## Everyday Mathematics 4

##### v1.5
###### Usability
Our Review Process

Title ISBN Edition Publisher Year
Comprehensive Student Material Set 9780076952168 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040239 McGraw-Hill Education
Comprehensive Student Material Set 9780076952113 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040215 McGraw-Hill Education
Comprehensive Student Material Set 9780076952151 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040222 McGraw-Hill Education
Comprehensive Student Material Set 9780076951048 McGraw-Hill Education
Comprehensive Student Material Set 9780076952205 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040246 McGraw-Hill Education
Comprehensive Student Material Set 9780076952106 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040208 McGraw-Hill Education
Comprehensive Student Material Set 9780076951512 McGraw-Hill Education
Comprehensive Classroom Resource Package Comprehensive Student Material Set McGraw-Hill Education
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## Report for Kindergarten

### Overall Summary

The materials reviewed for Everyday Mathematics 4 Kindergarten 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.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The materials reviewed for Everyday Mathematics 4 Kindergarten 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
Meets Expectations

#### 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 Everyday Mathematics 4 Kindergarten 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.

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Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Summative assessments include Beginning-of-Year, Mid-Year, and End-of-Year Assessments.

Materials assess grade-level standards. Examples include:

• Beginning-of-Year Assessment, Item 6, “Give children a bag with 20 connecting cubes. Say, ‘Show me 5 cubes.’ Note whether children count out 5 cubes and the strategies they use to keep track of their counting. You may wish to repeat with other numbers of cubes (up to 20) until the task becomes too challenging.” (K.CC.5)

• Mid-Year Assessment, Item 1B, “Prompt children to count by 10’s. Stop them when they reach 100 or when their counting becomes erratic. Look for children to count by 10’s through 50.” (K.CC.1)

• End-of-Year Assessment, Item 15, “Give children a bag with 15 craft sticks and tell them how many sticks it contains. First, ask them to predict how many bundles of 10 and how many single sticks they will have if they bundle the sticks in groups of 10. Then have them bundle the sticks in this way and write a number sentence to describe their grouping. Look for children to predict that they can decompose 15 into a group of 10 ones and 5 more ones and then bundle the craft sticks to show this decomposition. Also, look for them to record this grouping with an equation: 15=10+5 or 10+5=15.” (K.NBT.1)

##### Indicator {{'1b' | indicatorName}}

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Materials engage all students in extensive work with grade-level problems. Each lesson provides opportunities during Warm Up, Focus Activities, and Practice. Examples include:

• Lesson 1-6, Count and Sit, Focus: Playing Count and Sit, students' choral count from 0 to 10, “Have the mascot point to one child at a time to prompt each to say the next number. For example, the first child should say ‘1’, the next child should say ‘2’, and so on.” Lesson 4-5, Focus: Taking Ten-Frame Quick Looks, students are flashed ten frames containing different amounts of dots and are asked to remember what they saw after 3 seconds of looking at the ten-frame configuration. “Flash each image for about three seconds before removing (or covering) it and ask children to remember what they saw. To elicit flexible ways of thinking about each image, ask: What did you see? How did you see it?” Lesson 7-3, students are given a “secret” number, and count out the same amount of counters to put in a bag, “Give each child a stick-on note with a ‘secret’ number between 10 and 19 and a resealable plastic bag. Have children count out that number of small objects to put in their bags.” Students engage in extensive work with grade-level problems for K.CC.5, “Count to answer ‘how many?’ questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.”

• Lesson 1-9, Number Stories, Focus: Representing 5, students show different ways to make five fingers using 2 hands. Lesson 4-5, students look at 10 frames filled with different dot combinations and describe how they saw the dots, “I saw 2 and 1, which makes 3.” Lesson 7-12, Dice Addition, students roll 2 dice and add them together, “Give each player a ten frame and a pair of Dice Addition dice. Players roll their dice and announce the resulting addition equation (for example, 2+3=5).” Lesson 8-5, Dice Subtraction, students roll 2 dice and subtract them, “Give each player a blank ten frame and a pair of Dice Subtraction Dice. Players roll their dice and subtract the smaller number from the larger number. Then they state the subtraction equation and tell the difference (4 minus 2 equals 2, for example).” Lesson 9-6, “Roll and Record with Numeral Dice”, students roll 2 dot dice and find the total, “Give each pair of children two 1-6 numeral dice and explain that today they will play with these dice. Have them roll their dice and find the total. Ask: How did you find the total?” These games are also revisited in other lessons during the practice portion of the lesson. Students engage in extensive work with grade-level problems for K.OA.5, “Fluently add and subtract within 5.”

• Lesson 3-5, Longer or Shorter?, Focus: Sorting by Longer and Shorter, students compare strips of paper using the words “longer” and “shorter” “Use strips of different lengths to show and explain the terms longer, shorter, and same length. Hold up pairs of strips and have children compare the strips and describe the relationships.” Lesson 4-9, students are introduced to a pan balance, and use the words “heavier” and “lighter” to describe objects placed in their outstretched hands. “Hold up the two containers you prepared with objects of different weights. Pass them around for children to compare. Ask: How are they the same? Different? Which feels heavier? Lighter? Emphasize that although the containers are the same size, when filled they are different weights: one is heavier; one is lighter. Have a child illustrate the comparison by holding each container in an outstretched arm like a human pan balance.” Lesson 9-5, students measure and weigh backpacks and compare how heavy or light each one is compared to another. “Show children the books they will use to fill the backpacks. Point out that all the books are about the same size, so they can make fair comparisons. Empty the backpacks of any contents and have children fill them with books. Together count the number of books in each backpack. Ask and discuss: Which backpack holds more books (has greater capacity)? Who do you know? With the books inside, which backpack do you think will weigh more? Why?” Students engage in extensive work with grade-level problems for 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. For example, directly compare the heights of two children and describe one child as taller/shorter.

