cube and only one way to win on the coin, the greater number of possible outcomes in the second game makes it less likely to provide a win.” (7.SP.5)
Unit 9: Putting It All Together, Section B: Making Connections, Lesson 7: More Expressions and Equations, Activity 2: A Souvenir Stand, Problem 5, students develop conceptual understanding of writing expressions with three unknown quantities. “The souvenir stand sells hats, postcards, and magnets. They have twice as many postcards as hats, and 100 more magnets than postcards. The souvenir stand sells all these items and makes a total profit of $953.25. a. Write an equation that represents this situation. b. How many of each item does the souvenir stand sell? Explain or show your reasoning.” (7.EE.1)
Materials provide opportunities for students to demonstrate conceptual understanding throughout the grade level independently. Examples include:
Unit 5: Rational Number Arithmetic, Section B: Adding and Subtracting Rational Numbers, Lesson 4: Money and Debts, Warm Up: Concert Tickets, students develop conceptual understanding about positive and negative integers. “Priya wants to buy three tickets for a concert. She has earned $135 and each ticket costs $50. She borrows the rest of the money she needs from a bank and buys the tickets. a. How can you represent the amount of money that Priya has after buying the tickets? b. How much more money will Priya need to earn to pay back the money she borrowed from the bank? c. How much money will she have after she pays back the money she borrowed from the bank?” (7.NS.1)
Unit 6: Expressions, Equations, and Inequalities, Section D: Writing Equivalent Expressions, Lesson 19: Expanding and Factoring, Cool Down: Equivalent Expressions, students independently develop conceptual understanding of expanding and factoring using the distributive property to write equivalent expressions. “If you get stuck, use a diagram to organize your work. a. Expand to write an equivalent expression: -(-2x + 4y). b. Factor to write an equivalent expression: 26a - 10.” (7.EE.1)
Unit 8: Probability and Sampling, Section B: Probabilities of Multi-step Events, Lesson 9: Multi-Step Experiments, Activity 2: Cubes and Coins, Problem 2, students independently develop conceptual understanding of probabilities for multi-step experiments. “Suppose you roll two number cubes. What is the probability of getting: a. Both cubes showing the same number? b. Exactly one cube showing an even number? c. At least one cube showing an even number? d. Two values that have a sum of 8? e. Two values that have a sum of 13?” (7.SP.8)
Indicator 2B
Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.
The materials reviewed for Open Up Resources Grade 7 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
According to the Course Guide sections “About These Materials” and “Design Principles”, “Each unit begins with a pre-assessment that helps teachers gauge what students know about both prerequisite and upcoming concepts and skills, so that teachers can gauge where students are and make adjustments accordingly. The initial lesson in a unit is designed to activate prior knowledge and provide an easy entry to point to new concepts, so that students at different levels of both mathematical and English language proficiency can engage productively in the work. As the unit progresses, students are systematically introduced to representations, contexts, concepts, language and notation. As their learning progresses, they make connections between different representations and strategies, consolidating their conceptual understanding, and see and understand more efficient methods of solving problems, supporting the shift towards procedural fluency. The distributed practice problems give students ongoing practice, which also supports developing procedural proficiency.” Materials develop procedural skills and fluency throughout the grade level. Examples include:
Unit 4: Proportional Relationships and Percentages, Lesson 5: Say It with Decimals, Student Work Time, students develop procedural skill and fluency as they convert rational numbers to decimals using long division. “A calculator gives the following decimal representations for some unit fractions: ½ = 0.5, ⅓ = 0.3333333, ¼ = 0.25, ⅕ = 0.2, ⅙ = 0.1666667…” Students answer, “What do you notice? What do you wonder?” Problem 1, “Use long division to express each fraction as a decimal. a. 9/25, b. 11/30, c. 4/11.” (7.NS.2d)
Unit 6: Expression, Equations and Inequalities, Section B, Solving Equations of the Form px + q = r and p(x + q) = r, Lesson 12: Solving Problems about Percent Increase or Decrease, Activity 2: Sale on Shoes, Problem 1, students develop procedural skill and fluency as they solve equations involving percent increase or decrease. “A store is having a sale where all shoes are discounted by 20%. Diego has a coupon for $3 off of the regular price for one pair of shoes. The store first applies the coupon and then takes 20% off of the reduced price. If Diego pays $18.40 for a pair of shoes, what was their original price before the sale and without the coupon?” (7.EE.4a)
Unit 7, Angles, Triangles, and Prisms, Section A: Angle Relationships, Lesson 2, Adjacent Angles, Practice Problems, students develop procedural skill and fluency as they use facts about supplementary, complementary angles to find angle pairs. Problem 1, “Angles A and C are supplementary. Find the measure of angle C.” Problem 2, a. List two pairs of angles in square CDFG that are complementary. Name three angles that sum to 180°.” (7.G.5)
Materials allow students to demonstrate procedural skills and fluency independently throughout the grade level. Examples include:
Unit 6: Expressions, Equations, and Inequalities, Section B: Solving Equations of the Form px + q = r and p(x + q) = r, Lesson 10: Different Options for Solving One Equation, Cool Down: Solve Two Equations, students independently demonstrate procedural skill and fluency as they solve equations using the distributive property or by dividing each side of an equation by a number. “Solve each equation. Show or explain your method. a. 8.88 = 4.44(x - 7) b. 5(y + ) = -13.” (7.EE.4a)
Unit 7: Angles, Triangles, and Prisms, Section A: Angle Relationships, Lesson 3: Nonadjacent Angles, Cool Down: Finding Angle Pairs, students independently demonstrate procedural skill and fluency as they use facts about supplementary, complementary, vertical, and adjacent angles to find angle pairs. “a. Name two pairs of complementary angles in the diagram. b. Name two pairs of supplementary angles in the diagram. c. Draw another angle to make a pair of vertical angles. Label your new angle with its measure.” A diagram with angle measures is shown. (7.G.5)
Unit 8: Probability and Sampling, Lesson 16: Estimating Population Proportions, Activity 1, Reaction Times, Problems 1 - 4, students independently demonstrate procedural skill and fluency as they convert rational numbers to decimals. “The track coach at a high school needs a student whose reaction time is less than 0.4 seconds to help out at track meets. All the twelfth graders in the school measured their reaction times. Your teacher will give you a bag of papers that list their results. Problem 1, Work with your partner to select a random sample of 20 reaction times, and record them in the table. Problem 2, What proportion of your sample is less than 0.4 seconds? Problem 3, Estimate the proportion of all twelfth graders at this school who have a reaction time of less than 0.4 seconds. Explain your reasoning. Problem 4, There are 120 twelfth graders at this school. Estimate how many of them have a reaction time of less than 0.4 seconds.” (7.NS.2d)
Indicator 2C
Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.
The materials reviewed for Open Up Resources Grade 7 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics.
According to the Course Guide, in sections “About These Materials” and “Design Principles,” “Students have opportunities to make connections to real-world contexts throughout the materials. Frequently, carefully-chosen anchor contexts are used to motivate new mathematical concepts, and students have many opportunities to make connections between contexts and the concepts they are learning. Additionally, most units include a real-world application lesson at the end. In some cases, students spend more time developing mathematical concepts before tackling more complex application problems, and the focus is on mathematical contexts.”
Materials include multiple routine and non-routine applications of mathematics throughout the grade level. Examples include:
Unit 5: Rational Number Arithmetic, Section F: Let’s Put It to Work, Lesson 17: The Stock Market, Activity 3: Your Own Stock Portfolio, students engage in a non-routine application problem as they apply operations with rational numbers to solve new values and changes in the stock market. “Your teacher will give you a list of stocks. a. Select a combination of stocks with a total value close to, but no more than, $100. b. Using the new list, how did the total value of your selected stocks change?” Teachers distribute “Stock Prices” and students use their completed “Changes in Stock Prices After 3 Months” page. (7.EE.3)
Unit 7: Angles, Triangles, and Prisms, Section C: Solid Geometry, Lesson 16: Applying Volume and Surface Area, Activity 2: Filling the Sandbox, students engage in a routine application problem using knowledge of proportional relationships, volume, and surface area. “The daycare has two sandboxes that are both prisms with regular hexagons as their bases. The smaller sandbox has a base area of 1,146 in² and is filled 10 inches deep with sand. a. It took 14 bags of sand to fill the small sandbox to this depth. What volume of sand comes in one bag? (Round to the nearest whole cubic inch.) b. The daycare manager wants to add 3 more inches to the depth of the sand in the small sandbox. How many bags of sand will they need to buy? c. The daycare manager also wants to add 3 more inches to the depth of the sand in the large sandbox. The base of the large sandbox is a scaled copy of the base of the small sandbox, with a scale factor of 1.5. How many bags of sand will they need to buy for the large sandbox? d. A lawn and garden store is selling 6 bags of sand for $19.50. How much will they spend to buy all the new sand for both sandboxes?” (7.RP.A)
Unit 9: Putting in all Together, Section A: Running a Restaurant, Lesson 3: More Costs of Running a Restaurant, Activity 1: Are We Making Money? Problem 1, students engage in a non-routine application problem modeling income and expenses. “Restaurants have many more expenses than just the cost of the food. a. Make a list of other items you would have to spend money on if you were running a restaurant. b. Identify which expenses on your list depend on the number of meals ordered and which are independent of the number of meals ordered. c. Identify which of the expenses that are independent of the number of meals ordered only have to be paid once and which are ongoing. d. Estimate the monthly cost for each of the ongoing expenses on your list. Next, calculate the total of these monthly expenses. (7.NS.3)
Materials provide opportunities for students to independently demonstrate multiple routine and non-routine applications of the mathematics throughout the grade level. Examples include:
Unit 4: Proportional Relationships and Percentages, Section D: Let’s Putto Work, Lesson 15: Error Intervals, Cool Down: An Anglers’ Dilemma, students independently engage in a non-routine application problem to understand of a range of possible values for measurements based on a percent error tolerance. “A fisherman weighs an ahi tuna (a very large fish) on a scale and gets a reading of 135 pounds. The reading on the scale may have an error of up to 5%. What are two possible values for the actual weight of the fish?” (7.RP.3)
Unit 5: Rational Number Arithmetic, Section D: Four Operations with Rational Numbers, Lesson 14: Solving Problems with Rational Numbers, Cool Down: Charges and Checks, students independently engage in a routine application problem applying operations with rational numbers. “Lin’s sister has a checking account. If the account balance ever falls below zero, the bank charges her a fee of $5.95 per day. Today, the balance in Lin’s sister’s account is -$2.67. a. If she does not make any deposits or withdrawals, what will be the balance in her account after 2 days? b. In 14 days, Lin’s sister will be paid $430 and will deposit it into her checking account. If there are no other transactions besides this deposit and the daily fee, will Lin continue to be charged $5.95 each day after this deposit is made? Explain or show your reasoning.” (7.NS.3)
Unit 6: Expressions, Equations, and Inequalities, Section A, Representing Situations of the Form px + q = r and p(q + x) = r, Lesson 2: Reasoning About Context with Tape Diagrams (Part 1), Practice Problems, Problem 3, students independently engage in a non-routine application problem using tape diagrams to explain and solve equations. “Andre wants to save $40 to buy a gift for his dad. Andre’s neighbor will pay him weekly to mow the lawn, but Andre always gives a $2 donation to the food bank in weeks when he earns money. Andre calculates that it will take him 5 weeks to earn the money for his dad’s gift. He draws a tape diagram to represent the situation. a. Explain how the parts of the tape diagram represent the story. b. How much does Andre’s neighbor pay him each week to mow the lawn?” (7.EE.3)
Indicator 2D
The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.
The materials reviewed for Open Up Resources Grade 7 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.
All three aspects of rigor are present independently throughout each grade level. Examples include:
Unit 2: Introducing Proportional Relationships, Section B: Representing Proportional Relationships with Equations, Lesson 6: Using Equations to Solve Problems, Practice Problems, Problem 2, students develop procedural skill and fluency as they use equations to solve problems involving a proportional relationship. “Elena has some bottles of water that each hold 17 fluid ounces. a. Write an equation that relates the number of bottles of water (b) to the total volume of water (w) in fluid ounces. b. How much water is in 51 bottles? c. How many bottles does it take to hold 51 fluid ounces of water?” (7.RP.2)
Unit 3: Measuring Circles, Section B: Area of a Circle, Lesson 7: Exploring the Area of a Circle, Warm-up: Estimating Areas, students demonstrate conceptual understanding as they use their knowledge of area of polygons to estimate the area of a circle. “Your teacher will show you some figures. Decide which figure has the largest area. Be prepared to explain your reasoning.” Students are shown a rectangle, circle, and parallelogram. (7.G.4)
Unit 6: Expressions, Equations, and Inequalities, Section A: Representing Situations of the Form px + q = r and p(x + q) = r, Lesson 6: Distinguishing Between Two Types of Situations, Activity 2: Even More Situations, Diagrams, and Equations, Are you ready for more? students apply their understanding of representing and solving equations for given real-world situations. “A tutor is starting a business. In the first year, they start with 5 clients and charge $10 per week for an hour of tutoring with each client. For each year following, they double the number of clients and the number of hours each week. Each new client will be charged 150% of the charges of the clients from the previous year. a. Organize the weekly earnings for each year in a table. b. Assuming a full-time week is 40 hours per week, how many years will it take to reach full time and how many new clients will be taken in that year? c. After reaching full time, what is the tutor’s annual salary if they take 2 weeks of vacation? d. Is there another business model you’d recommend for the tutor? Explain your reasoning.” (7.EE.4)
Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout each grade level. Examples include:
Unit 2: Introducing Proportional Relationships, Section A: Representing Proportional Relationships with Tables, Lesson 3: More About Constant of Proportionality, Activity 2: Pittsburgh to Phoenix, students demonstrate conceptual understanding as they apply their knowledge of the relationship between constant of proportionality and constant speed. “On its way from New York to San Diego, a plane flew over Pittsburgh, Saint Louis, Albuquerque, and Phoenix traveling at a constant speed. Complete the table as you answer the questions. Be prepared to explain your reasoning. a. What is the distance between Saint Louis and Albuquerque? b. How many minutes did it take to fly between Albuquerque and Phoenix? c. What is the proportional relationship represented by this table? d. Diego says the constant of proportionality is 550. Andre says the constant of proportionality is 9. Do you agree with either of them? Explain your reasoning.” A table of time, distance, and speed is provided with some values missing for each city segment. (7.RP.2)
Unit 6: Expressions, Equations, and Inequalities, Section C: Inequalities, Lesson 17: Modeling with Inequalities, Practice Problems, Problem 2, students develop procedural skill and fluency as they apply their understanding of writing and solving inequalities. “a. In the cafeteria, there is one large 10-seat table and many smaller 4-seat tables. There are enough tables to fit 200 students. Write an inequality whose solution is the possible number of 4-seat tables in the cafeteria. b. 5 barrels catch rainwater in the schoolyard. Four barrels are the same size, and the fifth barrel holds 10 liters of water. Combined, the 5 barrels can hold at least 200 liters of water. Write an inequality whose solution is the possible size of each of the 4 barrels. c. How are these two problems similar? How are they different?” (7.EE.4)
Unit 8: Probability and Sampling, Section B: Probabilities of Multi-Step Events, Lesson 9: Multi-Step Experiments, Activity 3: Pick a Card, Problem 3, students develop conceptual understanding and procedural skill and fluency as they find probability of events. “Imagine there are 5 cards. They are colored red, yellow, green, white and black. You mix up the cards and select one of them without looking. Then, without putting that card back, you mix up the remaining cards and select another one. What is the probability that: a. You get a white card and a red card (in either order)? b. You get a black card (either time)? c. You do not get a black card (either time)? d. You get a blue card? e. You get 2 cards of the same color? f. You get 2 cards of different colors?” (7.SP.8)
Criterion 2.2: Math Practices
Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).
