Kindergarten - Gateway 1

The materials reviewed for Reveal Math Kindergarten meet expectations for assessing grade level content, and if applicable, content from earlier grades. Summative Assessments include Unit Assessments (Forms A and B), Unit Performance Tasks, Benchmark Assessments, and an End of the Year Summative Assessment. Also included in the digital Teacher Center are editable, auto- scored assessments. Reveal Math does include assessments on the faces of three dimensional shapes, which is above grade level. Unit 1 does not include a Unit Assessment or Performance Task.

Examples of grade-level assessment items include:

• In Unit 2, Numbers to 5, Digital Unit Assessment, Form A, Item 5, “Compare the groups. Look at the group of tigers and the group of zebras. Which group is less than the other group?” A group of two tigers and a group of four zebras is displayed. (K.CC.6)

• In Unit 6, Understand Addition, Unit Assessment, Form A, Item 1, “3 butterflies are flying. 4 more join them. Draw butterflies to show how many in all.” (K.OA.1) 

• In Unit 10, Numbers 16 to 19, Performance Task, Part E, “Alia takes 18 pennies and puts them in 2 piles. She puts 10 pennies in one pile. How many pennies will be in the other pile? Write the numbers to complete the equation to represent the situation.” (K.NBT.1)

• Benchmark Assessment 3, Item 2, “How many more dots are needed to make 10? [7] Write the number to show how many more dots.” A ten-frame with 3 spaces filled in is shown. (K.OA.3)

• Summative Assessment, Item 7, “Which numbers are missing?  27, 28, __, 30, 31, __, 33. Circle all the correct answers.” The choices are: “26, 29, 32, 34.” [29, 32](K.CC.2)

Example of above grade-level assessment item that could be omitted or modified:

• Summative Assessment, Item 9, A cylinder, a sphere and a cube are shown, “Which solids have faces? Circle all the correct answers.” (K.G.2) Recognizing three-dimensional shapes having specified attributes, such as faces, occurs in Grade 2. (2.G.1)

The materials reviewed for Reveal Math Kindergarten meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. Within the materials, all standards are represented, and most meet the full intent of the grade-level standard. However, the materials provide limited opportunities for all students to engage in extensive work with grade-level problems to meet the full intent of standard K.OA.4.

Examples where the materials engage all students in extensive work with grade-level problems to meet the full intent of the standard include:

• In Lesson 3-8, Compare Objects in Groups, Differentiate, Build Proficiency, Digital Additional Practice Book: Compare Objects in Groups, Exercise 4, “How can you draw to show equal groups?” Students draw any size group of no more than 10 objects to demonstrate understanding how equal groups are formed. This exercise engages students with the full intent of K.CC.6, identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

• In Lesson 6-4, Represent and Solve Addition Problems, Practice and Reflect, On My Own, Exercise 2, “Use counters or drawings to show one way to solve the problem. Then write an equation to match. Sally has 3 kickballs. How many can she put in the red bin and how many in the green bin?” Students draw a picture to represent the problem and fill in the addends in the equation  3 = ___ + ___. This exercise engages students with the full intent of 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.

• In Lesson 10-6, Decompose 18 and 19, Number Routine, Break Apart, “Tell students that they should break apart 19 in three different ways.” (16 in the digital format) Teacher prompts include, “What do we mean when we say ‘break apart’ a number? How did you break apart 19? Did anyone draw a picture? How did that help? Did anyone use ten-frames and counters? Show us how you used those tools.” Decomposing and composing exercises throughout Unit 10 address the full intent of  K.NBT.1, compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones, and provide extensive work with grade-level problems.

• In Lesson 12-5, Count to Find Out How Many, Differentiate, Build Proficiency, Game Station: Which Number Comes Next Race, “Directions: Decide who will go first. When it is your turn, pick a card. Count by ones. Say which number comes next. The answer keeper checks your answer with the answer key. If you are correct, move your game piece the number of spaces shown on the card. If you are not correct, stay on your space. Now it is the next player’s turn. The first player to reach the Finish line wins the game.” This engages students with K.CC.2, count forward beginning from a given number within the known sequence (instead of having to begin at 1).