The materials provide opportunities for all students to engage with the full intent of Kindergarten standards through a consistent lesson structure. According to the Teacher’s Lesson Guide, Problem-based Instruction “Everyday Mathematics builds problem-solving into every lesson. Problem-solving is in everything they do. Warm-up Activity- Lessons begin with a quick, scaffolded Mental Math and Fluency exercise. Daily Routines - Reinforce and apply concepts and skills with daily activities. Math Message - Engage in high cognitive demand problem-solving activities that encourage productive struggle. Focus Activities - Introduce new content with group problem-solving activities and classroom discussion. Summarize - Discuss and make connections to themes of the focus activity. Practice Activities - Lessons end with a spiraled review of content from past lessons.” Examples of full intent include:

• Lesson 1-1, Partner Match, Focus: Playing Count and Sit, students play a game to practice the counting sequence. “Explain that for today’s game, your starting number is 1 and your target number is 10. Begin counting with 1 and go around the circle with each child saying the next number in the sequence.” Lesson 4-6, Focus: Counting and Moving With Teens, students are introduced to teen numbers and extend the counting sequence to 19, “Count from 1 to 10 together. Ask: What number comes after 10? Show the portion of your Growing Number Line spanning the numbers 10 through 19 and introduce these as the teen numbers…Count these numbers together as you point to them…” Lesson 5-12, students use a number-grid poster to count by 1s, then by 10s to 100, “Review the Number-Grid Poster by counting by 1s and then by 10s to 100, while you or a child point to the numbers.” Students engage in the full intent of K.CC.1, “Count to 100 by ones and by tens.”

• Lesson 2-5, Pocket Problems, Focus: Solving Pocket Problems, students use counters and a “pocket” to create addition and subtraction problems within 5, “Use five or fewer counters as your starting number and only add or take away one or two counters at first. Each time, have children use their counters to show how many are in the pocket after counters are added or taken away.” Lesson 2-12, students act out number stories within 5, “This morning some squirrels were playing in my yard. 4 squirrels were in a tree and 2 were burying acorns. How many squirrels were there in all? (Parts-and-total problem) Invite children to act out each story or to use counters, fingers, or drawing to model the story as you tell it.” Lesson 5-10, Focus: Using the Addition Symbol, introduces students to the addition symbol drawn on a craft stick. “Give each child 1 craft stick, about 10 counters, and a sheet of construction paper or a slate as a work surface. Show children how to put the craft stick vertically in the middle of their paper or slate. Tell one of the number stories you created and have children model it with counters.” Lesson 6-8, Focus: Using the Subtraction Symbol, students are introduced to the subtractions symbol drawn on a craft stick. “Give each child a craft stick, a sheet of construction paper or a slate as a work surface, and about 10 counters. Tell a ‘take-away’...number story and guide children in modeling the story with counters. Students engage in the full intent of K.OA.1, “Represent addition and subtraction with objects, fingers, mental images, drawings, sounds.”

• Lesson 6-4, Solid-Shapes Museum, Focus: Creating a Solid-Shapes Museum, students are introduced to solid figures, and pass them around to each other while describing what they see and feel. “Hold up a cylindrical object, such as a soup can. Say: The shape of this ____ is similar to a cylinder. Ask children to describe the cylinder in many ways. Lesson 6-5, Focus: Comparing Flat and Solid Shapes, students are introduced to the terms 2-dimensional and 3-dimensional shapes and describe the differences. Students then use solid shapes to “stamp” the faces on paper to create flat shapes. “ In a small group, have children stamp different faces of various solid shapes onto paper. Ask questions to encourage them to make predictions before stamping.” Lesson 7-4, Playing Solid-Shapes Match Up, students describe shapes as 2- or 3- dimensional, “Show children an object from the Solid-Shapes Museum, and invite them to name the object (sphere or cone, for example) and describe it in detail. Ask whether the object is 2- or 3- dimensional, and prompt children to explain their thinking.” Students engage in the full intent of K.G.3, “Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").”

Materials do not provide opportunities for all students to engage with the full intent or extensive work with K.NBT.1, “Compose and decompose numbers from 11 to 19 into ten ones and some further ones.” Examples include:

• K.NBT.1 is addressed in 5 lessons: Lesson 5-6 Focus (20-30 minutes), Lesson 5-8 Focus (20-30 minutes), Lesson 7-3 Focus (20-30 minutes), Lesson 8-6, Focus (20-30 minutes), and Lesson 8-13 Focus (20-30 minutes). Five opportunities over the course of a school year do not provide opportunities for extensive work with K.NBT.1.

• K.NBT.1 is addressed in “Number of the Day” Routine 1, students track the number of the day on a growing number line and represent the number with objects. This activity is done as a class and does not provide individual opportunities for students to engage in the full intent of a major learning standard of the grade.

#### Criterion 1.2: Coherence

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

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When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major work of each grade.

• There are 9 instructional sections, of which 7 sections address major work of the grade or supporting work connected to major work of the grade, approximately 78%.

• There are 117 lessons, of which 83 address major work of the grade or supporting work connected to the major work of the grade, approximately 71%.

• In total, there are 170 days of instruction (125 days of lessons and 45 flex days), of which 86 days address major work of the grade or supporting work connected to the major work of the grade, approximately 51%.

• Within the 45 Flex days, the percentage of major work or supporting work connected to major work could not be calculated because the materials suggested list of differentiated activities does not include explicit instructions. Therefore, it cannot be determined if all students would be working on major work of the grade.

A lesson analysis is most representative of the materials. As a result, approximately 71% of the materials focus on the major work of the grade.

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Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Digital materials’ Main Menu links to the “Spiral Tracker” which provides a view of how the standards spiral throughout the curriculum. The Lesson Landing Page contains a Standards section noting standards covered by the lesson. Teacher Edition contains “Correlation to the Standards for Mathematics” listing all grade-level standards and correlating lessons. Examples include:

• Lesson 1-2, Introduction to Pattern Blocks, Focus: Exploring Pattern Blocks, students are introduced to 6 pattern blocks. The teacher asks, “How many sides does the square have? Name or point to another shape with four sides. Do all the shapes with four sides look the same?” This connects supporting standard K.G.2, “Correctly name shapes regardless of their orientations or overall size,” to the major work of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”

• Lesson 2-7, Day 2-Introduction to Sorting, Focus: Solving the Open Response Problem, students sort a collection of items according to attributes into different categories and then count the items, “As children work, circulate and provide support and guidance for sharing objects and working together, as well as for sorting Ask questions such as: How would you describe this group of objects you created? What is the same about the objects in this group? What is different between this group and that group of objects? What is your rule for sorting your objects? How many objects are in each group? Which has the most? The fewest?” This connects the supporting work of K.MD.1, “Describe measurable attributes of objects, such as length and weight. Describe several measurable attributes of a single object,” to the major work of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”

• Lesson 3-1, Pattern-Block Graph, Focus: Graphing Pattern Blocks, students sort pattern blocks into different categories and then compare the categories by answering questions involving fewer and greater, “Place a handful of pattern blocks where children can see them. Have children share ways they could sort the blocks. If no one mentions it, suggest sorting the blocks by shape and invite children to help you do this. Ask: How can we find out which shape has the most? the least (fewest)?” This connects the supporting work of K.MD.3, “Classify objects into given categories; count the numbers of objects in a category,” 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.”