Indicator 2E
Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources Grade 7 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year. Course Guide, How to Use the Materials, Noticing and Assessing Student Progress in Mathematical Practices, The Standards for Mathematical Practices Chart, “The unit-level Mathematical Practice chart is meant to highlight a handful of lessons in each unit that showcase certain Mathematical Practices. Some units, due to their size or the nature of their content, may have fewer predicted chances for students to engage in a particular Mathematical Practice. A dash in the chart indicates that there may not be enough opportunities to reliably look for this Mathematical Practice in the unit. One primary place Mathematical Practice 4 is tagged is the optional modeling lesson at the end of each unit. Aside from these lessons, optional activities and lessons are not included in this chart.” The Mathematical Practices are also identified in Lesson Preparation Narratives and Lesson Activities Narratives for some lessons.
There is intentional development of MP1 to meet its full intent in connection to grade-level content. Students make sense of problems and persevere in solving them as they work with the teacher's support and independently throughout the units. Examples include:
Unit 1: Scale Drawings, Section A: Scaled Copies, Lesson 1: What are Scaled Copies, Lesson Narrative, “This lesson is designed to be accessible to all students regardless of prior knowledge, and to encourage students to make sense of problems and persevere in solving them (MP1) from the very beginning of the course.” Activity 2: Pairs of Scaled Polygons, students use a variety of strategies to match polygons with their scaled copies. “Your teacher will give you a set of cards that have polygons drawn on a grid. Mix up the cards and place them all face up. a. Take turns with your partner to match a pair of polygons that are scaled copies of one another. For each match you find, explain to your partner how you know it’s a match. For each match your partner finds, listen carefully to their explanation, and if you disagree, explain your thinking. b. When you agree on the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches. c. Select one pair of polygons to examine further. Draw both polygons on the grid. Explain or show how you know the one polygon is a scaled copy of the other.”
Unit 3: Measuring Circles, Section B: Area of a Circle, Lesson 9: Applying Area of Circles, Lesson Narrative, “In previous lessons, students estimated the area of circles on a grid and explored the relationship between the circumference and the area of a circle to see that A = . In this lesson, students apply this formula to solve problems involving the area of circles as well as shapes made up of parts of circles (MP1 and MP2) and other shapes such as rectangles. These calculations require composition and decomposition recalling work from grade 6.” Warm Up: Still Irrigating the Field, students actively engage in problem solving as they calculate the the exact area of a circle from an estimate. “The area of this field is about 500,000 . What is the field’s area to the nearest square meter? Assume that the side lengths of the square are exactly 800m. A. 502,400 B. 502,640 C. 502,655 D. 502,656 E. 502,857 ” Students are shown a circle inside of a square with an unknown radius.
Unit 7: Angles, Triangles, and Prisms, Section C: Solid Geometry, Lesson 13: Decomposing Bases for Area, Lesson Narrative, “In this lesson, students continue working with the volume of right prisms. They encounter prisms where the base is composed of triangles and rectangles, and decompose the base to calculate the area. They also work with shapes such as heart-shaped boxes or house-shaped figures where they have to identify the base in order to see the shape as a prism and calculate its volume (MP1).” Activity 1: A Box of Chocolates, students monitor and evaluate their progress as they find the volume of a heart-shaped box. “A box of chocolates is a prism with a base in the shape of a heart and a height of 2 inches. Here are the measurements of the base (diagram of heart base with measurements provided). To calculate the volume of the box, three different students have each drawn line segments showing how they plan on finding the area of the heart-shaped base (Lin’s, Jada’s, and Diego’s plans are shown). For each student’s plan, describe the shapes the student must find the area of and the operations they must use to calculate the total area. a. Although all three methods could work, one of them requires measurements that are not provided. Which one is it? b. Between you and your partner, decide which of you will use which of the remaining two methods. c. Using the quadrilaterals and triangles drawn in your selected plan, find the area of the base. d. Trade with a partner and check each other’s work. If you disagree, work to reach an agreement. e. Return their work. Calculate the volume of the box of chocolates.”
There is intentional development of MP2 to meet its full intent in connection to grade-level content. Students reason abstractly and quantitatively as they work with the teacher's support and independently throughout the units. Examples include:
Unit 1: Scale Drawings, Section B: Scale Drawings, Lesson 7: Scale Drawings, Instructional Routine, “Students measure lengths on a scale drawing and use a given scale to find corresponding lengths on a basketball court (MP2). Because students are measuring to the nearest tenth of a centimeter, some of the actual measurements they calculate will not have the precision of the official measurements. For example, the official measurement is 0.9 m.” Activity 1: Sizing Up a Basketball Court, students attend to the meaning of quantities as they explore scale. “Your teacher will give you a scale drawing of a basketball court. The drawing does not have any measurements labeled, but it says 1 centimeter represents 2 meters. Problem 1, measure the distances on the scale drawing that are labeled a-d to the nearest tenth of a centimeter Record your results in the first row of the table. Problem 2, The statement ‘1 cm represents 2 m’ is the scale of the drawing. It can also be expressed as ‘1 cm to 2 m’ or ‘1 cm for every 2 m’. What do you think the scale tells us? Problem 3, How long would each measurement from the first question be on an actual basketball court? Explain or show your reasoning. Problem 4, On an actual basketball court, the bench area is typically 9 meters long. a. Without measuring, determine how long the bench area should be on the scale drawing. b. Check your answer by measuring the bench area on the scale drawing. Did your prediction match your measurement?”
Unit 5: Rational Number Arithmetic, Section C: Multiplying and Dividing Rational Numbers, Lesson 9: Multiplying Rational Number, Lesson Narrative, “The purpose of this lesson is to develop the rules for multiplying two negative numbers. Students use the familiar fact that distance = velocity x time to make sense of this rule. They interpret negative time as time before a chosen starting time and then figure out what the position is of an object moving with a negative velocity at a negative time. An object moving with a negative velocity is moving from right to left along the number line. At a negative time it has not yet reached its starting point of zero, so it is to the right of zero, and therefore its position is positive. So a negative velocity times a negative time gives a positive position. When students connect reasoning about quantities with abstract properties of numbers, they engage in MP2.” Activity 1: Backwards in Time, Problem 1, students explain the numbers and symbols in an equation as they find velocity end points. “A traffic safety engineer was studying travel patterns along a highway. She set up a camera and recorded the speed and direction of cars and trucks that passed by the camera. Positions to the east of the camera are positive, and to the west are negative. Here are some positions and times for one car: a. In what direction is this car traveling? b.What is the velocity?” Students are given a table of values ranging from -180 to 120 for position and -3 to 2 for time.
Unit 6: Expressions, Equations, and Inequalities, Section C: Inequalities, Lesson 16: Interpreting Inequalities, Lesson Narrative, “In this lesson and the next, we move on to applying inequalities to solve problems. The Warm Up is a review of the work in the previous lesson about solving inequalities when no context is given. Then students interpret and solve inequalities that represent real-life situations, making sense of quantities and their relationships in the problem (MP2).”Activity 2: Club Activities Display, students understand the relationships between problem scenarios and mathematical representations. “Your teacher will assign your group one of the situations from the last task. Create a visual display about your situation. In your display: Explain what the variable and each part of the inequality represent. Write a question that can be answered by the solution to the inequality. Show how you solved the inequality. Explain what the solution means in terms of the situation.” Sample task, “They start at 12 feet and then lose 3 feet per minute. If x is the number of minutes they hike, then 3x is the change in elevation. Their elevation must be above -37 feet; perhaps this is the bottom of the cliff.”
Indicator 2F
Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources Grade 7 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year. Course Guide, How to Use the Materials, Noticing and Assessing Student Progress in Mathematical Practices, The Standards for Mathematical Practices Chart, “The unit-level Mathematical Practice chart is meant to highlight a handful of lessons in each unit that showcase certain Mathematical Practices. Some units, due to their size or the nature of their content, may have fewer predicted chances for students to engage in a particular Mathematical Practice. A dash in the chart indicates that there may not be enough opportunities to reliably look for this Mathematical Practice in the unit. One primary place Mathematical Practice 4 is tagged is the optional modeling lesson at the end of each unit. Aside from these lessons, optional activities and lessons are not included in this chart.” The Mathematical Practices are also identified in Lesson Preparation Narratives and Lesson Activities Narratives for some lessons.
Students construct viable arguments in connection to grade-level content as they work with the teacher's support and independently throughout the units. Examples include:
Unit 1: Scale Drawings, Section A: Scaled Copies, Lesson 3: Making Scaled Copies, Lesson Narrative, “In the previous lesson, students learned that we can use scale factors to describe the relationship between corresponding lengths in scaled figures. Here they apply this idea to draw scaled copies of simple shapes on and off a grid. They also strengthen their understanding that the relationship between scaled copies is multiplicative, not additive. Students make careful arguments about the scaling process (MP3), and have opportunities to use tools like tracing paper or index cards strategically (MP5).” Activity 2: Which Operations? (Part 1), “Diego and Jada want to scale this polygon so the side that corresponds to 15 units in the original is 5 units in the scaled copy. Diego and Jada each use a different operation to find the new side lengths. Here are their finished drawings. a. What operation do you think Diego used to calculate the lengths for his drawing? b. What operation do you think Jada used to calculate the lengths for her drawing? c. Did each method produce a scaled copy of the polygon? Explain your reasoning.”
Unit 3: Measuring Circles, Section A: Circumference of a Circle, Lesson 2: Exploring Circles, Instructional Routines, “This Warm Up prompts students to compare two figures and use the characteristics of those figures to help them sketch a possible third figure that has various characteristics of each. It invites students to explain their reasoning and hold mathematical conversations (MP3), and allows you to hear how they use terminology and talk about figures and their properties before beginning the upcoming lessons on circles. There are many good answers to the question and students should be encouraged to be creative.” Warm Up: How Do You Figure? “Here are two figures. Figure C looks more like Figure A than like Figure B. Sketch what Figure C might look like. Explain your reasoning.”
Unit 7: Angles, Triangles and Prisms, Section B: Drawing Polygons with Given Conditions, Lesson 10: Drawing Triangles (Part 2), Launch, “Arrange students in groups of 2. Tell students that they should attempt to create a triangle with the given specifications. If they can create one, they should attempt to either create at least one more or justify to themselves why there is only one. If they cannot create any, they should show some valid attempts to include as many pieces as they can and be ready to explain why they cannot include the remaining conditions.” Activity 2, Three Angles, “Problem 1: Use the applet to draw triangles. Draw as many different triangles as you can with each of these sets of measurements: a. One angle measures 50° , one measures 60° , and one measures 70° . b. One angle measures 50° , one measures 60° , and one measures 100°. Problem 2: Did either of these sets of measurements determine one unique triangle? How do you know?”
Students critique others' reasoning concerning grade-level content as they work independently with the teacher's support throughout the units. Examples include:
Unit 2: Introducing Proportional Relationships, Section D: Representing Proportional Relationships with Graphs, Lesson 10: Introducing Graphs of Proportional Relationships, Instructional Routines, “Students work in pairs to match tables to graphs and to practice articulating their reasoning (MP3). This task is intended to foster understanding of correspondences between tables and graphs. Students sort the graphs and justify their sorting schemes. Then, they compare the way they sorted their graphs with a different group. The purpose of this activity is to illustrate the idea that the graph of a proportional relationships is a line through the origin. Students will not have the tools for a formal explanation until grade 8. Demonstrate how the matching activity works and how to have mathematical dialogue about the decisions being made (see the instructions in the task statement). When students finish the activity, they use an answer key to check their answers. If adjustments need to be made, students discuss any errors they made.” Activity 2: Matching Tables and Graphs, “Your teacher will give you papers showing tables and graphs. a. Examine the graphs closely. What is the same and what is different about the graphs? b. Sort the graphs into categories of your choosing. Label each category. Be prepared to explain why you sorted the graphs the way you did. c. Take turns with a partner to match a table with a graph. For each match you find, explain to your partner how you know it is a match. For each match your partner finds, listen carefully to their explanation. If you disagree, work to reach an agreement. Pause here so your teacher can review your work. d. Trade places with another group. How are their categories the same as your group’s categories? How are they different? e. Return to your original place. Discuss any changes you may wish to make to your categories based on what the other group did. f. Which of the relationships are proportional? g. What have you noticed about the graphs of proportional relationships? Do you think this will hold true for all graphs of proportional relationships?”
Unit 3: Measuring Circles, Section A: Circumference of a Circle, Lesson 5: Circumference and Wheels, Instructional Routine, “This Warm Up reminds students of the meaning and rough value of π. They apply this reasoning to a wheel and will continue to study wheels throughout this lesson. Students critique the reasoning of others (MP3).” Warm Up: A Rope and a Wheel, “Han says that you can wrap a 5-foot rope around a wheel with a 2-foot diameter because is less than pi. Do you agree with Han? Explain your reasoning.”