• Lesson 13-2, Build and Draw 2-Dimensional Shapes, Practice & Reflect, On My Own,  Exercise 1, students are shown a circle. “How can you draw a circle? Trace the circle. Then draw a circle.” Exercise 2, students are shown a square. “How can you draw a square? Trace the square. Then draw a square.” Exercise 3, students are shown a hexagon. “How can you draw a hexagon? Trace the hexagon. Then draw a hexagon.” All of these exercises provide extensive work with K.G.5, model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

• In Lesson 14-3, Compare Heights, Launch, Notice and Wonder, students compare measurable attributes of two objects when provided with images of two different sized plants, “How are they the same? How are they different? Teaching Tip: If students mention attributes such as the color or type of plants, encourage them to begin thinking about height comparison by asking, What can you say about the size of the plants?” This exercise engages students with the full intent of standard K.MD.2, directly compare two objects with a measurable attribute in common, to see which object  has “more of”/”less of” the attribute, and describe the difference.

The materials reviewed for Reveal Math Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

Within the materials, at least 65% of instructional time addresses the major work of the grade, including supporting work connected to major work. For example:

• There are 14 Units, of which 12.5 address major work, or supporting work connected to major work of the grade, approximately 89%.

• There are 88 lessons, of which 77 address major work, or supporting work connected to major work, approximately 88%.

• There are 150 days of instruction, 131 of which address major work, or supporting work connected to major work, approximately 87%.

The materials contained discrepancies regarding the number of days per unit, and guidance was not given as to how those days were accounted for, therefore, a lesson level analysis is most representative of the materials. As a result, approximately 88% of the instructional materials focus on major work of the grade.

The materials reviewed for Reveal Math Kindergarten meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Standards K.G.5 and K.G.6 are not always connected to major work of the grade, but the separation is mathematically reasonable.

Examples of supporting work engaging simultaneously with major work of the grade, when appropriate include:

• In Lesson 4-4, Launch, Which Doesn’t Belong, Pose Purposeful Questions, the supporting work of K.MD.3 classify objects into given categories, connects to the major work of K.CC.1, count to 100 by ones and tens, and K.CC.5, count to answer “how many?” questions, as students count the objects in each category. “How are the groups the same? How are the groups different? Which group doesn’t belong? How can you use color to describe the groups? How can you use shape to describe the groups? How can you use size to describe the groups? How can you use numbers to describe the groups?” (5 purple crayons, 5 yellow pencils, 3 purple markers, 5 purple flowers)

• In Lesson 5-3, Hexagons, Practice & Reflect, On My Own, Exercise 3, the materials connect the supporting work of K.G.2, correctly name shapes regardless of their orientations or overall size, to the major work of K.CC.5, count to answer “how many?” questions, as students count the number of sides in a given shape. “Which shapes have 6 sides? Circle the shapes with 6 sides.”

• In Lesson 11-2, Cubes, Practice & Reflect, On My Own, Exercise 5, Extend Your Thinking, connects the supporting work of K.G.4, analyze and compare two- and three-dimensional shapes, to the major work of K.CC.5, count to answer “how many?” questions, as students count the number of faces on a cube and circle the correct number when provided with three numerals. “How many faces does a cube have? Circle the number of faces.” [6] 

• In Lesson 13-3, Compose 2-Dimensional Shapes, Differentiate, Extended Thinking, Differentiation Resource Book, Exercise 1, the supporting work of K.G.6, compose simple shapes to form larger shapes, connects to the major work of K.CC.3, write numbers from 0 to 20, as students count to find the number of triangles that make up the hexagon. “How many triangles is this shape made of?” Students count the triangles and write the number “6” on the blank below the hexagon.

• In Lesson 13-4, Compare and Contrast 3-Dimensional Shapes, Differentiate, Reinforce Understanding, Differentiation Resource Book, Exercise 1, the supporting work of K.G.4, analyze and compare two- and three-dimensional shapes, connects to the major work of K.CC.6, identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, when they compare shapes based on defining attributes. “How can you compare the shapes? Put an X on the shape that is different.”

The materials reviewed for Reveal Math Kindergarten 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. The materials contain connections from supporting work to supporting work, and connections from major work to major work throughout the grade-level materials when appropriate.