• Lesson 4-1, Attribute Blocks, Focus: Exploring Attribute Blocks, students classify and sort attribute blocks by their shape and size and count and compare the number of blocks in each group, “Sort the blocks by color as children watch. Then have the children explain why each group of blocks belongs together. Ask: How did I sort the blocks? What was my sorting rule? Why do these blocks belong together? How are they alike? How are they different? How many blocks are in each group? Are there more red blocks or blue blocks?” This connects the supporting work of K.MD.3, “Classify objects into given categories; count the numbers of objects in a category” and K.G.2 “Correctly name shapes regardless of their orientations or overall size,” 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.”

• Lesson 9-4, Backpack Math: Height, Width, and Area, Focus: Measuring and Comparing Backpacks, students compare the heights of two different backpacks using connecting cubes to measure, “Have children use connecting cubes to measure the heights and widths of their backpacks, record their findings (and their partner’s) on their My First Math Book pages, and compare the measurements. As children work, circulate and ask: How tall (or wide) is your backpack? Your partner's? Which backpack is taller (or wider).” This connects the supporting work of K.MD.1, “Describe measurable attributes of objects, such as length and weight. Describe several measurable attributes of a single object,” to the major work of K.CC.7, “Compare two numbers between 1 and 10 presented as written numerals.”

##### Indicator {{'1e' | indicatorName}}

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 Everyday Mathematics 4 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 Teacher Edition contains a Focus section in each Section Organizer identifying major and supporting clusters covered. There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. Examples include:

• Lesson 1-8, Class Age Graph, Focus: Making an Age Graph, students practice counting the number of students in different age groups and then discuss which line has more or less people, “Compare the number of children in different age groups. Ask: Which age has more (the most) children? How many more 5-year olds are there than 6-year olds?” This connects the major work of K.CC.A, “Know number names and the count sequence” to the major work of K.CC.C, “Compare numbers.”

• Lesson 2-3, Getting to Know Triangles, Focus: Getting to Know Triangles, students identify and describe triangles using their attributes, then find or draw pictures of triangles to create a collage, “Conclude by inviting children to create a class triangle collage or several group collages. Have them cut triangles from magazines and glue them to the posterboard triangle or draw them on directly.” This connects the supporting work of K.G.A, “Identify and describe shapes” to the supporting work of K.G.B, “Analyze, compare, create, and compose shapes.”

• Lesson 2-12, Number Stories, Practice: Revisiting Shape Collages, students sort shape cards onto the proper collage and describe their sorting attributes, “With the class, sort the triangle, rectangle, and circle Shape Cards onto the proper collage and review what each shape family has in common. Look at the remaining Shape Cards and prompt children to identify ways they might group some of them (curved shapes, for example).” This connects the supporting work of K.G.A, “Identify and describe shapes” to the supporting work of K.G.B, “Analyze, compare, create, and compose shapes.”

• Lesson 4-12, Top-It With Number Cards, Focus: Playing Top-It with Number Cards, students pick two number cards from a deck to compare, “Pick two cards from the deck. Have children say the numbers and tell you which number is greater (more, higher) and which number is less (fewer, lower). Ask: How do you know which number is greater?” This connecte the major work of K.CC.A, “Know number names and the count sequence,” to the major work of K.CC.C, “Compare numbers.”

• Lesson 5-8, Teens on Double Ten Frames, Focus: Playing Teens on Double Ten Frames, students take turns spinning on a 10-20 Spinner and placing the number of counters on their double ten frame. Students compare their double ten frames and the student with the largest number wins the round, “In pairs, have children take turns spinning a number and placing that number of counters on their double ten frame using the ‘10 and some more’ approach (filling one ten frame first). After each child has a turn, they compare their double ten frames. The child with the largest number wins the round. (Vary the game by having the smallest number win the round).” This connects the major work of K.CC.C, “Compare numbers” to the major work of K.NBT.A, “Work with numbers 11-19 to gain foundations for place value.”

• Lesson 6-9, Disappearing Train, Focus: Playing Disappearing Train, students roll a subtraction die marked with -1, -2, and -3. Students roll the die and use a snap cube train to take away the matching number of cubes, “For example, if you have 9 train cars and roll 2, say ‘I had 9 train cars. I rolled ‘minus 2,’ so I take 2 cubes from my train. How many cars do I have now? How do you know?’” This connects the major work of K.CC.B, “Count to tell the number of objects” 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.”

• Lesson 8-2, Marshmallow and Toothpick Shapes, Focus: Modeling Shapes, students create 2-D and 3-D shapes with toothpicks and marshmallows, “Promote exploration, description, and discovery with prompts such as: How did you make the window? What shapes did you use? How do you make a pyramid? How many marshmallows and toothpicks do you need? Can you make a shape with sides that are different lengths? How could you attach those triangles to each other? What shape will you make if you attach those two cubes?” This connects 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.”

##### Indicator {{'1f' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten 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.

Materials relate grade-level concepts to prior knowledge from earlier grades. Each Section Organizer contains a Coherence section with “Links to the Past” containing information about how focus standards developed in prior units and grades. Examples include:

• Teacher’s Lesson Guide, Section 1 Organizer, Coherence, “Links to the Past” for K.CC.1, “In PreK, children learned and practiced the count sequence through 10 (and beyond as ready) through playful counting games, songs, and movement activities.”