Unit 5: Rational Number Arithmetic, Section B: Adding and Subtracting Rational Numbers, Lesson 5: Representing Subtraction, Instructional Routines, “The purpose of this activity is to apply the representation students have used while adding signed numbers, as well as the relationship between addition and subtraction, to begin subtracting signed numbers. Students are given number line diagrams showing one addend and the sum. They are asked to figure out what the other addend would be. Students examine how these addition equations with missing addends can be written using subtraction by analyzing and critiquing the reasoning of others (MP3).” Activity 1: Subtraction with Number Lines, Problem 1, “Here is an unfinished number line diagram that represents a sum of 8. a. How long should the other arrow be? b. For an equation that goes with this diagram, Mai writes 3 + ? = 8. Tyler writes 8 - 3 = ?. Do you agree with either of them? c. What is the unknown number? How do you know?”
Indicator 2G
Materials support the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources Grade 7 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year. Course Guide, How to Use the Materials, Noticing and Assessing Student Progress in Mathematical Practices, The Standards for Mathematical Practices Chart, “The unit-level Mathematical Practice chart is meant to highlight a handful of lessons in each unit that showcase certain Mathematical Practices. Some units, due to their size or the nature of their content, may have fewer predicted chances for students to engage in a particular Mathematical Practice. A dash in the chart indicates that there may not be enough opportunities to reliably look for this Mathematical Practice in the unit. One primary place Mathematical Practice 4 is tagged is the optional modeling lesson at the end of each unit. Aside from these lessons, optional activities and lessons are not included in this chart.” The Mathematical Practices are also identified in “Lesson Preparation Narratives” and “Lesson Activities Narratives” for some lessons.
There is intentional development of MP4 to meet its full intent in connection to grade-level content. Students make sense of problems and persevere in solving them as they work with the teacher's support and independently throughout the units. Examples include:
Unit 2: Introducing Proportional Relationships, Section E: Let’s Put It to Work, Lesson 14: Four Representations, Instructional Routines, “In this activity, students choose from different lists of things to define their own proportional and nonproportional relationships. Some of the things on the list will be familiar and others will be unfamiliar. This is a significant change from previous activities where students were always given two quantities and they had to decide if they were proportional or not. This new step gives students the opportunity to think about what quantities are related to some of the items on the lists, which is an important step of modeling with mathematics (MP4).” Activity 1: One Scenario, Four Representations, students use the math they know to define proportional and nonproportional relationships. “1. Select two things from different lists. Make up a situation where there is a proportional relationship between quantities that involve these things. 2. Select two other things from the lists, and make up a situation where there is a relationship between quantities that involve these things, but the relationship is not proportional. 3. Your teacher will give you two copies of the ‘One Scenario, Four Representations’ sheet. For each of your situations, describe the relationships in detail. If you get stuck, consider asking your teacher for a copy of the sample response. 1. Write one or more sentences describing the relationship between the things you chose. 2. Make a table with titles in each column and at least 6 pairs of numbers relating the two things. 3. Graph the situation and label the axes. 4. Write an equation showing the relationship and explain in your own words what each number and letter in your equation means. 5. Explain how you know whether each relationship is proportional or not proportional. Give as many reasons as you can.” Student suggestions lists contain the following categories: creatures, length, time, volume, body parts, area, weight, and substance.
Unit 4: Proportional Relationships and Percentages, Section C: Applying Percentages, Lesson 13: Measurement Error, Lesson Narrative, “This is the first of three lessons where students encounter the idea of percent error. Unlike situations involving percent increase and percent decrease, where there is an initial amount and a final amount, situations expressed with percent error involve a measured amount and a correct amount. The measurement error is the positive difference between the measured amount and the correct amount, and the percent error is the measurement error expressed as a percentage of the correct amount. In this first lesson students see how measurement error can arise in two different ways: from the level of precision in the measurement device, and from human error. In this lesson students encounter one of the important aspects of mathematical modeling, namely that mathematical representations are usually an approximation of the real situation (MP4).” Activity 1: Measuring a Soccer Field, students identify important information that would cause measurement error to calculate percent error. “A soccer field is 120 yards long. Han measures the length of the field using a 30-foot-long tape measure and gets a measurement of 358 feet, 10 inches. a. What is the amount of the error? b. Express the error as a percentage of the actual length of the field.”
Unit 8: Probability and Sampling, Section A: Probabilities of Single Step Events, Lesson 6: Estimating Probabilities Using Simulation, Lesson Narrative, “Students follow a process similar to what they used in previous lessons for calculating relative frequencies (the activities in which students were rolling a 1 or 2 on a number cube or drawing a green block out of a bag). The distinction in this lesson is that the outcomes students are tracking are from an experiment designed to represent the outcome of some other experiment that would be harder to study directly. Students see that a simulation depends on the experiment used in the simulation being a reasonable stand-in for the actual experiment of interest (MP4).” Activity 1: Diego’s Walk, students model a situation using an appropriate strategy to estimate the probability of a real-world event by simulating the experience with a chance experiment. “a. Your teacher will give your group the supplies for one of the three different simulations. Follow these instructions to simulate 15 days of Diego’s walk. The first 3 days have been done for you. Simulate one day: If your group gets a bag of papers, reach into the bag, and select one paper without looking inside. If your group gets a spinner, spin the spinner, and see where it stops. If your group gets two number cubes, roll both cubes, and add the numbers that land face up. A sum of 2–8 means Diego has to wait. Record in the table whether or not Diego had to wait more than 1 minute. Calculate the total number of days and the cumulative fraction of days that Diego has had to wait so far. On the graph, plot the number of days and the fraction that Diego has had to wait. Connect each point by a line. If your group has the bag of papers, put the paper back into the bag, and shake the bag to mix up the papers.Pass the supplies to the next person in the group. b. Based on the data you have collected, do you think the fraction of days Diego has to wait after the 16th day will be closer to 0.9 or 0.7? Explain or show your reasoning. c. Continue the simulation for 10 more days. Record your results in this table and on the graph from earlier. d. What do you notice about the graph? e. Based on the graph, estimate the probability that Diego will have to wait more than 1 minute to cross the crosswalk.”
There is intentional development of MP5 to meet its full intent in connection to grade-level content. Students use appropriate tools strategically as they work with support of the teacher and independently throughout the units. Examples include:
Unit 2: Introducing Proportional Relationships, Section B: Representing Proportional Relationships with Equations, Lesson 5: Two Equations for Each Relationship, Instructional Routines, “The theme continues by asking students to make sense of the two rates associated with a given proportional relationship. Here, students are asked to reason from an equation rather than a table, although they may find it helpful to create a table or graph (MP5). In this particular example, students work with both number of gallons per minute and number of minutes per gallon. Monitor for students who are using different ways to decide if the cooler was filling faster before or after the flow rate was changed.” Activity 2: Filling a Water Cooler, students choose appropriate tools and strategies as they determine which cooler is filling at a faster rate. “It took Priya 5 minutes to fill a cooler with 8 gallons of water from a faucet that was flowing at a steady rate. Let w be the number of gallons of water in the cooler after t minutes. a. Which of the following equations represent the relationship between w and t? Select all that apply. a. w = 1.6t b. w = 0.625t c. t = 1.6w d. t = 0.625w b. What does 1.6 tell you about the situation? c. What does 0.625 tell you about the situation? d. Priya changed the rate at which water flowed through the faucet. Write an equation that represents the relationship of w and t when it takes 3 minutes to fill the cooler with 1 gallon of water. d. Was the cooler filling faster before or after Priya changed the rate of water flow? Explain how you know.”
Unit 3: Measuring Circles, Section B, Area of a Circle, Lesson 7: Exploring the Area of a Circle, Lesson Narrative, “This lesson is the first of two lessons that develop the formula for the area of a circle. Students start by estimating the area inside different circles, deepening their understanding of the concept of area as the number of unit squares that cover a region, and discovering that area (unlike circumference) is not proportional to diameter. Next, they investigate how the area of a circle compares to the area of a square that has side lengths equal to the circle’s radius. Students may choose tools strategically from their geometry toolkits to help them make these comparisons (MP5).” Activity 1: Estimating Areas of Circles, students choose appropriate tools and strategies as they estimate the area inside several circles. “Your teacher will assign your group two circles of different sizes. a. Set the diameter of your assigned circle and use the applet to help estimate the area of the circle. Note: to create a polygon, select the Polygon tool, and click on each vertex. End by clicking the first vertex again. For example, to draw triangle ABC, click on A-B-C-A. b. Record the diameter in column D and the corresponding area in column A for your circles and others from your classmates. c. In a previous lesson, you graphed the relationship between the diameter and circumference of a circle. How is this graph the same? How is it different?”
Unit 5: Rational Number Arithmetic, Section B: Adding and Subtracting Rational Numbers, Lesson 2: Changing Temperature, Instructional Routines, “In this activity, students use what they learned in the previous activity to find temperature differences and connect them to addition equations. Students who use number line diagrams are using tools strategically (MP5). Students may draw number line diagrams in a variety of ways; what matters is that they can explain how their diagrams represent the situation. Students may think of these questions in terms of subtraction; that is completely correct, but the discussion should focus on how to think of these situations in terms of addition. Students will have an opportunity to connect addition and subtraction in a future lesson.”Activity 2: Winter Temperatures, students choose appropriate tools and strategies as they find temperature differences and write appropriate addition equations to represent the situation. “One winter day, the temperature in Houston is 8° Celsius. Find the temperatures in these other cities. Explain or show your reasoning. a. In Orlando, it is 10° warmer than it is in Houston. b. In Salt Lake City, it is 8° colder than it is in Houston. c. In Minneapolis, it is 20° colder than it is in Houston. d. In Fairbanks, it is 10° colder than it is in Minneapolis. e. Use the thermometer applet to verify your answers and explore your own scenarios.”
Indicator 2H
Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources Grade 7 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year. Course Guide, How to Use the Materials, Noticing and Assessing Student Progress in Mathematical Practices, The Standards for Mathematical Practices Chart, “The unit-level Mathematical Practice chart is meant to highlight a handful of lessons in each unit that showcase certain Mathematical Practices. Some units, due to their size or the nature of their content, may have fewer predicted chances for students to engage in a particular Mathematical Practice. A dash in the chart indicates that there may not be enough opportunities to reliably look for this Mathematical Practice in the unit. One primary place Mathematical Practice 4 is tagged is the optional modeling lesson at the end of each unit. Aside from these lessons, optional activities and lessons are not included in this chart.” The Mathematical Practices are also identified in Lesson Preparation Narratives and Lesson Activities’ Narratives for some lessons.
There is intentional development of MP6 to meet its full intent in connection to grade-level content. Students attend to precision as they work with support of the teacher and independently throughout the units. Examples include:
Unit 1: Scale Drawings, Section B: Scale Drawings, Lesson 11: Scales Without Units, Instructional Routines, “In this activity, students explore the connection between a scale with units and one without units. Students are given two equivalent scales (one with units and the other without) and are asked to make sense of how the two could yield the same scaled measurements of an actual object. They also learn to rewrite a scale with units as a scale without units. Students will need to attend to precision (MP6) as they work simultaneously with scales with units and without units. A scale of 1 inch to 16 feet is very different than a scale of 1 to 16, and students have multiple opportunities to address this subtlety in the activity. As students work, identify groups that are able to reason clearly about why the two scales produce the same scale drawing. Two different types of reasoning to expect are: Using the two scales and the given dimensions of the parking lot to calculate and verify the student calculations. Thinking about the meaning of the scales, that is, in each case, the actual measurements are 180 times the measurements on the scale drawing.” Activity 2: Same Drawing, Different Scales, students attend to precision as they scale a parking lot. “A rectangular parking lot is 120 feet long and 75 feet wide. Lin made a scale drawing of the parking lot at a scale of 1 inch to 15 feet. The drawing she produced is 8 inches by 5 inches. Diego made another scale drawing of the parking lot at a scale of 1 to 180. The drawing he produced is also 8 inches by 5 inches. a. Explain or show how each scale would produce an 8 inch by 5 inch drawing. b. Make another scale drawing of the same parking lot at a scale of 1 inch to 20 feet. Be prepared to explain your reasoning. c. Express the scale of 1 inch to 20 feet as a scale without units. Explain your reasoning.”
Unit 3: Measuring Circles, Section A: Circumference of a Circle, Lesson 4: Applying Circumference, Lesson Narrative, “In this lesson, students use the equation C = d to solve problems in a variety of contexts. They compute the circumference of circles and parts of circles given diameter or radius, and vice versa. Students develop flexibility using the relationships between diameter, radius, and circumference rather than memorizing a variety of formulas. Understanding the equation C = 2r will help with the transition to the study of area in future lessons. Students think strategically about how to decompose and recompose complex shapes (MP7) and need to choose an appropriate level of precision for and for their final calculations (MP6).” Activity 2: Around the Running Track, students attend to precision as they compute the length of a figure that is composed of half-circles and straight line segments. “The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at each end. a. What is the distance around the inside of the track? Explain or show your reasoning. b. The track is 9.76 m wide all the way around. What is the distance around the outside of the track? Explain or show your reasoning.”
Unit 4: Proportional Relationships and Percentages, Section C: Applying Percentages, Lesson 12: Finding the Percentage, Activity 2: Info Gap: Sporting Goods, Instructional Routines, “The purpose of this info gap activity is for students to identify the essential information needed to determine the total savings after various discounts are applied to different items. The info gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).” Activity 2: Info Gap: Sporting Goods, students attend to precision as they identify important information needed to find total savings after discounts are applied. “Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner. If your teacher gives you the problem card: 1. Silently read your card and think about what information you need to be able to answer the question. 2. Ask your partner for the specific information that you need. 3. Explain how you are using the information to solve the problem. Continue to ask questions until you have enough information to solve the problem. 4. Share the problem card and solve the problem independently. 5. Read the data card and discuss your reasoning. If your teacher gives you the data card: 1. Silently read your card. 2. Ask your partner “What specific information do you need?” and wait for them to ask for information. If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information. 3. Before sharing the information, ask “Why do you need that information?” Listen to your partner’s reasoning and ask clarifying questions. 4. Read the problem card and solve the problem independently. 5. Share the data card and discuss your reasoning. Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.”