Connections between major clusters or domains include:

• In Lesson 2-9, Compare Numbers to 5, Differentiate, Build Proficiency, Digital Additional Practice Book: Compare Numbers to 5, Exercise 2, connects the major work of K.CC.C, compare numbers, to the major work of K.CC.B, count to tell the number of objects, as students determine which digit is less, then draw that number of objects. “Which number is less? [3 or 1] Draw objects to show each number. Circle the number that is less.”

• In Lesson 3-11, Write Numbers to 6, Practice & Reflect, On My Own, Exercise 4, connects the major work of K.CC.B, count to tell the number of objects, to K.CC.A, know number names and the count sequence, as students count the number of objects shown and write the number to show how many. “How many shovels? Write the number.”

• In Lesson 6-3, Represent and Solve Put Together Problems, Practice & Reflect, On My Own, Exercise 1, connects the major work of K.CC.A, know number names and the count sequence, to the major work of K.OA.A, understand addition as putting together and adding to, and understand subtraction as taking apart and taking from, as students represent an addition story and write an equation. “Use counters or drawings to represent the addition story. Then write an equation to match. Two soccer balls and 4 volleyballs are on the shelf. How many balls are on the shelf?”

• In Lesson 8-4, Ways to Decompose 6 and 7, Practice & Reflect, On My Own, Exercise 1, connects the major work of K.OA.A, understand addition as putting together and adding to, and understand subtraction as taking apart and taking from, to the major work of K.CC.B, count to tell the number of objects, as students decompose a number and write an equation. Exercise 1, students are shown six soccer balls in a row, “How can you decompose 6? Circle groups to show a way to decompose 6. Write the equation to match.  ____ = ____ + ____.”  

• In Lesson 9-3, Decompose 11, 12, and 13, Differentiate, Build Proficiency, Digital Additional Practice Book: Decompose 11, 12, and 13, Exercise 1, connects the major work of K.NBT.A, work with numbers 11-19 to gain foundations for place value, to the major work of K.CC.A, know number names and the count sequence, as students decompose a number of objects and write an equation. Exercise 1, students are shown a picture of 11 flowers, “How can you decompose 11? Circle groups to decompose 11 into ten ones and some more ones. Write the equation to match.  11= ____ + ____.”  

• In Lesson 10-5, Make 18 and 19, Practice & Reflect, On My Own, Exercise 4, Error Analysis, connects the major cluster of K.NBT.A, work with numbers 11-19 to gain foundations for place value, to the major cluster of K.OA.A, understand addition as putting together and adding to, and understand subtraction as taking apart and taking from, as students compose the number 18 from a group of 10 ones and some more. “There are 18 scissors. Jill says the missing number in the equation is 8. Mandy says the missing number is 9. Complete the equation to show who is correct.” A picture of 2 rows of 9 scissors each is shown. The equation is “10 + __ = 18.” 

Connections between supporting clusters or domains include:

• In Lesson 4-1, Alike and Different, Launch, Notice & Wonder, Pose Purposeful Questions, connects the supporting work of K.MD.A, describe and compare measurable attributes, to the supporting work of K.MD.B, classify objects and count the number of objects in each category, as students are shown an image of different sizes and types of writing utensils and are asked to describe similarities and differences within the object set. “Think of ways that two of the objects are the same. How are they the same? How are they different from the other objects? What is the same about the objects? What is one object we could add that would be the same as all the objects shown?”

• In Lesson 4-2, Sort Objects Into Groups, Practice & Reflect, On My Own, Exercise 3, Extend Your Thinking, connects the supporting work of K.MD.B, classify objects and count the number of objects in each category, to the supporting work of K.G.A, identify and describe shapes, as students sort two dimensional shapes and identify how they sorted them. Students are shown 1 yellow triangle, 1 purple circle, 1 blue triangle, 2 blue squares, 1 purple triangle, and 1 yellow circle. “How can you sort the shapes? Draw lines to the bins. Draw on the bins to show how you sorted.” Reflect, “How are the objects sorted?” 