• Teacher’s Lesson Guide, Section 4 Organizer, Coherence, “Links to the Past” for K.MD.1, “Children described lengths of objects in Kindergarten lessons 1-1 and 3-5. In Pre-K, children used the terms big and small to describe measurable attributes and began to learn about different size dimensions, such as length and weight.”

• Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Past” for K.G.3, “In PreK, children explored both 2-dimensional and 3-dimensional shapes in a variety of tactile, kinesthetic, and visual ways.”

Materials relate grade-level concepts to future work. Each Section Organizer contains a Coherence section with “Links to the Future” containing information about how focus standards lay the foundation for future lessons. Examples include:

• Teacher’s Lesson Guide, Section 2 Organizer, Coherence, “Links to the Future” for K.OA.2, “Throughout the year, children will solve addition and subtraction problems within 10 in a variety of contexts, including number stories, domino, and dice games, as well as other activities. In Grade 1, children will model and solve problems involving addition or subtraction of two numbers within 20.”

• Teacher’s Lesson Guide, Section 4 Organizer, Coherence, “Links to the Future” for K.MD.1, “In Kindergarten Sections 4 through 9, children will practice observing and describing an object's length, weight, and capacity, as well as describing several measurable attributes of a single object. In Grade 1, children will quantify length measurements as the number of same-size units that span a distance.”

• Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Future” for K.G.3, “In Section 6, children learn the difference between 2- and 3-dimensional shapes as they assemble and analyze objects for the Solid-Shapes Museum, and stamp different 2-dimensional faces of 3-dimensional shapes onto paper. They will continue to explore and compare 2-D and 3-D shapes, and the relationships between them, as they play Solid-Shapes Match Up in Section 7 and as they create both 2-D and 3-D shapes from marshmallows and toothpicks in Section 8.”

Materials contain content from future grades in some lessons that is not clearly identified. Examples include:

• Lesson 1-13, Shape Patterns, Focus: Patterning with Shapes, students use shapes to build patterns, “Build from children’s responses to explain that a pattern repeats or grows. Explain that they just saw two different kinds of patterns: a repeating pattern and a growing pattern. After the last pattern, have children turn to a partner and complete the sentence frame: I know this is a pattern because_______.”  This lesson is labeled K.G.1, “Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to” and K.G.2, “Correctly name shapes regardless of their orientations or overall size." Identifying patterns is a grade standard, 4.OA.5, “Generate a number or shape patterns that follow a given rule."

• Lesson 4-3, Favorite Color Graphs, Focus: Graphing Favorite Colors, “Model how to label the axes on the graph with the color names and the number of children who chose the color as their favorite. Explain that this is sometimes called a bar graph, and ask why it might have that name.” Students can choose from 6 colors, making 6 categories on the graph. This lesson is labeled K.MD.3, “Classify objects into given categories; count the number of objects in each category and sort the categories by count.” Using a bar graph with up to three categories is a Grade 1 standard (1.MD.4, “Organize, represent, and interpret data with up to three categories…”)

• Lesson 5-6, Teen Patterns, Practice: Solving Number Stories, students solve problems in their journals, “I saw some children swinging. One more child joined them. Then there were 9 children swinging. How many children were swinging at the beginning?” This lesson is labeled K.CC.5, “Count to answer ‘how many’ questions.” Starting with an unknown in a problem-solving situation is a Grade 1 standard, 1.OA.1, “Use addition and subtraction within 20 to solve word problems with unknowns in all positions."

##### Indicator {{'1g' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten can be completed within a regular school year with little to no modification to foster coherence between grades.

Recommended pacing information is found on page xxii of the Teacher’s Lesson Guide and online in the Instructional Pacing Recommendations. The materials include pacing for 170 days of instruction:

• There are 9 instructional sections with 117 lessons. Beginning in Section 2, Open Response/ Re-engagement lessons require 2 days of instruction adding 8 additional lesson days.

• There are 45 Flex Days that can be used for lesson extension, extra game time, differentiation, or connection activities; however, explicit teacher instructions are not provided.

• There are 3 embedded face-to-face assessments, Beginning-of-Year Assessment, Mid-Year Assessment, and End-of-Year Assessment, spanning multiple days.

The materials note that lessons are 45-60 minutes and consist of 3 components: Daily Routine: 10-15 minutes; Core Activity: Focus; 20-30 minutes; and Core Activity: Practice: 10-15 minutes.

### Rigor & the Mathematical Practices

The materials reviewed for Everyday Mathematics 4 Kindergarten 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
Meets Expectations

#### 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 Everyday Mathematics 4 Kindergarten 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' | indicatorName}}

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

All units begin with a Unit Organizer, Planning for Rich Math Instruction. This component indicates where conceptual understanding is emphasized within each lesson of the Unit. The Focus portion of each lesson introduces new content, designed to help teachers build their students’ conceptual understanding through exploration, engagement, and discussion. The materials include problems that develop conceptual understanding throughout the grade level, especially where called for in the standards. Examples include:

• Lesson 1-10, Quick Looks, Focus: Introducing Quick Looks, “Present the dot images in order from Cards 1 to 10. Flash each image and ask: ‘What did you see/How did you see it?’ To move children beyond counting, highlight strategies that involve decomposing the number by asking questions such as: ‘Did everyone understand Tamika’s strategy of seeing groups? Can someone say it for us again? Can you try her way on the next card?’” This activity supports the conceptual understanding of K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way” and K.CC.4, “Understand the relationship between numbers and quantities.”

• Lesson 2-5, Pocket Problems, Focus: Solving Pocket Problems, each student has ten counters to help them solve pocket problems. The teacher demonstrates by putting three counters in the pocket. Then the teacher shows one more counter and adds it to the pocket. Students use their counters to show how many are in the pocket now. Then the teacher takes all the objects out of the pocket and leads the class in counting the total. After practicing as a class adding to or taking away from the pocket, students work in pairs giving each other pocket problems. “Divide children into pairs and give each pair counters and an envelope to use as a paper pocket. Have one partner begin by posing a pocket problem, and the other partner use counters to represent and solve the problem. Then have partners reverse roles. Encourage them to show, rather than tell, what they are doing, just as you did when you modeled the problems.” This activity supports conceptual understanding of K.OA.1, “Represent addition and subtraction with objects, fingers, mental images, drawings, or sounds.”