Students attend to the specialized language of mathematics as they work with the support of the teacher and independently throughout the units. Examples include:
Unit 2: Introducing Proportional Relationships, Section A: Representing Proportional Relationships with Tables, Lesson 2: Introducing Proportional Relationships with Tables, Instructional Routines, “This task is designed to encourage students to use a unit rate. Its context is intended to be familiar so that students can focus on mathematical structure (MP7) and the new terms (MP6) constant of proportionality and proportional relationships. If students are having difficulty understanding the scenario, consider drawing discrete diagrams like this: This can be followed by a double number line diagram. Correspondences among the diagrams can be identified.” Activity 2: Making Bread Dough, students use the specialized language of mathematics as they find equivalent ratios and define proportional relationships for given situations. “A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of honey to flour. Complete the table as you answer the questions. Be prepared to explain your reasoning. a. How many cups of flour do they use with 20 tablespoons of honey? b. How many cups of flour do they use with 13 tablespoons of honey? c. How many tablespoons of honey do they use with 20 cups of flour? d. What is the proportional relationship represented by this table?”
Unit 3: Measuring Circles, Section A: Circumference of a Circle, Lesson 2: Exploring Circles, Instructional Routines, “The purpose of this activity is to continue developing the idea that we can measure different attributes of a circle and to practice using the terms diameter, radius, and circumference. Students reason about these attributes when three different-sized circles are described as “measuring 24 inches” and realize that the 24 inches must measure a different attribute of each of the circles. Describing specifically which part of a circle is being measured is an opportunity for students to attend to precision (MP6).” Activity 2: Measuring Circles, students use the specialized language of mathematics as they determine which attributes of a circle are being measured. “Priya, Han, and Mai each measured one of the circular objects from earlier. Priya says that the bike wheel is 24 inches. Han says that the yo-yo trick is 24 inches. Mai says that the glow necklace is 24 inches. a. Do you think that all these circles are the same size? b. What part of the circle did each person measure? Explain your reasoning.”
Unit 8: Probability and Sampling, Section A: Probabilities of Single Step Events, Lesson 2: Chance Experiments, Lesson Narrative, “In this lesson students investigate chance events. They use language like impossible, unlikely, equally likely as not, likely, or certain to describe a likelihood of a chance event. Students engage in MP1 by making sense of situations and sorting them into these categories. In some cases, a value is assigned to the likelihood of an event using a fraction, decimal, or percentage chance. By comparing loose categories early and numerical quantities later, students are attending to precision (MP6) when sorting the scenarios. Later, students will connect this language to more precise numerical values on their own.” Activity 1: How Likely Is It?, students use the specialized language of mathematics as they group scenarios based on their likelihood of occurring. “Label each event with one of these options: impossible, unlikely, equally likely as not, likely, and certain. a. You will win grand prize in a raffle if you purchased 2 out of the 100 tickets. b. You will wait less than 10 minutes before ordering at a fast food restaurant. c. You will get an even number when you roll a standard number cube. d. A four-year-old child is over 6 feet tall. e. No one in your class will be late to class next week. f. A flipped coin lands on heads. g. It will snow at our school on July 1. h. The sun will set today before 11:00 p.m. i. Spinning this spinner will result in green. j. Spinning this spinner will result in yellow.”
Indicator 2I
Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for Open Up Resources Grade 7 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year. Course Guide, How to Use the Materials, Noticing and Assessing Student Progress in Mathematical Practices, The Standards for Mathematical Practices Chart, “The unit-level Mathematical Practice chart is meant to highlight a handful of lessons in each unit that showcase certain Mathematical Practices. Some units, due to their size or the nature of their content, may have fewer predicted chances for students to engage in a particular Mathematical Practice. A dash in the chart indicates that there may not be enough opportunities to reliably look for this Mathematical Practice in the unit. One primary place Mathematical Practice 4 is tagged is the optional modeling lesson at the end of each unit. Aside from these lessons, optional activities and lessons are not included in this chart.” The Mathematical Practices are also identified in Lesson Preparation Narratives and Lesson Activities Narratives for some lessons.
There is intentional development of MP7 to meet its full intent in connection to grade-level content. Students look for and use the structure as they work with the teacher's support and independently throughout the units. Examples include:
Unit 1: Scale Drawings, Section A: Scaled Copies, Lesson 2, Corresponding Parts and Scale Factors, Lesson Narrative, “This lesson develops the vocabulary for talking about scaling and scaled copies more precisely (MP6), and identifying the structures in common between two figures (MP7). Specifically, students learn to use the term corresponding to refer to a pair of points, segments, or angles in two figures that are scaled copies. Students also begin to describe the numerical relationship between the corresponding lengths in two figures using a scale factor. They see that when two figures are scaled copies of one another, the same scale factor relates their corresponding lengths. They practice identifying scale factors. A look at the angles of scaled copies also begins here. Students use tracing paper to trace and compare angles in an original figure and its copies. They observe that in scaled copies the measures of corresponding angles are equal.” Activity 1: Corresponding Parts, students look for and explain the structure of corresponding angles in a figure and having the same measure as its scaled copy. “One road sign for railroad crossings is a circle with a large X in the middle and two R’s—with one on each side. Here is a picture with some points labeled and two copies of the picture. Drag and turn the moveable angle tool to compare the angles in the copies with the angles in the original. a. Complete this table to show corresponding parts in the three figures. b. Is either copy a scaled copy of the original figure? Explain your reasoning. c. Use the moveable angle tool to compare angle KLM with its corresponding angles in Copy 1 and Copy 2. What do you notice? d. Use the moveable angle tool to compare angle NOP with its corresponding angles in Copy 1 and Copy 2. What do you notice?”
Unit 4: Proportional Relationships and Percentages, Section B, Percent Increase and Decrease, Lesson 9: More and Less than 1%, Lesson Narrative, “Until now, students have been working with whole number percentages when they solve percent increase and percent decrease problems. As they move towards more complex contexts such as interest rates, taxes, tips, and measurement error, they will encounter percentages that are not necessarily whole numbers. A percentage is a rate per 100, and now that students are working with ratios of fractions and their associated rates, they can work with fractional amounts per 100. In this lesson students consider situations where fractional percentages arise naturally. They also consider how to calculate a fractional percentage using a whole number percentage as a reference and dividing by 10 or 100. For example, if you know that 1% of 200 is 2, you can use the structure of the base-ten system to reason that 0.1% of 200 is 0.2 and 0.01% of 200 is 0.02 (MP7).” Activity 1: Waiting Tables, students analyze problems and look for representations to calculate the percentage of appetizers, entrees and desserts. “During one waiter’s shift, he delivered appetizers, entrées, and desserts. What percentage of the dishes were desserts? appetizers? entrées? What do your percentages add up to? a. What percentage of the dishes were desserts? appetizers? entrées? b. What do your percentages add up to?” Students use an applet to complete the problem and are shown a diagram stating 18 desserts, 13 entrées, and 9 appetizers were served.
Unit 8: Probability and Sampling, Section B: Probabilities of Multi-step Events, Lesson 8: Keeping Track of All Possible Outcomes, Lesson Narrative, “In this lesson, students practice listing the sample space for a compound event. They make use of the structure (MP7) of tree diagrams, tables, and organized lists as methods of organizing this information. Students notice that the total number of outcomes in the sample space for an experiment that can be thought of as being performed as a sequence of steps can be found by multiplying the number of possible outcomes for each step in the experiment (MP8).” Activity 1: Lists, Tables, and Trees, Problem 1, students look and explain the structure of probability as they write the sample spaces of multi-step experiments and explore their use in different situations. “Consider the experiment: Flip a coin, and then roll a number cube. Elena, Kiran, and Priya each use a different method for finding the sample space of this experiment. Elena carefully writes a list of all the options: Heads 1, Heads 2, Heads 3, Heads 4, Heads 5, Heads 6, Tails 1, Tails 2, Tails 3, Tails 4, Tails 5, Tails 6. Kiran makes a table. Priya draws a tree with branches in which each pathway represents a different outcome. a. Compare the three methods. What is the same about each method? What is different? Be prepared to explain why each method produces all the different outcomes without repairing any. b. Which method do you prefer for this situation?”
There is intentional development of MP8 to meet its full intent in connection to grade-level content. Students look for and express regularity in repeated reasoning as they work independently with the teacher's support throughout the units. Examples include:
Unit 1: Scale Drawings, Section A: Scaled Copies, Lesson 5: The Size of the Scale Factor, Lesson Narrative, “In this lesson, students deepen their understanding of scale factors in two ways: 1. They classify scale factors by size (less than 1, exactly 1, and greater than 1) and notice how each class of factors affects the scaled copies (MP8), and 2. They see that the scale factor that takes an original figure to its copy and the one that takes the copy to the original are reciprocals (MP7). This means that the scaling process is reversible, and that if Figure B is a scaled copy of Figure A, then Figure A is also a scaled copy of Figure B. Students also continue to apply scale factors and what they learned about corresponding distances and angles to draw scaled copies without a grid.” Activity 1: Scaled Copies Card Sort, students make generalizations as they examine how the size of the scale factor is related to the original figure and the scaled copy. “Your teacher will give you a set of cards. On each card, Figure A is the original and Figure B is a scaled copy. a. Sort the cards based on their scale factors. Be prepared to explain your reasoning. b. Examine cards 10 and 13 more closely. What do you notice about the shapes and sizes of the figures? What do you notice about the scale factors? c. Examine cards 8 and 12 more closely. What do you notice about the figures? What do you notice about the scale factors?”
Unit 4: Proportional Relationships and Percentages, Section B: Percent Increase or Decrease, Lesson 8: Percent Increase or Decrease with Equations, Lesson Narrative, “In this lesson, students represent situations involving percent increase and percent decrease using equations. They write equations like y = 1.06x to represent growth of a bank account, and use the equation to answer questions about different starting amounts. They write equations like t - 0.25t = 12 or 0.75t = 12 to represent the initial price of a T-shirt that was $12 after a 25% discount. The focus of this unit is writing equations and understanding their connection to the context. In a later unit on solving equations the focus will be more on using equations to solve problems about percent increase and percent decrease. When students repeatedly apply a percent increase to a quantity and see that this operation be expressed generally by an equation, they engage in MP8.” Activity 3: Representing Percent Increase and Decrease: Equations, students describe equations to represent situations of percent increase and decrease. “The gas tank in dad’s car holds 12 gallons. The gas tank in mom’s truck holds 50% more than that. How much gas does the truck’s tank hold? Explain why this situation can be represented by the equation (1.5) 12 = t. Make sure that you explain what t represents.”
Unit 8: Probability and Sampling, Section B: Probabilities of Multi-Step Events, Lesson 7: Simulating Multi-Step Experiments, Instructional Routines, “In this activity, students continue to model real-life situations with simulations (MP4), but now the situations have more than one part. Finding the exact probability for these situations is advanced, but simulations are not difficult to run and an estimate of the probability can be found using the long-run results from simulations (MP8). If other simulation tools are not available, you will need the Blackline Master.” Activity 1: Alpine Zoom, students model simulations to find probabilities, “Alpine Zoom is a ski business that makes most of its money during spring break. To make money, it needs to snow at least 4 days out of the 10 days of spring break. Based on the weather forecast, there is a chance it will snow each day for the 10 days of break. Use the applet to simulate the weather for 10 days of break to see if Alpine Zoom will make money. In each trial, spin the spinner 10 times, and then record the number of 1’s that appeared in the row. The applet reports if the Alpine Zoom will make money or not in the last column. Click Next to get the spin button back to start the next simulation. a. Describe a chance experiment that you could use to simulate whether it will snow on the first day of break. b. How could this chance experiment be used to determine whether Alpine Zoom will make money? In each trial, spin the spinner 10 times, and then record the number of 1’s that appeared in the row. The applet reports if the Alpine Zoom will make money or not in the last column. Click Next to get the spin button back to start the next simulation. c.Based on your simulations, estimate the probability that Alpine Zoom will make money.”
Overview of Gateway 3
Usability
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports; Criterion 2, Assessment; Criterion 3, Student Supports.
Gateway 3
v1.5
Criterion 3.1: Teacher Supports
The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.
Indicator 3A
Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
The materials reviewed for Open Up Resources Grade 7 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
Within the Course Guide, several sections (Design Principles, A Typical Lesson, How to Use the Materials, and Key Structures in This Course) provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:
Resources, Course Guide, About These Materials, The Five Practices, “Selected activities are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011), also described in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014), and Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Kazemi & Hintz, 2014). These activities include a presentation of a task or problem (may be print or other media) where student approaches are anticipated ahead of time. Students first engage in independent think-time followed by partner or small-group work on the problem. The teacher circulates as students are working and notes groups using different approaches. Groups or individuals are selected in a specific, recommended sequence to share their approach with the class, and finally the teacher leads a whole-class discussion to make connections and highlight important ideas.”
Resources, Course Guide, About These Materials, A Typical Lesson, “A note about optional activities: A relatively small number of activities throughout the course have been marked “optional.” Some common reasons an activity might be optional include: The activity addresses a concept or skill that is below grade level, but we know that it is common for students to need a chance to focus on it before encountering grade-level material. If the pre-unit diagnostic assessment (”Check Your Readiness”) indicates that students don’t need this review, an activity like this can be safely skipped. The activity addresses a concept or skill that goes beyond the requirements of a standard. The activity is nice to do if there is time, but students won’t miss anything important if the activity is skipped. The activity provides an opportunity for additional practice on a concept or skill that we know many students (but not necessarily all students) need. Teachers should use their judgment about whether class time is needed for such an activity. A typical lesson has four phases: 1. A Warm Up 2. One or more instructional activities 3. The lesson synthesis 4. A Cool Down.”
Resources, Course Guide, How To Use These Materials, Each Lesson and Unit Tells a Story, “The story of each grade is told in nine units. Each unit has a narrative that describes the mathematical work that will unfold in that unit. Each lesson in the unit also has a narrative. Lesson Narratives explain: The mathematical content of the lesson and its place in the learning sequence. The meaning of any new terms introduced in the lesson. How the mathematical practices come into play, as appropriate. Activities within lessons also have narratives, which explain: The mathematical purpose of the activity and its place in the learning sequence. What students are doing during the activity. What teacher needs to look for while students are working on an activity to orchestrate an effective synthesis. Connections to the mathematical practices, when appropriate.”