• In Lesson 13-1, Compare & Contrast 2-Dimensional Shapes, Math Probe, Exercises 1-2, connect the supporting work of K.G.B, analyze, compare, create, and compose shapes, to the supporting work of K.MD.A, describe and compare measurable attributes, as students use defining attributes to determine which shape is not like the others. “Circle the shape that is not like the others. Tell or show why.” Exercise 1 shows three different triangles and one quadrilateral. Exercise 2 shows three quadrilaterals and one triangle.

The materials reviewed for Reveal Math Kindergarten meet expectations that content from future grades is identified and related to grade-level work, and the instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. As this is Kindergarten, it is mathematically reasonable that there are no connections to a previous grade and that standards build conceptually throughout the year.

Content from future grades is identified within the chapters, units, and lessons; and is connected to grade-level work. Examples include:

• In Lesson 3-1, Count 6 and 7, Coherence, Now, includes K.CC.4, understand the relationship between numbers and quantities; connect counting to cardinality. “Students count objects to 7 and show the quantities using manipulatives or representations.” In Next, “Students count objects up to 19 (Unit 10). Students count to 120 (Grade 1).” 1.NBT.1, count to 120, starting at any number less than 120.

• In Unit 4, Sort, Classify, and Count Objects, Coherence, What Students Are Learning, includes K.MD.3, classify objects into given categories; count the number of objects in each category and sort the categories by count. “Students count to determine how many objects are in a group, understanding that the last number said represents the total number of objects, and sort groups according to the number of objects.” In What Students Will Learn, “In Grade 1, students organize data into groups of up to three categories and ask and answer questions about the reasons for their groupings.” 1.MD.4, organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

• In Lesson 7-4, Represent and Solve Subtraction Problems, Coherence, Now, includes  K.OA.1, represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations, and K.OA.2, solve addition and subtraction word problems, and add and subtract within 10. “Students apply their understanding of subtraction to represent and solve problems.” In Next, “Students will solve subtraction problems when the total, both parts, and one part part is unknown (Grade 1).” 1.OA.1, use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.

• In Lesson 12-3, Count by 10’s to 100, Coherence, Now, includes  K.CC.1, count to 100 by ones and tens. “Students apply their understanding of counting to count by 10s to 100. Students describe patterns when counting by 10s to 100.” In Next, “Students count from any number to 100 (Unit 12.). Students explore counting patterns to 120 (Grade 1).” K.CC.2, count forward beginning from a given number within the known sequence, and 1.NBT.1, count to 120, starting at any number less than 120. 

Examples where the instructional materials relate grade-level concepts explicitly to prior learning include: 

• In Lesson 8-8, Ways to Decompose 10, Coherence, Now, includes K.OA.3, decompose numbers less than or equal to 10 into pairs in more than one way. “Students apply their understanding of decomposing numbers to decompose 10 in different ways. Students explain how to decompose 10 in different ways.” In Previous, “Students represented and solved subtraction problems (Unit 7). Students decomposed 8 and 9.” K.OA.1, represent addition and K.NBT.1, compose and decompose numbers from 11 to 19 into ten ones and some further ones. “Students write numbers from 16 to 19. Students represent numbers from 16 to 19. Students compose and decompose numbers from 16 to 19.” In What Students Have Learned, “Students learned how to write and read numbers from 11 to 15. (Unit 9) Students learned how to represent numbers from 11 to 15. (Unit 9) students learned how to compose and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations, and K.OA.2, solve addition and subtraction word problems, and add and subtract within 10.

• In Lesson 9-1, Represent 11, 12, and 13, Coherence, Now, includes K.CC.3, write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20. “Students apply their understanding of numbers to count, read, and represent 11, 12, and 13.” In Previous,   “Students counted and represented numbers to 10 (Unit 3).” 

• In Unit 10, Numbers 16 to 19, Coherence, What Students Are Learning, includes K.CC.3, write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20, and decompose numbers from 11 to 15. (Unit 9)” 

• In Lesson 13-6, Describe 3-Dimensional Shapes in the World, Coherence, Now, includes K.G.1, describe objects in the environment using names of shapes, and describe the relative positions of these objects. “Students identify and describe 3-dimensional shapes in a real- world context.” In Previous, “Students described objects in their environment using names of shapes (Unit 11).” K.G.2, correctly name shapes regardless of their orientations or overall size.