• Lesson 4-8, Building Numbers, Focus: Decomposing Numbers, students compose and decompose numbers using connecting cubes and share their results. To assist students in making the connection between turnaround pairs and doubles the teacher asks, “What did you notice? Did you see any patterns?” This activity supports conceptual understanding of K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way.”

• Lesson 5-6, Teen Partners, Focus: Representing Teen Numbers, students use their fingers to compose and decompose numbers, “Hold up the 10 card from the Class Number Card set and have all children hold up 10 fingers. Ask: What number comes next? Hold up the 11 card and ask if anyone can think of a way to show 11 fingers. If no one suggests it, call on two children to work together. Choose one child to hold up all 10 fingers. Ask the other child how many fingers he or she must hold up so that together they show 11 fingers. Repeat with the number 15, having one child show 10 fingers and another child show 5 fingers.” This activity supports conceptual understanding of K.NBT.1, “Compose and decompose numbers from 11 to 19 into ten ones and some further ones.”

• Lesson 7-9, Bead Combinations, Focus: Exploring Number Combinations, students solve addition and subtraction problems, “Model how to make a counting loop by placing beads on a chenille stem and twisting (or tying) the ends together to close and fasten the loop. Have each child take one chenille stem, put 7 to 9 same-color beads on it, and make a loop. (Children will make bead combinations that add to 10 in Lesson 8-9, Practice.) Direct them to group their beads and write number sentences for four different groupings on the ‘My First Math Book’ page. Challenge children to divide their beads into three groups for the last box on the page.” This activity supports students’ conceptual understanding of K.OA.1, “Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.”

Home Links and Games provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include:

• Lesson 2-4, Number Board, Focus: Building a Number Board, students use counters and a blank number board to cover the spaces on their board with the appropriate number of objects. “Direct children to cover the spaces on their board with the appropriate number of objects. Circulate and confer with children about their counting and the ‘one more’ pattern.” This supports conceptual understanding of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”

• Lesson 3-2, Ten-Bean Spill, Home Link, students toss 10 pennies and sort them into groups of “heads” and “tails” and put them on a ten frame. Then they count the number of heads and tails and record the numbers. “Gently toss 10 pennies. Sort the pennies into groups of ‘heads’ and ‘tails’ and put them on the ten frame. Count the number of heads and the number of tails. You may want to record the numbers you find on the back of this page. Repeat at least three more times.” This activity supports the conceptual understanding of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”

• Lesson 5-10, The Addition Symbol (+), Home Link, students take turns with a family member telling and solving number stories that use addition. “Cut out the addition symbol (+). Take turns telling and solving number stories that use addition. For example: Two children were on the playground, and three more come to play. How many children were there altogether? Use pennies or other small objects and the addition symbol (+) to act out, or model, the stories. Draw or write one of your number stories below.” This activity supports the conceptual understanding of K.OA.1, “Represent addition with objects, fingers, acting out, or equations.”

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Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

All units begin with a Unit Organizer, Planning for Rich Math Instruction. This component indicates where procedural skill and fluency exercises are identified within each lesson of the Unit. The Mental Math Fluency exercises found at the beginning of each lesson develop fluency with basic facts and other skills that need to be automatic while engaging learners. The Practice portion of the lesson provides ongoing practice of skills from past lessons and units through activities and games. Examples include:

• Lesson 6-11, Hiding Bears, Practice: Counting to the Number of the Day, students count by 1s and 10s. “First, have children choral count by 1s to the Number of the Day. To practice counting on from different numbers, stop children during the sequence; then skip to a new number and have them restart. Next have children count by 10s and then 1s to the Number of the Day (10, 20, 30, 40, 50, 60, 61, 62…). Encourage children to use the number line to help them count if needed.” This activity provides an opportunity for students to develop fluency in K.CC.1, “Count to 100 by ones and by tens,” and K.CC.2, “Count forward beginning from a given number within the known sequence (instead of having to begin at 1).”

• Lesson 7-12, Dice Addition, Focus: Playing Dice Addition, students play with a partner, and each roll a set of the Addition Dice. Once they roll their dice they state the resulting addition equations such as, “$$2+3=5$$.” “The player with the highest total colors one space on a blank ten frame. If players have the same totals, they both color a space on their ten frames.” “The game ends when one player fills a ten frame.” This activity provides an opportunity for students to develop fluency in K.OA.5, “Fluently add and subtract within 5.”

• Lesson 8-11, Addition Top-It, Focus: Playing Addition Top-It, students play with a partner and each takes two cards from the top of the deck and places them face up. “Players add the two numbers and take turns stating their total. (4 plus 2 equals 6!)” The player with the higher total takes all 4 cards and the player with the most cards at the end wins. This activity provides an opportunity for students to develop fluency in K.OA.5, ”Fluently add and subtract within 5.”

• Routine 5: Survey, each week the teacher poses a survey question and students record their responses. Teachers choose how students record their answers. They can use a magnet and place it in the appropriate column, designate colored cubes for responses and students choose the cube that corresponds to their response, or students write their initials in the column on chart paper corresponding to their response. Once all responses are collected, “Appoint a Survey Helper who will make sure all children respond to the survey and can take the lead on counting and recording the results.” This weekly activity provides an opportunity for students to develop fluency in K.CC.1, “Count to 100 by ones and by tens,” and K.CC.3, “Write numbers from 0 to 20.”

Math Boxes, Home Links, Games, and Daily Routines provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade. Examples include:

• Lesson 5-11, Growing Train, Home Link, students add snacks, “Put a small number of snacks, such as cereal or raisins, on a table and count them. Cut out the addition symbol (+) and put it next to the snacks. Put another group of snacks next to the addition symbol and count them. Remove the addition symbol and put all the snacks together in one pile. Count the snacks and say how many there are all together.” This activity is repeated several times and provides an opportunity for students to independently demonstrate the procedural skill of K.CC.5, “Count to answer ‘how many’ questions about as many as 20.”

