Kindergarten - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 92% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations for Gateway 1, focus and coherence. Assessments represent grade-level work, and items that are above grade level can be modified or omitted. Students and teachers using the materials as designed would devote a majority of time to the major work of the grade. The materials are coherent and consistent with the standards.
Criterion 1.1: Focus
The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain assessment items that assess above grade-level content, but these can be modified or omitted.
Indicator 1a
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations for assessing grade-level content. Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.
Examples of assessment items aligned to above grade-level standards include:
- Chapter 8, Test A and Test B, Question 6, students write an "addition sentence" to match a given word problem. The matching addition sentences are 10 + 3 = 13 and 10 + 5 = 15 respectively. This is beyond the standard K.OA.2, solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
- Chapter 10, Test A and Test B, Question 6, students circle the number that represents the amount of bouncy balls using groups of 10s and 1s with solutions of 46 and 53 respectively. This aligns to 1.NBT.2.
Examples of assessment items aligned to grade-level standards include:
- Chapter 1, Test A, Questions 1-8, students count by 1s, write numbers up to 10, count to answer “how many”, and count in arranged and scattered configuration. (K.CC.1, K.CC.3-5)
- Chapter 2, Test B, Question 1, students compare groups and circle the group with the greater number of animals. (K.CC.6)
- Chapter 3, Test A, Questions 1-7, students count by 1s, write numbers up to 10, count to answer “how many”, and count arranged and scattered configurations. (K.CC.3-5)
- Chapter 4, Test B, Question 3, students compare two numerals and determine if they are equal. (K.CC.7)
- Chapter 6, Test A, Question 3, students solve the addition equation, “2+0=___”. (K.OA.5)
- Chapter 6, Test B, Question 5, students find the number that makes a 10 when added to 6, “6 +__=10”. (K.OA.4)
- Chapter 7, Test A, Question 5, students represent subtraction with objects and drawings. (K.OA.4)
- Chapter 10, Test A and Test B, Questions 1-4, students fill in the missing numbers on a 100s chart by circling the missing numbers. (K.CC.1)
- Chapter 10, Test A and Test B, Question 5, students fill in the missing numbers on a 100s chart when counting by ten from a given number. (K.CC.A)
Chapter 11, Test A and Test B, Question 6, “Use squares and rectangles to draw 5 windows and 1 door on the castle. Color the castle. Then write an 'addition sentence' to tell how many squares and rectangles you drew in all.” Test B states, “Use squares and rectangles to draw 6 windows and 1 door on the castle.” (K.OA.1)
Criterion 1.2: Coherence
Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations for spending a majority of class time on major work of the grade when using the materials as designed. Time spent on the major work was figured using chapters, lessons, and days. Approximately 71% of the time is spent on the major work of the grade.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet expectations for spending a majority of instructional time on major work of the grade. For Kindergarten, this includes all clusters within K.OA, K.NBT, and K.CC.
To determine the focus on major work, three perspectives were evaluated: the number of chapters devoted to major work, the number of lessons devoted to major work, and the number of weeks devoted to major work.
- The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 9 out of 13, which is approximately 69% of the instructional time.
- The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 68 out of 96, which is approximately 71% of the instructional time.
- The number of days devoted to major work (including assessments and supporting work connected to the major work) is 105 out of 148 days, which is approximately 71% of the instructional time.
A day-level analysis is most representative of the instructional materials because the number of days is not consistent within chapters and lessons. As a result, approximately 71% of the instructional materials focus on the major work of the grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet the expectations that the materials are coherent and consistent with the standards. The materials represent a year of viable content. Teachers using the materials would give their students extensive work in grade-level problems, and the materials describe how the lessons connect with the grade-level standards. However, above grade-level content is present and not identified.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Examples of the connections between supporting work and major work include the following:
- Chapter 4, Lesson 5, Think and Grow, connects K.MD.3 to major work K.CC.6 when students show a number of vehicles IN the water and number OUT of the water in the picture, then circle the category with the greater number of vehicles. Students connect to major work by writing a total number in each category (K.CC.3) before circling which number is greater (K.CC.7).
- Chapter 11, Lesson 1, Think and Grow, connects supporting standard K.G.4 to major work K.CC.5 and K.CC.3 when students count shapes to answer questions such as, “How many stickers in the picture have more than 4 vertices?”
- Chapter 11, Lesson 2, Think and Grow, connects supporting standard K.G.5 to major work K.CC.5 when students draw and color 10 triangle-shaped flags. This problem is also connected to major work K.OA.1 when students write an equation to match the picture.