Resources, Course Guide, Scope and Sequence lists each of the nine units, a Pacing Guide to plan instruction, and Dependency Diagrams. These Dependency Diagrams show the interconnectedness between lessons and units within Grade 7 and across all grades.
Resources, Glossary, provides a visual glossary for teachers that includes both definitions and illustrations. Some images use examples and nonexamples, and all have citations referencing what unit and lesson the definition is from.
Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Several components focus specifically on the content of the lesson. Examples include:
Unit 2: Introducing Proportional Relationships, Unit Overview, “Because this unit focuses on understanding what a proportional relationship is, how it is represented, and what types of contexts give rise to proportional relationships, the contexts have been carefully chosen. The first tasks in the unit employ contexts such as servings of food, recipes, constant speed, and measurement conversion, that should be familiar to students from the grade 6 course. These contexts are revisited throughout the unit as new aspects of proportional relationships are introduced. Associated with the contexts from the grade 6 course are derived units: miles per hour; meters per second; dollars per pound; or cents per minute. In this unit, students build on their grade 6 experiences in working with a wider variety of derived units, such as cups of flour per tablespoon of honey, hot dogs eaten per minute, and centimeters per millimeter. The tasks in this unit avoid discussion of measurement error and statistical variability, which will be addressed in later units. On using the terms quantity, ratio, proportional relationship, unit rate, and fraction. In these materials, a quantity is a measurement that is or can be specified by a number and a unit, e.g., 4 oranges, 4 centimeters, ‘my height in feet,’ or ‘my height’ (with the understanding that a unit of measurement will need to be chosen, MP6). The term ratio is used to mean a type of association between two or more quantities. A proportional relationship is a collection of equivalent ratios. A unit rate is the numerical part of a rate per 1 unit, e.g., the 6 in 6 miles per hour. The fractions and are never called ratios. The fractions and are identified as ‘unit rates’ for the ratio . In high school—after their study of ratios, rates, and proportional relationships—students discard the term ‘unit rate’, referring to a to b, a : b , and as ‘ratios.’ In grades 6–8, students write rates without abbreviated units, for example as ‘3 miles per hour’ or ‘3 miles in every 1 hour.’ Use of notation for derived units such as waits for high school—except for the special cases of area and volume. Students have worked with area since grade 3 and volume since grade 5. Before grade 6, they have learned the meanings of such things as sq cm and cu cm. After students learn exponent notation in grade 6, they also use and . A fraction is a point on the number line that can be located by partitioning the segment between 0 and 1 into equal parts, then finding a point that is a whole number of those parts away from 0. A fraction can be written in the form or as a decimal.”
Unit 4: Proportional Relationships and Percentages, Section C: Applying Percentages, Lesson 10: Tax and Tip, Lesson Narrative, “In this lesson students are introduced to contexts involving sales tax and tips. They can use tape diagrams and double number lines from their grade 6 work, but the lesson provides an opportunity to be more efficient by using an equation of the form y = kx. For example, if the tax rate is 6.2% they can calculate the tax, T, for any price, p, using the equation t = 0.062p. They do not necessarily write this equation out with variables, but rather repeatedly use it with specific values of p. By repeatedly calculating the tax for different prices and then generalizing the process they are engaging in expressing regularity in repeated reasoning (MP8). Questions about rounding naturally come up in this lesson. This lesson primarily involves dollar amounts, so it is sensible to round to the nearest cent (the nearest hundredth of a dollar). When students attend to precision and make decisions about what is the appropriate level of rounding, they engage in MP6.”
Unit 7: Angles, Triangles, and Prisms, Section C: Solid Geometry, Lesson 15: Distinguishing Volume and Surface Area, Activity 2: Card Sort: Surface Area or Volume, Instructional Routines, “The purpose of this activity is for students to sort cards with questions that have a context referring to either volume or surface area of a prism. In previous lessons, students focused on determining volume or surface area and the two concepts were never presented side by side. Here, students are asked to sort questions with a context to determine if it makes more sense to think about surface area or volume when answering the question. After sorting, students think about what information they need to answer a question and estimate reasonable measurements to calculate the answer to their question (MP2).”
Indicator 3B
Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
The materials reviewed for Open Up Resources Grade 7 meet expectations for containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their knowledge of the subject.
Unit Overviews, Instructional Routines, and Activity Synthesis sections within units and lessons include adult-level explanations and examples of the more complex grade-level concepts. Examples include:
Unit 1: Scale Drawings, Unit Overview, “Students begin by looking at copies of a picture, some of which are to scale, and some of which are not. They use their own words to describe what differentiates scaled and non-scaled copies of a picture. As the unit progresses, students learn that all lengths in a scaled copy are multiplied by a scale factor and all angles stay the same. They draw scaled copies of figures. They learn that if the scale factor is greater than 1, the copy will be larger, and if the scale factor is less than 1, the copy will be smaller. They study how area changes in scaled copies of an image.”
Unit 3: Measuring Circles, Section A: Circumference of a Circle, Lesson 3: Exploring Circumference, Activity 1: Measuring Circumference and Diameter, Instructional Routines, “In this activity, students measure the diameter and circumference of different circular objects and plot the data on a coordinate plane, recalling the structure of the first activity in this unit where they measured different parts of squares. Students use a graph in order to conjecture an important relationship between the circumference of a circle and its diameter (MP5). They notice that the two quantities appear to be proportional to each other. Based on the graph, they estimate that the constant of proportionality is close to 3 (a table of values shows that it is a little bigger than 3). This is their first estimate of pi. This activity provides good, grade- appropriate evidence that there is a constant of proportionality between the circumference of a circle and its diameter. Students will investigate this relationship further in high school, using polygons inscribed in a circle for example. To measure the circumference, students can use a flexible measuring tape or a piece of string wrapped around the object and then measure with a ruler. As students measure, encourage them to be as precise as possible. Even so, the best precision we can expect for the proportionality constant in this activity is ‘around 3’ or possibly ‘a little bit bigger than 3’. This could be a good opportunity to talk about how many digits in the answer is reasonable. To get a good spread of points on the graph, it is important to use circles with a wide variety of diameters, from 3 cm to 25 cm. If there are points that deviate noticeably from the overall pattern (6.SP.B.5c), discuss how measurement error plays a factor.”
Unit 6: Expressions, Equations, and Inequalities, Section B: Solving Equations in the Form px + q = r and p(x + q) = r, Lesson 10: Different Options for Solving One Equation, Activity 2: Solution Pathways, Activity Synthesis, “Reveal the solution to each equation and give students a few minutes to resolve any discrepancies with their partner. Display the list of equations in the task, and ask students to help you label them with which solution method was easier, either “divide first” or “distribute first.” Discuss any disagreements and the reasons one method is easier than the other. (There is really no right or wrong answer here. Some people might prefer moves that eliminate fractions and decimals as early as possible. Some might want to minimize the number of computations.)”
Materials contain adult-level explanations and examples of concepts beyond grade 7 so that teachers can improve their knowledge of the subject. Examples include:
Unit 1: Scaled Drawings, Unit 1 Overview, “Note that the study of scaled copies is limited to pairs of figures that have the same rotation and mirror orientation (i.e. that are not rotations or reflections of each other), because the unit focuses on scaling, scale factors, and scale drawings. In grade 8, students will extend their knowledge of scaled copies when they study translations, rotations, reflections, and dilations.”
Unit 2: Introducing Proportional Relationships, Unit 2 Overview, “In grades 6–8, students write rates without abbreviated units, for example as “3 miles per hour” or ‘3 miles in every 1 hour.’ Use of notation for derived units such as waits for high school—except for the special cases of area and volume. Students have worked with area since grade 3 and volume since grade 5. Before grade 6, they have learned the meanings of such things as sq cm and cu cm. After students learn exponent notation in grade 6, they also use and .”
Unit 3: Measuring Circles, Unit 3 Overview, “In the third and last section, students select and use formulas for the area and circumference of a circle to solve abstract and real-world problems that involve calculating lengths and areas. They express measurements in terms of or using appropriate approximations of to express them numerically. In grade 8, they will use and extend their knowledge of circles and radii at the beginning of a unit on dilations and similarity.”
Unit 5: Rational Number Arithmetic, Unit 5 Overview, “Note. In these materials, an expression is built from numbers, variables, operation symbols (+, - , , ), parentheses, and exponents. (Exponents—in particular, negative exponents—are not a focus of this unit. Students work with integer exponents in grade 8 and non-integer exponents in high school.) An equation is a statement that two expressions are equal, thus always has an equal sign. Signed numbers include all rational numbers, written as decimals or in the form .”
Indicator 3C
Materials include standards correlation information that explains the role of the standards in the context of the overall series.
The materials reviewed for Open Up Resources Grade 7 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.
Correlation information can be found within different sections of the Course Guide and the Standards section of each lesson. Examples include:
Resources, Course Guide, About These Materials, Task Purposes, “A note about standards alignments: There are three kinds of alignments to standards in these materials: building on, addressing, and building towards. Oftentimes a particular standard requires weeks, months, or years to achieve, in many cases building on work in prior grade-levels. When an activity reflects the work of prior grades but is being used to bridge to a grade-level standard, alignments are indicated as ‘building on’. When an activity is laying the foundation for a grade-level standard but has not yet reached the level of the standard, the alignment is indicated as ‘building towards’. When a task is focused on the grade-level work, the alignment is indicated as ‘addressing’.”
Resources, Course Guide, How To Use These Materials, Noticing and Assessing Student Progress in Mathematical Practices, “The unit-level Mathematical Practice chart is meant to highlight a handful of lessons in each unit that showcase certain Mathematical Practices. Some units, due to their size or the nature of their content, may have fewer predicted chances for students to engage in a particular Mathematical Practice. A dash in the chart indicates that there may not be enough opportunities to reliably look for this Mathematical Practice in the unit. One primary place Mathematical Practice 4 is tagged is the optional modeling lesson at the end of each unit. Aside from these lessons, optional activities and lessons are not included in this chart.”
Resources, Course Guide, Scope and Sequence, “In the unit dependency chart, an arrow indicates that a particular unit is designed for students who already know the material in a previous unit. Reversing the order would have a negative effect on mathematical or pedagogical coherence.” Unit Dependency Diagrams identify connections between units and Section Dependency Diagrams identify specific connections within the grade level.
Resources, Course Guide, Lesson and Standards, provides two tables: a Standards by Lesson table, and a Lessons by Standard table. Teachers can utilize these tables to identify standard/lesson alignment.
Unit 4: Proportional Relationships and Percentages, Section B: Percent Increase and Decrease, Lesson 7: One Hundred Percent, “Addressing 7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.”
The role of specific grade-level mathematics can be explained in Unit Overviews, Section Overviews, and Lesson Narratives. Examples include:
Unit 1: Scale Drawings, Overview, “In this unit, students study scaled copies of pictures and plane figures, then apply what they have learned to scale drawings, e.g., maps and floor plans. This provides geometric preparation for grade 7 work on proportional relationships as well as grade 8 work on dilations and similarity. Students begin by looking at copies of a picture, some of which are to scale, and some of which are not. They use their own words to describe what differentiates scaled and non-scaled copies of a picture. As the unit progresses, students learn that all lengths in a scaled copy are multiplied by a scale factor and all angles stay the same. They draw scaled copies of figures. They learn that if the scale factor is greater than 1, the copy will be larger, and if the scale factor is less than 1, the copy will be smaller. They study how area changes in scaled copies of an image.”
Unit 4: Proportional Relationships and Percentages, Section C: Applying Percentages, Section Overview, “In the third section of the unit, students begin by using their abilities to find percentages and percent rates to solve problems that involve sales tax, tip, discount, markup, markdown, and commission (MP2). The remaining lessons of the section continue the focus on situations that can be described in terms of percentages, but the situations involve error rather than change—describing an incorrect value as a percentage of the correct value rather than describing an initial amount as a percentage of a final amount (or vice versa).”
Unit 6: Expressions, Equations, and Inequalities, Section A: Representing Situations of the Form px + q = r and p(x + q) = r, Lesson 6: Distinguishing Between Two Types of Situations, Lesson Narrative, “The purpose of this lesson is to distinguish equations of the form px + q = r and p(x + q) = r. Corresponding tape diagrams are used as tools in this work, along with situations that these equations can represent. First, students sort equations into categories of their choosing. The main categories to highlight distinguish between the two main types of equations being studied. Then, students consider two stories and corresponding diagrams and write equations to represent them. They use these representations to find an unknown value in the story.”
Indicator 3D
Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The materials reviewed for Open Up Resources Grade 7 provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The materials include an introductory Family Letter, and the student edition contains lesson summaries and video lesson summaries. Examples include:
Resources, Family Letter, What supports are in the materials to help my student succeed?, “Each lesson includes a lesson summary that describes the key mathematical work of the lesson and provides worked examples when relevant. Students can use this resource if they are absent from class, to check their understanding of the day’s topics, and as a reference when they are working on practice problems or studying for an assessment. Each lesson is followed by a practice problem set. These problems help students synthesize their knowledge and build their skills. Some practice problems in each set relate to the content of the current lesson, while others revisit concepts from previous lessons and units. Distributed practice like this has been shown to be more effective at helping students retain information over time. Each lesson includes a few learning targets, which summarize the goals of the lesson. Each unit’s complete set of learning targets is available on a single page, which can be used as a self-assessment tool as students progress through the course. Family support materials are included several times in each unit. These materials give an overview of the unit's math content and provide a problem to work on with your student.”
Unit 4: Proportional Relationships and Percentages, Student Edition, Video Lesson Summaries, “Each video highlights key concepts and vocabulary included in one or more lessons in the unit. These lesson videos are based on the Lesson Summaries found at the end of each lesson. Here are some possible ways to use these videos: Keep informed on concepts and vocabulary learned in class. Review and check understanding of the included lessons. Watch and pause at key points to predict what comes next or think up other examples of vocabulary terms (the bolded words).Proportional Relationships with Fractions & Decimals (Lessons 4–5), Percent Increase and Decrease (Lessons 6–8), Applications of Percentages (Lessons 10–12), More Applications of Percentages (Lessons 14–15).”