• In Lesson 7-7, Representing Survey Data, Practice: Playing Roll and Record with Dot Dice, students roll a set of dice, determine the sum and write number sentences on slates, “$$3+2=5$$.” This activity provides an opportunity for students to develop fluency in K.OA.5, “Fluently add and subtract within 5.”

• Lesson 8-12, Function Machines, Practice: Playing Roll and Record with Dot Dice, students roll two dice, determine their total, and then record the total on the Roll and Record Grid. “As they play, help children develop addition fluency by encouraging them to solve as many combinations as they can from memory or using another efficient strategy.” This activity provides an opportunity for students to develop fluency in K.OA.5, “Fluently add and subtract within 5.”

• Lesson 9-3, “What’s My Rule?” with Numbers, Practice: Counting the Class Collection, students count the items in the class collection using groups or counting-on strategies and record them in their My First Math Book. “What do you notice about the number of ___ in our collection since we started it? Where was the largest jump in our total? Can you see it on the table? On the thermometer display? What else do you notice about the data and the displays? This activity provides an opportunity for students to independently demonstrate the procedural skill of K.CC.3, “Write numbers from 0 to 20,” K.CC.5, “Count to answer how many questions,” and K.CC.7, “Compare 2 numbers between 1 and 10 presented as written numerals.”

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Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

Materials include multiple routine and non-routine applications of mathematics throughout the grade level. Focus activities introduce new content, provide routine exercises, review recent learning, and provide challenging problem-solving tasks that help build conceptual understanding, procedural skill and fluency, and application of mathematics. Open Response lessons provide challenging problems that involve more than one strategy or solution. Home-Links relate to the Focus activity and provide informal mathematics activities for students to do at home. Examples of routine and non-routine applications of the mathematics include:

• Lesson 2-12, Number Stories, Focus: Telling and Acting out Number Stories, students solve change-to-more, change-to-less, and parts-and-total problems using counters, their fingers, or use drawings to model the story as the teacher tells it. “Davon was the snack helper today. He carried 3 apples to the table. Then he got 2 more apples. How many apples does Davon have now?” Students apply their understanding of K.OA.2, “Solve addition and subtraction word problems, and add and subtract within 10.”

• Lesson 3-6, Obstacle Course Positions, Home-Link: Simon Says, students play “Simon Says” using position words. “Play Simon Says with your family. Use positional words such as above, below, next to, in front of, and behind. Take turns being “Simon” (the leader). Use clues such as these: Simon says, put your finger below your chin. Simon says, put your foot next to your knee. Simon says, shake your hands behind your back. Wiggle your fingers above your head. (Don’t follow this command. Simon didn’t say!)” Students apply their understanding of K.G.1, “Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.”

• Lesson 5-3, Ten Bears on a Bus, Focus: Playing Ten Bears on a Bus, students play the game Ten Bears on a Bus to generate number combinations that add to 10. “4 yellow bears are on the bus, how many red bears must get on the bus to fill all 10 seats?” Students apply their understanding of K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way.”

• Lesson 5-7, Seats at the Party, Focus: Solving the Open Response Problem, students solve a comparison number story. “I was having a party. I put 4 chairs at the table. The doorbell rang, and I saw 7 friends at the door. Do I have enough chairs for all my friends? How do you know?” This activity provides the opportunity for students to apply their understanding of K.OA.2, “Solve addition and subtraction word problems, and add and subtract within 10.”

Materials provide opportunities for students to independently demonstrate multiple routine and non-routine applications of the mathematics throughout the grade level. Independent Problem Solving provides “additional opportunities for children to apply the content they have learned during the section to solve non-routine problems independently. These problems often feature: applying math in the real world, multiple representations, drawing information or data from pictures, tables, or graphs, and opportunities for children to choose tools to support their problem-solving.” Examples of independent demonstration of routine and non-routine applications of the mathematics include:

• Independent Problem Solving 3a, “to be used after Lesson 3-4”, Problem 1, students compare numbers. “Jonah and Carla went on a walk to collect rocks. They dumped their rocks into 2 piles.” Students are shown a picture of 2 piles of rocks. 1 pile has 6 rocks, and 1 pile has 7 rocks. “Who found more rocks? Use words or pictures to explain how you know.” This activity provides the opportunity for students to independently demonstrate 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.”

• Independent Problem Solving 5b, “to be used after 5-11”, Problem 1, students write and represent addition number stories from a picture with birds, flowers, and butterflies. “Draw and write an “adding” number story that goes with the picture above.” Problem 2, “Solve your number story. Draw and use words to explain how you got your answer.” This activity provides the opportunity for students to independently demonstrate understanding of K.OA.2, “Solve addition and subtraction word problems, and add and subtract within 10.”

• Independent Problem Solving 6a, “to be used after Lesson 6-8”, Problem 1, students write a number story to represent subtraction using a given image. “Draw and write a “take-away” (subtracting) number story that goes with the picture above.” Students independently demonstrate their understanding of 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.”

• Independent Problem Solving 9b, “to be used after Lesson 9-9”, Problem 2, students create their own number story using a number sentence. “Draw and write a number story about animals or toys that could go with this number sentence: 4+ ___ =5.” This activity provides the opportunity for students to independently demonstrate K.OA.2, “Solve addition and subtraction word problems, and add and subtract within 10,” K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way” and K.OA.4, “For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.”

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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 Everyday Mathematics 4 Kindergarten 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 the grade. Examples where materials attend to conceptual understanding, procedural skill and fluency, or application include:

• Lesson 4-2, Shapes By Feel, Practice: Playing Roll and Record, students play a dice game using a Roll and Record Grid. Students roll a die, and fill in a box in a column with the matching number, “Have children fill a Roll and Record grid independently (at least until one column is full) or play Dice Race with a small group or partner. In Dice Race, children choose a target number and see who fills that column on their grid first.” This activity develops the procedural skill of K.CC.5, “Count to answer ‘how many’ questions about as many as 20 things.”

• Lesson 4-13, Number-Grid Exploration, Practice: Comparing Capacities, students are shown various containers of different sizes filled with beans or other pourable materials and a reference container to compare quantities, “Have a child choose one. Ask: Do you think this container holds more or less than the mug? How can we find out? As needed, model pouring the beans from the mug into the other container to compare capacities. Have children work in a small group to compare various containers to the reference container.” This activity provides the opportunity to apply the understanding of K.MD.2, “Directly compare 2 objects with a measurable attribute in common to see which object has more or less of the attribute.”