- Chapter 11, Lesson 6, Think and Grow, connects supporting standard K.G.6 to major work K.CC.5 when students use pattern blocks to trace and create a new shape, then count and write how many pattern blocks they used.
- Chapter 12, Lesson 4, Think and Grow, students connect supporting standard K.G.5 to major work K.CC.5 when students draw the shape of the flat surfaces of a cylinder, then count and write the number of flat surfaces.
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
Instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that the amount of content designated for one grade-level is viable for one year.
As designed, the instructional materials can be completed in 148 days with each lesson counting as one day. The minimum time per class period is 45 minutes, with the recommended time of 60-70 minutes. A pacing guide can be found in the Teachers Guide. Kindergarten is divided into 13 Chapters. The 148 days include the following:
- 96 days of Lessons.
- 13 days of Lesson Opener Activities - Each Chapter begins with a chapter opener.
- 26 days for “Connect and Grow” Activities - Two days per chapter are dedicated to these activities which include a performance task and chapter practice on one day and centers on the other day.
- 13 days for Chapter Assessments - Each chapter has a final chapter assessment.
Indicator 1e
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Kindergarten partially meet expectations for being consistent with the progressions in the Standards. The presence of above grade-level content distracts from all students engaging with extensive work of the grade.
The Teacher Edition includes a “Progression Through the Grades” chart which outlines each domain and its accompanying clusters, and which chapters address each cluster. Additionally, tables are provided to identify which lessons address specific standards. The beginning of each chapter includes an overview table “Progressions Through the Grades” that shows the content from the previous and future grade levels, and “Laurie’s Overview” where the math in the chapter is explained and connected to prior and future work of the grade. For example:
- The "Progression Through the Grades" chart states: Kindergarten “Name, count, and write numbers within 5. Pair each number name with an object. Determine that the last number stated names the total. Count objects in different arrangements. Order numbers within 5 both forward and backward. Understand that the next number stated is one number greater. “ Grade 1 “Represent, write, and solve ‘Add To’ and ‘Put Together’ problems with unknowns. Write and solve addition number sentences. Solve addition word problems. Represent, write, and solve ‘Take From’ and ‘Take Apart’ problems with unknowns. Write and solve subtraction number sentences. Solve subtraction word problems. Solve addition and subtraction comparison problems.”
The instructional materials develop according to the grade-by-grade progressions. For example, in the Teacher Edition, Chapter 6, Lesson 3, addresses Standard K.CC.5:
- Explore and Grow: “Directions: Use counters to act out the story. There are 4 pencils in the case. Write the number. There are 3 crayons in the case. Write the number. Tell how many objects are in the case now.”
- Think and Grow: “Directions: Circle the groups to put them together. Then write an addition sentence to tell how many objects there are in all.”
- Apply and Grow Practice: “Directions: Circle the groups to put them together. Then write an addition sentence to tell how many objects there are in all.”
- Think and Grow: Modeling Real Life: “Directions: You have 5 balls of red clay and 1 ball of blue clay. Draw and color the balls of clay. Then write an addition sentence to tell how many balls of clay you have in all.”
- Practice: additional practice problems are included.
Throughout the instructional materials, above grade-level content is present. This content is not identified as above grade-level, and distracts students from engaging with extensive work with grade-level mathematics to meet the full intent of grade-level standards. For example:
- Chapter 9, Lesson 6, Think and Grow, “Compare the numbers of red dots and blue dots. Circle the number that is greater than the other number.” Followed by, “Compare the numbers of yellow dots and red dots. Draw a line through the number that is less than the other number.” The numbers used are “20 and 17” and “14, 18, and 11.” (1.NBT.3)
- Chapter 10 content is aligned to above grade-level standards. For example:
- Chapter Practice, students count by 10 from any number; examples: “9 - 19, 29, 39; 46 - 56, 66, 76.” (1.NBT.4, 1.NBT.6)
- Lesson 5, Explore and Grow, students “circle the number that shows how many”, but the picture has groups of tens and ones. (1.NBT.2)
- Lessons 6, Explore and Grow, students count by tens “off the decade” (1.NBT.1). In the Think and Grow, students start counting from a number other than 10. Students “count the milk cartons. Circle the number that tells how many. (25)" This is presented in two groups of 10 and 5 ones.