Unit 5: Rational Number Arithmetic, Section C: Multiplying and Dividing Rational Numbers, Lesson 12: Negative Rates, Student Edition, Lesson Summary, “We saw earlier that we can represent speed with direction using signed numbers. Speed with direction is called velocity. Positive velocities always represent movement in the opposite direction from negative velocities. We can do this with vertical movement: moving up can be represented with positive numbers, and moving down with negative numbers. The magnitude tells you how fast, and the sign tells you which direction. (We could actually do it the other way around if we wanted to, but usually we make up positive and down negative.)”
Indicator 3E
Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.
The materials reviewed for Open Up Resources Grade 7 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.
The materials explain and provide examples of the program's instructional approaches and include and reference research-based strategies. Both the instructional approaches and the research-based strategies are included in the Course Guide. Examples include:
Resources, Course Guide, About These Materials, Design Principles, The Five Practices, “Selected activities are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011), also described in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014), and Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Kazemi & Hintz, 2014). These activities include a presentation of a task or problem (may be print or other media) where student approaches are anticipated ahead of time. Students first engage in independent think-time followed by partner or small-group work on the problem. The teacher circulates as students are working and notes groups using different approaches. Groups or individuals are selected in a specific, recommended sequence to share their approach with the class, and finally the teacher leads a whole-class discussion to make connections and highlight important ideas.”
Resources, Course Guide, How to Use These Materials, Instructional Routines, “The kind of instruction appropriate in any particular lesson depends on the learning goals of that lesson. Some lessons may be devoted to developing a concept, others to mastering a procedural skill, yet others to applying mathematics to a real-world problem. These aspects of mathematical proficiency are interwoven. These lesson plans include a small set of activity structures and reference a small, high-leverage set of teacher moves that become more and more familiar to teachers and students as the year progresses. Some of the instructional routines, known as Mathematical Language Routines (MLR), were developed by the Stanford University UL/SCALE team. The purpose of each MLR is described here, but you can read more about supports for students with emerging English language proficiency in the Supports for English Language Learners section.”
Resources, About These Materials, What is a “Problem-Based” Curriculum, Attitudes and Beliefs We Want to Cultivate, “Many people think that mathematical knowledge and skills exclusively belong to “math people.” Yet research shows that students who believe that hard work is more important than innate talent learn more mathematics. We want students to believe anyone can do mathematics and that persevering at mathematics will result in understanding and success. In the words of the NRC report Adding It Up, we want students to develop a “productive disposition—[the] habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.”
Indicator 3F
Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for Open Up Resources Grade 7 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.
In the Course Guide, Materials, there is a list of required materials for each unit and each lesson. Lessons that do not have materials are indicated by none; lessons that need materials have a list of all the materials needed. Examples include:
Resources, Course Guide, Required Materials, “blank paper, coins, colored pencils, compasses, cylindrical household items, drink mix, empty toilet paper roll, four-function calculators, fruits or vegetables, geometry toolkits, glue or gluesticks, graph paper, grocery store circulars, index cards, internet-enabled device, knife, maps or satellite images of the school grounds, markers, measuring cup, measuring spoons, measuring tapes, measuring tools, metal paper fasteners, meter sticks, metric and customary unit conversion charts, mixing containers, number cubes, paint, paper bags, paper clips, paper plates, pattern blocks, pre-assembled polyhedra, protractors, receipt tape, recipes, rulers, rulers marked with centimeters, rulers marked with inches, scissors, small disposable cups, snap cubes, sticky notes, stopwatches, straightedges, straws, string, tape, tools for creating a visual display, trundle wheels, water, yardsticks.”
Unit 2: Introducing Proportional Relationships, Section D: Representing Proportional Relationships with Graphs, Lesson 12: Using Graphs to Compare Relationships, Required Materials, “colored pencils, rulers.”
Unit 6: Expressions, Equations, and Inequalities, Section C: Inequalities, Lesson 16: Interpreting Inequalities, Required Materials, “tools for creating a visual display.”
Indicator 3G
This is not an assessed indicator in Mathematics.
Indicator 3H
This is not an assessed indicator in Mathematics.
Criterion 3.2: Assessment
The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for Assessment. The materials identify the content standards and mathematical practices assessed in formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance, and suggestions for following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.
Indicator 3I
Assessment information is included in the materials to indicate which standards are assessed.
The materials reviewed for Open Up Resources Grade 7 meet expectations for having assessment information included in the materials to indicate which standards are assessed.
The materials consistently and accurately identify grade-level content standards for formal assessments in the Lesson Cool Down, Mid-Unit Assessments and End-of-Unit Assessments within each assessment answer key. Examples include:
Resources, Course Guide, Assessments, Summative Assessments, “All summative assessment problems include a complete solution and standard alignment. Multiple-choice and multiple response problems often include a reason for each potential error a student might make. Restricted constructed response and extended response items include a rubric.”
Unit 5: Rational Numbers Arithmetic, Unit Assessments, End-of-Unit Assessment, Version B, Problem 2, “7.NS.A.1.c, A sunken ship is resting at 3,000 feet below sea level. Directly above the ship, a whale is swimming 1,960 feet below sea level. Directly above the ship and the whale is a plane flying at 8,500 feet above sea level. Select the true statement. A. The distance between the heights of the whale and the plane is -10,460 feet. B. The difference in height between the whale and the plane is 10,460 feet. C. The difference in height between the whale and the ship is -1,040 feet. D. The distance between the heights of the whale and the ship is 1,040 feet.”
Unit 7: Angles, Triangles, and Prisms, Section B: Drawing Polygons with Given Conditions, Lesson 7: Building Polygons (Part 2), Cool Down: Finishing Elena’s Triangles, “7.G.A.2, a. Elena is trying to draw a triangle with side lengths 4 inches, 3 inches, and 5 inches. She uses her ruler to draw a 4 inch line segment AB. She uses her compass to draw a circle around point B with radius 3 inches. She draws another circle, around point A with radius 5 inches. What should Elena do next? Explain and show how she can finish drawing the triangle. B. Now Elena is trying to draw a triangle with side lengths 4 inches, 3 inches, and 8 inches. She uses her ruler to draw a 4 inch line segment AB. She uses her compass to draw a circle around point B with radius 3 inches. She draws another circle, around point A with radius 8 inches. Explain what Elena’s drawing means.”
Unit 8: Probability and Sampling, Unit Assessments, Mid-Unit Assessment, Version A, Problem 4, “7.SP.C.8b, “A movie theater sells 3 different sizes of popcorn: small, medium, and large. An order of popcorn comes with 3 different topping choices: butter, cheese, or caramel. How many unique ways can you order a bag of popcorn? (You can only select one topping.)”
The materials consistently and accurately identify grade-level mathematical practice standards for formal assessments. Examples include:
Resources, Course Guide, How to Use These Materials, Noticing and Assessing Student Progress in Mathematical Practices, How Can You Use the Mathematical Practices Chart, “No single task is sufficient for assessing student engagement with the Standards for Mathematical Practice. For teachers looking to assess their students, consider providing students the list of learning targets to self-assess their use of the practices, assigning students to create and maintain a portfolio of work that highlights their progress in using the Mathematical Practices throughout the course, monitoring collaborative work and noting student engagement with the Mathematical Practices. Because using the mathematical practices is part of a process for engaging with mathematical content, we suggest assessing the Mathematical Practices formatively. For example, if you notice that most students do not use appropriate tools strategically (MP5), plan in future lessons to select and highlight work from students who have chosen different tools. Since the Mathematical Practices in action can take many forms, a list of learning targets for each Mathematical Practice is provided to support teachers and students in recognizing when engagement with a particular Mathematical Practice is happening. The intent of the list is not that students check off every item on the list. Rather, the ‘I can’ statements are examples of the types of actions students could do if they are engaging with a particular Mathematical Practice.
Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practice Student Facing Learning Targets, “MP4: I Can Model with Mathematics: I can wonder about what mathematics is involved in a situation. I can come up with mathematical questions that can be asked about a situation. I can identify what questions can be answered based on data I have. I can identify information I need to know and don’t need to know to answer a question. I can collect data or explain how it could be collected. I can model a situation using a representation such as a drawing, equation, line plot, picture graph, bar graph, or a building made of blocks. I can think about the real-world implications of my model.”
Indicator 3J
Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The materials reviewed for Open Up Resources Grade 7 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Materials provide opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance. Examples include:
Resources, Course Guide, Assessments, Summative Assessments, End-of-Unit Assessments, “All summative assessment problems include a complete solution and standard alignment. Multiple-choice and multiple response problems often include a reason for each potential error a student might make. Restricted constructed response and extended response items include a rubric. Unlike formative assessments, problems on summative assessments generally do not prescribe a method of solution.”
Unit 1: Scale Drawings, End-of-Unit Assessment, Version B, Problem 6, students reason about map scaling. “There are two different maps of California. The scale on the first map is 1 cm to 20 km. The distance from Fresno to San Francisco is 15 cm. The scale on the second map is 1 cm to 100 km. What is the distance from Fresno to San Francisco on the second map? Explain your reasoning.” Solution, “Minimal Tier 1 response: Work is complete and correct. Sample: Lengths on the second map are five times smaller because 1 cm represents 20 km instead of 100 km. Divide 15 cm by 5 to get 3 cm. Tier 2 response: Work shows general conceptual understanding and mastery, with some errors. Sample errors: multiplication or division errors in otherwise correct work; work involves a correct substantive intermediate step (such as the actual distance from Fresno to San Francisco) but goes wrong after that; one mistake involving an “upside down” scale factor (or multiplying when division is called for); a correct answer without explanation. Tier 3 response: Significant errors in work demonstrate lack of conceptual understanding or mastery. Sample errors: work does not involve proportional reasoning; an incorrect answer without explanation, even if close; multiple mistakes that involve inversion of scale factors.”
Unit 4: Proportional Relationships and Percentages, End-of-Unit Assessment, Version B, Problem 2, students find percent error. “A graduated cylinder actually contains 7.5 milliliters of water. When Han measures the volume of the water inside the graduated cylinder, his measurement is 7 milliliters. Which of these is closest to the percent error for Han’s measurement? A. 107.1% B. 93.3% C. 7.1% D. 6.7%” Solution, “D.”
Materials provide opportunities to determine students' learning and general suggestions to teachers for following up with students. Examples include:
Resources, Course Guide, Assessments, Pre-Unit Diagnostic Assessments, “What if a large number of students can’t do the same pre-unit assessment problem? Teachers are encouraged to address below-grade skills while continuing to work through the on-grade tasks and concepts of each unit, instead of abandoning the current work in favor of material that only addresses below-grade skills. Look for opportunities within the upcoming unit where the target skill could be addressed in context. For example, an upcoming activity might require solving an equation in one variable. Some strategies might include: ask a student who can do the skill to present their method, add additional questions to the Warm Up with the purpose of revisiting the skill, add to the activity launch a few related equations to solve, before students need to solve an equation while working on the activity, pause the class while working on the activity to focus on the portion that requires solving an equation. Then, attend carefully to students as they work through the activity. If difficulty persists, add more opportunities to practice the skill, by adapting tasks or practice problems.”
Resources, Course Guide, Assessments, Cool Downs, “What if the feedback from a Cool Down suggests students haven’t understood a key concept? Choose one or more of these strategies: Look at the next few lessons to see if students have more opportunities to engage with the same topic. If so, plan to focus on the topic in the context of the new activities. During the next lesson, display the work of a few students on that Cool Down. Anonymize their names, but show some correct and incorrect work. Ask the class to observe some things each student did well and could have done better. Give each student brief, written feedback on their Cool Down that asks a question that nudges them to re-examine their work. Ask students to revise and resubmit. Look for practice problems that are similar to, or involve the same topic as the Cool Down, then assign those problems over the next few lessons.”
Unit 3: Measuring Circles, End-of-Unit Assessment, Version A, Problem 1, students calculate the area of a circle. “A circle has radius 50 cm. Which of these is closest to its area? A. 157 B. 314 C. 7,854 D. 15,708 .” Guidance for teachers, “If students struggle to calculate the area of a circle, provide additional instruction either in a small group or individually using OUR Math Grade 7 Unit 3 Lesson 7 Activity 3 and Practice Problems 1-3.”
Indicator 3K
Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
The materials reviewed for Open Up Resources Grade 7 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level/ course-level standards and practices across the series.