• Lesson 8-5, Dice Subtraction, Focus: Playing Dice Subtraction, each student is given a blank ten frame and a pair of Dice Subtraction dice. Students take turns rolling the dice and subtracting the smaller number from the larger number, then state the subtraction equation and the difference to their partner. The student with the smallest difference colors one space on their ten frame. The winner is the student who fills their ten frame first, “As you model several rounds of the game, ask children to share strategies for subtracting.” This activity develops a conceptual understanding of K.OA.1, “Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.”

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single unit of study throughout the materials. Examples include:

• Lesson 4-6, Moving With Teens, Focus: Counting and Moving with Teens, students use a number line to extend the counting sequence beyond 10 to include teen numbers, “What is the same about these numbers? How are they different from the numbers 1 through 9? Why do you think they are called teen numbers?” Students then read numbers from 10-19 Class Number cards. Students develop a conceptual understanding of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality,” and fluency of K.CC.A, “Know number names and the count sequence.”

• Lesson 6-10, Attribute Spinner, Focus: Playing Attribute Spinner, students play a game with three attribute spinners: size, color, and shape, “Players take turns spinning and choosing the block that has the attributes shown on all three spinners (the large, blue triangle, for example). To end their turn, players describe the block to confirm that it matches all the attributes on the spinners.” Students develop a conceptual understanding of K.G.2, “Correctly name shapes regardless of their orientations or overall size,” and application of K.MD.1, “Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.”

• Lesson 8-13, Name-Collection Posters, Focus: Making Name-Collection Posters, the teacher writes the number 10 at the top of the chart paper and draws a filled in ten frame, and writes 5 = 5 on the paper. Students are asked to share other ways to show or name 10 and the teacher adds their responses, “Ask the class to think of other ways they can name, or show 10. As they share, record or have children record their ideas on the chart paper.” Students develop conceptual understanding of K.OA.A, “Understand addition as putting together and adding to, and subtraction as taking apart and taking from,” while applying an understanding of K.NBT.1, “Compose and decompose numbers from 11 to 19.”

#### Criterion 2.2: Math Practices

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations  for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

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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 Everyday Mathematics 4 Kindergarten 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.

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice).

Materials provide 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 support of the teacher and independently throughout the units. Examples include:

• Lesson 3-12, Monster Squeeze, Focus: Playing Monster Squeeze, students use a variety of strategies to identify a number between two other numbers. Using the 0-10 section of the Growing Number Line and a monster to the left of 0 and on top of 11, the teacher facilitates students guessing his/her number. “If they guess too high, reply: Your number is too high. My number is less than that number. Move the right-hand monster along the number line until it covers the number guessed.” “If they guess too low, say: Your number is too low. My number is greater than that number. Move the left-hand monster to cover the number that was guessed. As children play, help them make sense of the game and strategic guessing by discussing questions such as: Why did you guess that number? What would be a good next guess? Why? Could the ‘mystery’ number be___? Why or why not?”

• Lesson 4-5, Ten-Frame Quick looks, Focus: Taking Ten-Frame Quick Looks, students practice mentally composing and decomposing numbers on ten frames to develop fact strategies by understanding the information presented. “Flash each image for about three seconds before removing (or covering) it and ask children to remember what they saw. To elicit flexible ways of thinking about each image, ask: What did you see? How did you see it?

• Lesson 9-12, Subtraction Top-It, Focus: Preparing for a Math Celebration, students make sense of answers when determining how many items will be needed for the class party using a guest list. “Figure out how many chairs, tables, napkins, plates, utensils, and food items are needed for the party using the list of expected guests.”

• Independent Problem Solving 7b, “to be used after Lesson 7-10”, Problem 1, students use a variety of strategies to solve a word problem. “Marco had 7 balloons on a windy day. Two of Marco’s balloons popped when the wind blew them into a branch. a) How many are left? ___ balloons b) Write a number sentence to model what happened to the balloons.”

Materials provide 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 support of the teacher and independently throughout the units. Examples include:

• Lesson 1-7, Class Birthdays, Practice: Getting to Know Numbers (3), students attend to the meaning of quantities when collecting items of 3 for their number-collection bags. “Revisit Lesson 1-5, pages 56 - 59. Focus on 3 as the featured number. Add a 3-cube tower and the label 3 to your growing connecting-cube display. Ask: What will tomorrow’s tower look like? How do you know? Have pairs of children create and save number-collection bags with 3 items. (Children who need support creating 3 collections may use the number strip on Math Masters, page TA3.) Use as many of the other suggested “featured number” activities from the original lesson as time permits. Consider reading, telling, or acting out a story that features 3 characters, such as “The Three Little Pigs,” “Goldilocks and The Three Bears,” or “The Three Billy Goats Gruff.” Ask children why they think so many stories feature the number 3!”

• Lesson 2-2, Top-It With Dot Cards, Focus: Playing Top-It with Dot Cards, students demonstrate understanding of mathematical representations as they turn over dot cards and make comparisons to determine who has more dots. The player with more dots takes both cards, “If the cards have an equal number of dots (the same number), both players turn over another card and the player with the greatest number of dots takes all four cards.” As the children play the game, the teacher asks, “How do you know how many dots each card has? How can you figure out which card has more, or a greater number of, dots? How can you be sure? Sample answers: I count the dots. I know that 5 comes after 3, so 5 is more than 3. I see that this card is more full than that card.”

• Lesson 8-6, Craft-Stick Bundles, Focus: Bundling Craft Sticks, students discuss number representations as they work in pairs to estimate the number of sticks in a bag, then bundle the sticks into 10 sticks and some more sticks, “Have children bundle the sticks into groups of 10 and re-count the sticks by 10s and 1s. Model how to record their findings by showing the number as 10 and some 1s, on a double ten frame, and as an equation.”

• Independent Problem Solving 3b, “to be used after Lesson 3-10”, Problem 1, students represent the number 4 in four different ways. “Show four different 4 cards. Use dots for the blank cards and ten frames for the others.” Students are given a picture with four playing cards, 2 blank and 2 with ten frames on them.