- Chapter 13, Lesson 4, Explore and Grow, students use color tiles to measure objects. (1.MD.2)
Each Unit contains an “About the Math” section that connects the math to prior knowledge. Laurie’s Notes: Preparing to Teach connects prior knowledge to the content of the lesson. For example:
- Teacher Edition, Chapter 1, Lesson 1, Laurie’s Notes, Preparing to Teach, “Many students are able to orally count numbers, meaning they can recite the sequence one, two, three, and so on. A second and different skill is connecting the sequence of the words one, two, three and so on in a one-to-one correspondence with objects being counted. In this first lesson, students use one-to-one correspondence to count one or two objects and tell how many objects are in a group. They should understand that the last number they count is the total number of objects.”
- Teacher Edition, Chapter 2, Lesson 2, Laurie’s Notes, Preparing to Teach, “Give two students unequal amounts of snacks and they will know it! They can usually tell when the quantities are the same as, or equal. Students compare groups of objects by matching each object from one group to an object from another group. When matching, students can see if each object has a 'partner'. The term 'partner' helps students recognize when two groups of quantities are the same. This also prepares students to recognize quantities that are odd or even.”
Indicator 1f
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
The instructional materials for Big Ideas Math: Modeling Real Life Kindergarten meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, and they provide problems and activities that connect two or more clusters in a domain or two or more domains when the connections are natural and important.
Examples of learning objectives visibly shaped by CCSSM cluster headings include:
- Chapter 2, Lesson 3, Apply and Grow, “Show and tell whether one group has a lesser number of objects than another group.” Students use counters to show the number of rabbits and to show the number of rabbit holes. Students are then asked are there fewer rabbits or fewer holes. This is shaped by the cluster heading K.CC.C.
- Chapter 8, Lesson 11, Apply and Grow, “Understand the numbers 18 and 19.” Students circle 10 objects, then draw dots in a 10-frame to show how many objects are circled. Then students draw dots in the bottom ten frame to show how many more objects there are. They complete a number sentence to match the drawing (example: 19=10+9). This is framed by the cluster heading K.NBT.A.
- Chapter 8, Lesson 3, Apply and Grow, the learning objective is visibly shaped by the cluster heading K.NBT.A. For example, “Directions: Circle 10 objects. Draw dots in the ten frame to show how many more objects are circled. Draw dots in the five frame to show how many more objects that are. Use the frames to write an addition sentence.”
Examples of problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, include:
- Chapter 3, Lesson 2, Think and Grow, connects knowing number names and the count sequence (K.CC.A) and count to tell the number of objects (K.CC.B). For example, “Directions: Count the objects. Say the number. Trace and write the number. Count the instruments. Say the number. Write the number.”
- Chapter 4, Lesson 2, Think and Grow, connects count to tell the number of objects (K.CC.B) with compare numbers (K.CC.C). For example in Question 2, students “count the number of objects in each group. Write the number. Circle the number that is greater than the other number.”
- Chapter 4, Lesson 5, Think and Grow, students “Show the number of vehicles in the water and the number of vehicles NOT in the water. Circle the category with the greater number of vehicles.” This connects comparing numbers (K.CC.C) to classifying objects and counting the number of objects in each category (K.MD.B).
- Chapter 5, Lesson 1, Think and Grow, connects major cluster headings understand addition as putting together and adding to, and understand subtraction as taking apart and taking from (K.OA.A) and count to tell the number of objects (K.CC.B). For example, “Directions: 3 and 4 Count each type of dog. Write each number. Count all of the dogs. Write the number for the whole.”
- Chapter 8, Lesson 7, Think and Grow, connects working with numbers 11-19 to gain foundations for place value (K.NBT.A) with counting to tell the number of objects (K.CC.B) and knowing number names and the count sequence (K.CC.A) by having the students “Circle ten flowers. Draw dots in the top ten frame to show how many flowers are circled. Draw dots in the bottom ten frame to show how many more flowers there are. Use the ten frames to write an addition sentence.”
- Chapter 12, Lesson 4, Think and Grow, students “Circle the cone. Draw a rectangle around the cylinder. Tell why your answers are correct.” This connects identify and describe shapes (K.G.A) to analyze, create, compare, and compose shapes (K.G.B).
- Chapter 12, Lesson 5, Think and Grow, students “Use your materials to build one of the three-dimensional shapes shown. Circle the three-dimensional shape that you build.” This connects the clusters identify and describe shapes (K.G.A) and analyze, create, compare, and compose shapes (K.G.B).