Formative assessments include lesson activities, Cool Downs, and Practice Problems in each unit section. Summative assessments include Mid-Unit Assessments and End-of-Unit Assessments. Assessments regularly demonstrate the full intent of grade-level content and practice standards through various item types, including multiple-choice, multiple response, short answer, restricted constructed response, and extended response. Examples include:
Unit 3: Measuring Circles, End-Of-Unit Assessment, Version A, Problem 7, students analyze and make sense of a problem by working to understand the information in the problem and the question asked. “A groundskeeper needs grass seed to cover a circular field, 290 feet in diameter. A store sells 50-pound bags of grass seed. One pound of grass seed covers about 400 square feet of field. What is the smallest number of bags the groundskeeper must buy to cover the circular field. Explain or show your reasoning.” (MP1)
Unit 4: Proportional Relationships and Percentages, Section A: Proportional Relationships with Fractions, Lesson 4: Half As Much Again, Practice Problems, Problem 3, students use distributive property to represent a situation. “Write a story that can be represented by the equation y = x + x.” (7.RP.2)
Unit 6: Expressions, Equations, and Inequalities, Section B: Solving Equations of the Form px + q = r and p(x + q) = r, Lesson 7: Reasoning About Solving Equations (Part I), Cool Down: Solve the Equation, students solve equations. “Solve the equation. If you get stuck, try using a diagram. 5x + = ." (7.EE.4a)
Unit 6: Expressions, Equations, and Inequalities, Mid-Unit Assessment, Version A, Problem 2, students recognize both the insight to be gained from a tape diagram, and its limitations. “Select all the situations that can be represented by the tape diagram. A. Clare buys 4 bouquets, each with the same number of flowers. The florist puts an extra flower in each bouquet before she leaves. She leaves with a total of 99 flowers. B. Andre babysat 5 times this past month and earned the same amount each time. To thank him, the family gave him an extra $4 at the end of the month. Andre earned $99 from babysitting. C. A family of 5 drove to a concert. They paid $4 for parking, and all of their tickets were the same price. They paid $99 in total. D. 5 bags of marbles each contain 4 large marbles and the same number of small marbles. Altogether, the bags contain 99 marbles. E. Han is baking five batches of muffins. Each batch needs the same amount of sugar in the muffins, and each batch needs four extra teaspoons of sugar for the topping. Han uses 99 total teaspoons of sugar.” (MP5)
Unit 7: Angles, Triangles, and Prisms, End-of-Unit Assessment, Version A, Problem 2, students identify cross sections of a square pyramid. “A square pyramid is sliced parallel to the base and halfway up the pyramid. Which of these describes the cross section? A. A square smaller than the base B. A quadrilateral that is not a square C. A square the same size as the base D. A triangle with a height the same as the pyramid.” (7.G.3)
Unit 8: Probability and Sampling, End-of-Unit Assessment, Version B, Problem 7, students use statistical measures to compare data sets. “Students are conducting a class experiment to see if there is a meaningful difference between two groups of plants that have begun to sprout leaves. The teacher randomly selects 8 plants from each group and counts the number of leaves on each plant. Group A: 2, 2, 3, 3, 5, 5, 7 Group B: 10, 9, 7, 8, 10, 12, 14, 10 Is there a meaningful difference between the two groups? Show all calculations that lead to your answer.” (7.SP.3 and 7.SP.4)
Indicator 3L
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
The materials reviewed for Open Up Resources Grade 7 provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
The general accommodations are provided in the Course Guide in the section Universal Design for Learning and Access for Students with Disabilities. These assessment accommodations are offered at the program level and are not specific to each assessment. Examples include:
Resources, Course Guide, Supports for Students with Disabilities, Instructional Strategies That Support Access, Eliminate Barriers, “Eliminate any unnecessary barriers that students may encounter that prevent them from engaging with the important mathematical work of a lesson. This requires flexibility and attention to areas such as the physical environment of the classroom, access to tools, organization of lesson activities, and means of communication.”
Resources, Course Guide, Supports for Students with Disabilities, Instructional Strategies That Support Access, Processing Time, “Increased time engaged in thinking and learning leads to mastery of grade-level content for all students, including students with disabilities. Frequent switching between topics creates confusion and does not allow for content to deeply embed in the mind of the learner. Mathematical ideas and representations are carefully introduced in the materials in a gradual, purposeful way to establish a base of conceptual understanding. Some students may need additional time, which should be provided as required.”
Resources, Course Guide, Supports for Students with Disabilities, Instructional Strategies That Support Access, Visual Aids, “Visual aids such as images, diagrams, vocabulary anchor charts, color coding, or physical demonstrations are suggested throughout the materials to support conceptual processing and language development. Keeping relevant visual aids posted in the classroom supports independence by allowing students to access them as needed, and is especially beneficial for students with challenges related to working or short term memory.”
Resources, Course Guide, Supports for Students with Disabilities, Instructional Strategies That Support Access, Manipulatives, “Physical manipulatives help students make connections between concrete ideas and abstract representations. Often, students with disabilities benefit from hands-on activities, which allow them to make sense of the problem at hand and communicate their own mathematical ideas and solutions.”
Criterion 3.3: Student Supports
The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for Open Up Resources 6-8 Math Grade 7 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Indicator 3M
Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
The materials reviewed for Open Up Resources Grade 7 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics, as suggested in each lesson. According to the Resources, Course Guide, Supports for Students with Disabilities, “Supplemental instructional strategies, labeled ‘Supports for Students with Disabilities,’ are included in each lesson. They are designed to help teachers meet the individual needs of a diverse group of learners. Each is aligned to one of the three principles of Universal Design for Learning, to provide multiple means of engagement, representation, or action and expression, and includes a suggested strategy to increase access and eliminate barriers. These lesson specific supports can be used as needed to help students succeed with a specific activity, without reducing the mathematical demand of the task, and can be faded out as students gain understanding and fluency.” Examples of supports for special populations include:
Unit 2: Introducing Proportional Relationships, Section C: Comparing Proportional and Nonproportional Relationships, Lesson 7: Comparing Relationships with Tables, Activity 1: Visiting the Skate Park, Supports for Students with Disabilities, “Action and Expression: Executive Functions, To support development of organizational skills, check in with students within the first 2–3 minutes of work time. Check to make sure students have accounted for the cost of the vehicle in their calculations of the total entrance cost for 4 people and 10 people. Provides accessibility for: Memory, Organization.”
Unit 6: Expressions, Equations, and Inequalities, Section A: Representing Situations of the Form px + q = r and p(x + q) = r, Lesson 5: Reasoning About Equations and Tape Diagrams (Part 2), Warm Up: Algebra Talk: Seeing Structure, Supports for Students with Disabilities, “Representation: Comprehension, To support working memory, provide students with sticky notes or mini whiteboards. Provides accessibility for: Memory, Organization.”
Unit 8: Probability and Sampling, Section B: Probability of Multi-step Events, Lesson 9: Multi- Step Experiments, Activity 1: Spinning a Color and Number, Supports for Students with Disabilities, “Representation: Perception, Provide access to concrete manipulatives. Provide spinners for students to view or manipulate. These hands-on models will help students identify characteristics or features, and support finding outcomes for calculating probabilities. Provides accessibility for: Visual-Spatial Processing, Conceptual Processing.”
Indicator 3N
Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
The materials reviewed for Open Up Resources Grade 7 meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
While there are no instances where advanced students do more assignments than classmates, materials provide multiple opportunities for students to investigate grade-level content at a higher level of complexity. These are found after activities and labeled “Are You Ready for More?” According to the Resources, Course Guide, How To Use The Materials, Are You Ready For More? “Select classroom activities include an opportunity for differentiation for students ready for more of a challenge. We think of them as the ‘mathematical dessert’ to follow the ‘mathematical entrée’ of a classroom activity. Every extension problem is made available to all students with the heading “Are You Ready for More?” These problems go deeper into grade-level mathematics and often make connections between the topic at hand and other concepts. Some of these problems extend the work of the associated activity, but some of them involve work from prior grades, prior units in the course, or reflect work that is related to the K–12 curriculum but a type of problem not required by the standards. They are not routine or procedural, and they are not just “the same thing again but with harder numbers.” Examples include:
Unit 1: Scaled Drawings, Section A: Scaled Copies, 2: Corresponding Parts and Scale Factors, Activity 2: Scaled Triangles, Are You Ready For More? “Choose one of the triangles that is not a scaled copy of Triangle O. Describe how you could change at least one side to make a scaled copy, while leaving at least one side unchanged.”
Unit 4: Proportional Relationships and Percentages, Section A: Proportional Relationships with Fractions, Lesson 2: Ratio and Rates with Fractions, Activity 2: Comparing Running Speeds, Are You Ready for More? “Nothing can go faster than the speed of light, which is 299,792,458 meters per second. Which of these are possible? a. Traveling a billion meters in 5 seconds. b. Traveling a meter in 2.5 nanoseconds. (A nanosecond is a billionth of a second.) c. Traveling a parsec in a year. (A parsec is about 3.26 light years and a light year is the distance light can travel in a year.)”
Unit 7: Angles, Triangles, and Prisms, Section A: Angle Relationships, Lesson 4: Solving for Unknown Angles, Activity 2: What’s the Match? Are You Ready for More? “What is the angle between the hour and minute hands of a clock at 3:00?”
Indicator 3O
Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
The materials reviewed for Open Up Resources Grade 7 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
Students engage with problem-solving in a variety of ways. Per the Course Guide, each lesson consists of four stages, beginning with a Warm Up, which prepares students for the day’s lesson or strengthens their procedural skills. After the Warm Up, students participate in one to three activities with their purpose explained in the Activity Narrative. Then students engage in the Lesson Synthesis to consolidate their learning from the lesson. This is followed by a Cool Down where students independently demonstrate their understanding of the day’s learning. Examples of varied approaches include:
Unit 3: Measuring Circles, Section C: Let’s Put it to Work, Lesson 10: Distinguishing Circumference and Area, Activity 1: Card Sort: Circle Problems, students solve real world circumference and area problems. “Your teacher will give you cards with questions about circles. a. Sort the cards into two groups based on whether you would use the circumference or the area of the circle to answer the question. Pause here so your teacher can review your work. b. Your teacher will assign you a card to examine more closely. What additional information would you need in order to answer the question on your card? c. Estimate measurements for the circle on your card. d. Use your estimates to calculate the answer to the question.”
Unit 5: Rational Number Arithmetic, Section B: Adding and Subtracting Rational Numbers, Lesson 6: Subtracting Rational Numbers, Cool Down: A Subtraction Expression, students solve subtraction expressions. “Select all of the choices that are equal to -5 - (-12). A. -7 B. 7 C. The difference between -5 and -12. D. The difference between -12 and -5. E. (-5) + 12 F. (-5) + (-12)”
Unit 8: Probability and Sampling, Section C: Sampling, Lesson 11: Comparing Groups, Warm Up: Notice and Wonder: Comparing Heights, students compare line plots of heights of volleyball players and gymnasts. “What do you notice? What do you wonder?” Activity Synthesis, “Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After each response, ask the class if they agree or disagree and to explain alternative ways of thinking, referring back to the images each time. If the definitive difference in height does not come up during the conversation, ask students to discuss this idea. The next activity looks more closely at comparing these data sets. It is not necessary to have students calculate anything (mean, median, MAD, IQR) yet.”
Indicator 3P
Materials provide opportunities for teachers to use a variety of grouping strategies.
The materials reviewed for Open Up Resources Grade 7 provide opportunities for teachers to use a variety of grouping strategies.
Suggested grouping strategies are consistently present within the activity Launch and include guidance for whole group, small group, pairs, or individuals. Examples include:
Unit 1: Scale Drawings, Section B: Scale Drawings, Lesson 9: Creating Scale Drawings, Activity 1: Bedroom Floor Plan, Launch, “Tell students that a floor plan is a top-view drawing that shows a layout of a room or a building. Floor plans are usually scale drawings. Explain that sometimes the scale of a drawing is not specified, but we can still tell the scale if we know both the scaled and actual lengths. Arrange students in groups of 2. Give students 4–5 minutes of quiet work time and partner discussion.”
Unit 3: Measuring Circles, Section A: Circumference of a Circle, Lesson 3: Exploring Circumference, Activity 1: Measuring Circumference and Diameter, Launch, “Arrange students in groups of 2–4. Distribute 3 circular objects and measuring tapes or string and rulers to each group. Especially if using string and rulers, it may be necessary to demonstrate the method for measuring the circumference. Ask students to complete the first two questions in their group, and then gather additional information from two other groups (who measured different objects) for the third question. If using the digital activity, students can work in groups of 2–4. They only need the applet to generate data for their investigation.”
Unit 6: Expression, Equations, and Inequalities, Section C: Inequalities, Lesson 15: Efficiently Solving Inequalities, Warm Up: Lots of Negatives, Launch, “Give students 3 minutes of quiet time followed by a whole-class discussion.”
Indicator 3Q
Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The materials reviewed for Open Up Resources Grade 7 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
Teachers consistently provide guidance to support students who read, write, and/or speak in a language other than English, providing scaffolds for them to meet or exceed grade-level standards. According to the Resources, Course Guide, Supports for English Language Learners, Design, “Each lesson includes instructional strategies that teachers can use to facilitate access to the language demands of a lesson or activity. These support strategies, labeled ‘Supports for English Language Learners,’ stem from the design principles and are aligned to the language domains of reading, writing, speaking, listening, conversing, and representing in math (Aguirre & Bunch, 2012). They provide students with access to the mathematics by supporting them with the language demands of a specific activity without reducing the mathematical demand of the task. Using these supports will help maintain student engagement in mathematical discourse and ensure that the struggle remains productive. Teachers should use their professional judgment about which routines to use and when, based on their knowledge of the individual needs of students in their classroom.” Examples include:
Unit 1: Scare Drawings, Section A: Scaled Copies, Lesson 4: Scaled Relationships, Activity 1: Three Quadrilaterials (Part 2), Supports for English Language Learners, “Speaking: MLR7 Compare and Connect, Use this routine to call attention to the different ways students may identify scale factors. Display the following statements: “The scale factor from EFGH to IJKL is 3,” and “The scale factor from EFGH to IJKL is .” Give students 2 minutes of quiet think time to read and consider whether either or both of the statements are correct. Invite students to share their initial thinking with a partner before selecting 2–3 students to share with the class. In this discussion, listen for and amplify any comments that refer to the order of the original figure and its scaled copy, as well as those who identify corresponding vertices and distances. Draw students’ attention to the different ways to describe the relationships between scaled copies and the original figure. Design Principle: Maximize linguistic & cognitive meta-awareness.”
Unit 4: Proportional Relationships and Percentages, Section A: Proportional Relationships with Fractions, Lesson 3: Revisiting Proportional Relationships, Activity 2: Swimming, Manufacturing, and Painting, Supports for English Learners, “Writing: MLR3 Critique, Correct, and Clarify, Present an incorrect response to the question about mixing 4 quarts of blue paint. For example, ‘Since there are 0.3 quarts of blue paint to white paint, you need 1.2 quarts of white paint.’ Prompt students to identify the error (e.g., ask students, ‘Do you agree with the statement? Why or why not?’), and then write a correct version. This helps students evaluate, and improve on, the written mathematical arguments of others. Design Principle: Maximize linguistic & cognitive meta-awareness.”
Unit 6: Expressions, Equations and Inequalities, Section C: Inequalities, Lesson 13: Reintroducing Inequalities, Activity 1: The Roller Coaster, Supports for English Learners, “Conversing, Writing: MLR5 Co-Craft Questions and Problems, Use this routine to help students consider the context of the first problem and to increase awareness about language used to describe situations involving inequalities. Begin by displaying only the initial text and photo of the roller coaster, without revealing the follow-up questions. In groups of 2, invite students to write down mathematical questions they have about this situation. Ask pairs to share their questions with the whole class. Amplify questions that highlight the mathematical language of ‘at least’. Design Principles: Cultivate conversation, Maximize linguistic & cognitive meta-awareness.”
Indicator 3R
Materials provide a balance of images or information about people, representing various demographic and physical characteristics.
The materials reviewed for Open Up Resources Grade 7 provide a balance of images or information about people, representing various demographic and physical characteristics.
Materials represent a variety of genders, races, and ethnicities. All are indicated with no biases and represent different populations. Names refer to various backgrounds, such as Priya, Han, Mai, and Diego. Settings include rural, urban, and multicultural environments. Examples include:
Unit 2: Introducing Proportional Relationships, Section D: Representing Proportional Relationships with Graphs, Lesson 12: Using Graphs to Compare Relationships, Cool Down: Revisiting the Amusement Park, “Noah and Diego left the amusement park’s ticket booth at the same time. Each moved at a constant speed toward his favorite ride. After 8 seconds, Noah was 17 meters from the ticket booth, and Diego was 43 meters away from the ticket booth. a. Which line represents the distance traveled by Noah, and which line represents the distance traveled by Diego? Label each graph with one name. b. Explain how you decided which line represents which person’s travel?”
Unit 4: Proportional Relationships and Percentages, Section B: Percent Increase and Decrease, Lesson 8: Percent Increase and Decrease with Equations, Practice Problems, Problem 2, “Elena’s aunt bought her a $150 savings bond when she was born. When Elena is 20 years old, the bond will have earned 105% interest. How much will the bond be worth when Elena is 20 years old?”
Unit 6: Expressions, Equations, and Inequalities, Section A: Representing Equations in the form px + q = r and p(x + q) = r, Lesson 6: Distinguishing between Two Types of Situations, Practice Problems, Problem 4, “Elena walked 20 minutes more than Lin. Jada walked twice as long as Elena. Jada walked for 90 minutes. The equation s(x + 20) = 90describes this situation. Match each amount in the story with the expression that represents it. a. x b. x + 20 c. 2(x + 20) d. 90 1. The number of minutes that Jada walked. 2. The number of minutes that Elena walked. 3. The number of minutes that Lin walked.”
Indicator 3S
Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.
The materials reviewed for Open Up Resources Grade 7 partially provide guidance to encourage teachers to draw upon student home language to facilitate learning.
The materials include a Spanish version of the Family Letter. According to the Course Guide, Supports for English Language Learners, “This curriculum builds on foundational principles for supporting language development for all students. This section aims to provide guidance to help teachers recognize and support students’ language development in the context of mathematical sense-making. Embedded within the curriculum are instructional routines and practices to help teachers address the specialized academic language demands in math when planning and delivering lessons, including the demands of reading, writing, speaking, listening, conversing, and representing in math (Aguirre & Bunch, 2012). Therefore, while these instructional routines and practices can and should be used to support all students learning mathematics, they are particularly well-suited to meet the needs of linguistically and culturally diverse students who are learning mathematics while simultaneously acquiring English.”
Indicator 3T
Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
The materials reviewed for Open Up Resources Grade 7 provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
Materials connect to the linguistic, cultural, and conventions used in mathematics to support student learning. Examples include:
Unit 2: Introducing Proportional Relationships, Section B: Representing Proportional Relationships with Equations, Lesson 4: Proportional Relationships and Equations, Practice Problems, Problem 2, “On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance in miles, d, to the number of hours flying, t, is t = d. How long will it take the airplane to travel 800 miles?”
Unit 3: Measuring Circles, Section B: Area of a Circle, Lesson 8: Relating Area to Circumference, Practice Problems, Problem 4, “The Carousel on the National Mall has 4 rings of horses. Kiran is riding on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is. a. In one rotation of the carousel, how much farther does Mai travel than Kiran? b. One rotation of the carousel takes 12 seconds. How much faster does Mai travel than Kiran?”
Unit 7: Angles, Triangles, and Prisms, Section C: Solid Geometry, Lesson 11: Slicing Solids, Practice Problems, Problem 5, “Two months ago, the price, in dollars, of a cell phone was c. a. Last month, the price of the phone increased by 10%. Write an expression for the price of the phone last month. b. This month, the price of the phone decreased by 10%. Write an expression for the price of the phone this month. c. Is the price of the phone this month the same as it was two months ago? Explain your reasoning.”
Indicator 3U
Materials provide supports for different reading levels to ensure accessibility for students.
The materials reviewed for Open Up Resources Grade 7 provide supports for different reading levels to ensure accessibility for students.
In Resources, Course Guide, Supports for Students with Disabilities, Representation, “Teachers can reduce barriers and leverage students’ individual strengths by inviting students to engage with the same content in different ways. Supports that align to this principle offer instructional strategies that provide students with multiple means of representation and include suggestions that offer alternatives for the ways information is presented or displayed, help develop students’ understanding and use of mathematical language and symbols; illustrate connections between and across mathematical representations using color and annotations, identify opportunities to activate or supply background knowledge, and describe organizational methods and approaches designed to help students internalize learning.” Examples include:
Resources, Course Guide, Supports for English Language Learners, Mathematical Language Routines, Mathematical Language Routine 6: Three Reads, Purpose, “To ensure that students know what they are being asked to do, create opportunities for students to reflect on the ways mathematical questions are presented, and equip students with tools used to actively make sense of mathematical situations and information (Kelemanik, Lucenta, & Creighton, 2016). This routine supports reading comprehension, sense-making, and meta-awareness of mathematical language. It also supports negotiating information in a text with a partner through mathematical conversation.” How it Happens, “In this routine, students are supported in reading a mathematical text, situation, or word problem three times, each with a particular focus. The intended question or main prompt is intentionally withheld until the third read so that students can concentrate on making sense of what is happening in the text before rushing to a solution or method. Read #1: Shared Reading (one person reads aloud while everyone else reads with them) The first read focuses on the situation, context, or main idea of the text. After a shared reading, ask students ‘what is this situation about?’ This is the time to identify and resolve any challenges with any non-mathematical vocabulary. (1 minute) Read #2: Individual, Pairs, or Shared Reading After the second read, students list any quantities that can be counted or measured. Students are encouraged not to focus on specific values. Instead they focus on naming what is countable or measurable in the situation. It is not necessary to discuss the relevance of the quantities, just to be specific about them (examples: ‘number of people in her family’ rather than ‘people’, ‘number of markers after’ instead of’“markers’). Some of the quantities will be explicit (example: 32 apples) while others are implicit (example: the time it takes to brush one tooth). Record the quantities as a reference to use when solving the problem after the third read. (3–5 minutes) Read #3: Individual, Pairs, or Shared Reading During the third read, the final question or prompt is revealed. Students discuss possible solution strategies, referencing the relevant quantities recorded after the second read. It may be helpful for students to create diagrams to represent the relationships among quantities identified in the second read, or to represent the situation with a picture (Asturias, 2014). (1–2 minutes).”
Unit 2: Introducing Proportional Relationships, Section C: Comparing Proportional and Nonproportional Relationships, Lesson 9: Solving Problems about Proportional Relationships, Activity 1: Info Gap: Biking and Rain, Instructional Routines, “In this info gap activity, students write equations for several proportional relationships given in the contexts of a bike ride and steady rainfall. They use the equations to make predictions. The info gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).”
Unit 7: Angles, Triangles, and Prisms, Section A: Angle Relationships, Lesson 2: Adjacent Angles, Lesson Narrative, “In this lesson, students are introduced to the terms complementary, for describing two angles whose measures add to 90 degrees, and supplementary, for describing two angles whose measures add to 180 degrees. They practice finding an unknown angle given the measure of another angle that is complementary or supplementary. Many of the angles in this lesson share the same vertex as another angle, so students need to be careful when naming each angle (MP6) in addition to describing the relationship between pairs of angles.”
Indicator 3V
Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
The materials reviewed for Open Up Resources Grade 7 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Suggestions and/or links to manipulatives are consistently included within materials to support the understanding of grade-level math concepts. Examples include:
Unit 3: Measuring Circles, Section A: Circumference of a Circle, Lesson 2: Exploring Circles, Activity 3: Drawing Circles, Instructional Routines, “The purpose of this activity is to reinforce students’ understanding of the terms diameter, center, and radius and also for students to see what a compass is good for (MP5). Before using the compass, students first attempt to draw a circle freehand. Then, they recognize the compass as a strategic tool for drawing circles. However, the compass is useful not just for drawing circles but also for transferring lengths from one location to another for many different purposes. Students will apply this understanding in later units, for example, when they construct a triangle given the lengths of its three sides. This activity prepares students for that application by asking them to make the radius of the circle match another length they have already drawn. If this is a student’s first time using a compass, direct instruction may be needed on how to use one. The circles students draw may not be perfect, but as they gain more experience with a compass, they will improve. A digital version of the activity is provided for classrooms that do not have access to compasses but do have access to appropriate electronic devices.”
Unit 7: Angles, Triangles, and Prisms, Section A: Angle Relationships, Lesson 2: Adjacent Angles, Required Materials, “Cut blank paper in half so that each student can have 2 half sheets of paper. It is very important that these cuts are completely straight and exactly perpendicular to the sides being cut for this activity to work. Prepare to distribute scissors, straightedges, and protractors.”
Unit 8: Probability and Sampling, Section B: Probabilities of Multi-Step Events, Lesson 10: Designing Simulations, Required Preparation, “Every 3 students need 2 coins for the Breeding Mice activity. Print and cut up questions from the Designing Simulations Blackline Master. Use one question for every 3 students. Groups will need access to number cubes, protractors, rulers, compasses, paper clips, bags, snap cubes, and scissors to simulate their scenarios.”
Criterion 3.4: Intentional Design
The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.
The materials reviewed for Open Up Resources 6-8 Math Grade 7 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards; include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other; have a visual design that supports students in engaging thoughtfully with the subject that is neither distracting nor chaotic; and provides teacher guidance for the use of embedded technology to support and enhance student learning.
Indicator 3W
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.
The materials reviewed for Open-Up Resources Grade 7 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.
According to the Course Guide, About These Materials, “There are two ways students can interact with these materials. Students can work solely with printed workbooks or pdfs. Alternatively, if all students have access to an appropriate device, students can look at the task statements on that device and write their responses in a notebook or the print companion for the digital materials. It is recommended that if students are to access the materials this way, they keep the notebook carefully organized so that they can go back to their work later. Teachers can access the teacher materials either in print or in a browser. A classroom with a digital projector is recommended.” Applets are provided in various lessons. Examples include but are not limited to:
Unit 4: Proportional Relationships and Percentages, Section A: Proportional Relationships with Fractions, Lesson 2: Ratios and Rates with Fractions, Instructional Routines: “The digital version of the student materials includes an applet so that students can experiment with the context, because there are many related measurements within the context that can be hard to visualize. For example, the applet makes it clear that you can’t simply scale down the Mona Lisa and make it perfectly fit on the notebook, since the notebook and the Mona Lisa are not scaled copies of each other. It also serves to remind students that the length and width of the Mona Lisa have to be scaled by the same factor, or the image becomes distorted.” Launch, “The purpose of the applet is for experimenting and understanding the situation.”
Indicator 3X
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
The materials reviewed for Open Up Resources Grade 7 do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
According to the Course Guide, About These Materials, The Five Practices, “Selected activities are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011), also described in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014), and Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Kazemi & Hintz, 2014). These activities include a presentation of a task or problem (may be print or other media) where student approaches are anticipated ahead of time. Students first engage in independent think-time followed by partner or small-group work on the problem. The teacher circulates as students are working and notes groups using different approaches. Groups or individuals are selected in a specific, recommended sequence to share their approach with the class, and finally the teacher leads a whole-class discussion to make connections and highlight important ideas.” While the materials embed opportunities for mathematical community building through student task structures and discourse, materials do not reference digital technology.
Indicator 3Y
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
The materials reviewed for Open Up Resources Grade 7 have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
According to the Course Guide, How to Use These Materials, Each Lesson and Unit Tells a Story, “The story of each grade is told in nine units. Each unit has a narrative that describes the mathematical work that will unfold in that unit. Each lesson in the unit also has a narrative. Lesson Narratives explain: The mathematical content of the lesson and its place in the learning sequence. The meaning of any new terms introduced in the lesson. How the mathematical practices come into play, as appropriate. Activities within lessons also have narratives, which explain: The mathematical purpose of the activity and its place in the learning sequence. What students are doing during the activity. What teacher needs to look for while students are working on an activity to orchestrate an effective synthesis. Connections to the mathematical practices, when appropriate.” Examples from the materials include:
Each lesson follows a common format with the following components: Warm-up, one to three Activities, Lesson Synthesis, and Cool-down. The consistent structure includes a user-friendly layout as each lesson component is included in order from top to bottom on the page.
Student materials, in printed consumable format, include appropriate font size, direction amount and placement, and space on the page for students to show their mathematical thinking.
The teacher's digital format is easy to navigate and engaging. The printable Student Task Statements, Assessment PDFs, and workbooks provide ample space for students to capture calculations and write answers.
Indicator 3Z
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
The materials reviewed for Open-Up Resources Grade 7 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
Lessons containing applets provide teacher guidance for the use of embedded technology to support and enhance student learning. Examples include:
Unit 4: Proportional Relationships and Percentages, Section A: Proportional Relationships with Fractions, Lesson 2: Ratios and Rates with Fractions, Launch, “The purpose of the applet is for experimenting and understanding the situation. If using it, demonstrate how it works, and ask students to think about: How to use the applet to create scale copies of the Mona Lisa (both dimensions have to be adjusted by the same factor.) Is it possible to scale down the Mona Lisa so that it perfectly covers the notebook? (No, choices have to be made about what the final product will look like.)” Student Work Time, “The applet is here to help you experiment with the situation. (It won’t solve the problems for you.) Use the sliders to scale the image and drag the red circle to place it on the book. Measure the side lengths with the Distance or Length tool.”
Unit 8: Probability and Sampling, Section B: Probabilities of Multi-Step Events, Lesson 7: Simulating Multi-Step Experiments, Student Work Time, “Use the applet to simulate the weather for 10 days of break to see if Alpine Zoom will make money. In each trial, spin the spinner 10 times, and then record the number of 1’s that appeared in the row. The applet reports if the Alpine Zoom will make money or not in the last column. Click Next to get the spin button back to start the next simulation.”