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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 Everyday Mathematics 4 Kindergarten 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.

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice).

Materials provide support for the intentional development of MP3 by providing opportunities for students to construct viable arguments in connection to grade-level content. Examples include:

• Lesson 4-2, Shapes By Feel, Focus: Identifying Attributes of Shapes, students construct viable arguments as they choose specific shapes based on attributes. “Introduce the Feely Box and note that there are different shapes inside the box that children will touch but not see. Explain that you will give clues to help them choose shapes from the box, and they will then explain why they chose the shape. Select from the activities below, choosing prompts that are best suited to children’s skill levels.” Two of the possible activities state, “Have a child pick out two shapes that feel the same. Have the child show the shapes to the class and name them. Ask: How do you know that the shapes were the same? Name a shape and have a child find it by touch. Ask: How do you know you found a _____?”

• Lesson 5-2, Roll and Record with Dot Dice, Focus: Playing Roll & Record with Dot Dice, students construct viable arguments during a game of Roll & Record. After the game, a class chart is made recording each child’s winning number. Students analyze the results of the game and respond to questions, “Why did the middle numbers win most often? How many ways are there to get 2? Are there more ways to get 8? Why?”

• Independent Problem Solving 2a, “to be used after Lesson 2-3”, Problem 2, students construct viable arguments when shown different shapes and instructed to put an “X” on the shapes that are not triangles. “Draw one of the shapes you put an X on. Explain why it is not a triangle.”

Materials provide support for the intentional development of MP3 by providing opportunities for students to critique the reasoning of others in connection to grade-level content. Examples include:

• Lesson 8-7, Open Response Birds on Wires, Focus: Reengaging in the Problem, students critique the reasoning of others when they answer an open response problem about Birds on Wires. “Review the Birds on Wires open response problem. Tell children that today they will look at different ways some of them solved the problem. Begin by showing some correct and incorrect solutions you found in their work. Prompt children to describe and compare the two solutions by asking: Can both of these solutions be correct? Why or why not? How can we figure out the number of birds on the second wire if we have 4 birds on the first wire? Does the number of birds drawn on each wire match the numbers below it?”

• Lesson 9-1, Make My Design, Focus: Playing Make My Design, students critique the reasoning of others as they play a partner game where one student creates a design with pattern blocks, then uses that shape and positional language to describe the design to their partner. “Encourage the other partner to try to recreate the design from the instructions, asking for further description and clarification as needed.”

• Independent Problem Solving 1b, “to be used after Lesson 1-11”, Problem 1, students critique the reasoning of others when comparing two groups of orange slices. “Akesha and Micah are supposed to get the same amount of snacks. Akesha says this is fair. Micah says he doesn’t have as much. Who do you agree with and why?”

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Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Everyday Mathematics 4 Kindergarten 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.

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice).

Materials provide intentional development of MP4 to meet its full intent in connection to grade-level content. Students model with mathematics to solve real-world problems, identify important quantities to make sense of relationships, and represent them mathematically as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson  7-10, Class Number-Story Book, Focus: Creating Number Stories, students model a situation with pictures and mathematical symbols as they solve number stories. “Review how number stories can be recorded with pictures, numbers, and symbols. Tell a number story, such as: There were 4 squirrels on the ground. 1 squirrel ran up a tree. How many squirrels were still on the ground? Draw a picture to illustrate the story and invite the class to help you write a number sentence to model it, such as 4-1=3 or 4=1+3.”

• Independent Problem Solving 5a, “to be used after Lesson 5-4”, Problem 2, students model a situation with an appropriate representation as they put two shapes together. “Draw an object you see that is made from 2 or more shapes put together. Label the shapes that make up the object.”

• Independent Problem Solving 9b, “to be used after Lesson 9-9”, Problem 1, students use the math they know to solve problems and everyday situations when they use a number sentence to model a number story. “Draw and write a number story about snacks or people that could go with this number sentence: 5-2= ___.”

Materials provide intentional development of MP5 to meet its full intent in connection to grade-level content. Students use appropriate tools strategically as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 8-4, Interrupted Counting, Practice: Playing Hiding Bears, students choose appropriate strategies as they find the number of hiding bears. “Encourage them to use strategies such as counting on, modeling with fingers, or using known combinations of 10 to find the number of hiding bears.”

• Independent Problem Solving 2b, “to be used after Lesson 2-13”, students choose appropriate tools and strategies as they solve word problems involving addition and subtraction. “Problem 1, Kayla sorted the buttons in a box by shape. There were 2 square buttons, 3 round buttons, and 0 triangle buttons. Draw a picture of Kayla’s sorted buttons. How many buttons were there altogether? Problem 2, Kayla’s dad trades a round button for a square one. How many square and round buttons are there now? You may use counters, fingers, a drawing, or another tool to figure it out. Show or explain what you did.”

• Independent Problem Solving 4a, “to be used after Lesson 4-8”, Problem 1, students recognize both the insight to be gained from different tools/strategies and their limitations. “You may use cubes, counters, your fingers, or another tool to help you solve the problem below. 1a) Marisol and Nico are having a picnic. Draw one way Marisol and Nico can split up all 6 crackers. They don’t need the same amount. 1b) Draw a different way they can split up the crackers.”

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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 Everyday Mathematics 4 Kindergarten partially 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.

MP6 is explicitly identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Students attend to precision in connection to grade-level content as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 1-6, Count and Sit, Focus: Playing Count and Sit, students attend to precision while playing an oral counting game. “Conclude by making an intentional mistake on your turn and having children help you correct your mistake. Ask: Why is it important to count correctly on your turn? What helps you count correctly?”

• Lesson 2-11, Getting to Know Rectangles, Focus: Getting to Know Rectangles, students attend to precision by accurately describing shape attributes. “Show a square Shape Card. Have children say the word square and share what they notice about the shape with a partner. Ask: How many sides does the square have? Are the sides straight or curved? Are they the same length? How many vertices, or corners, does it have? What do they look like?

• Lesson 3-10, Number-Card Activities, Focus: Playing Number-Card Games, students attend to precision by matching fingers to objects. “Matching Sets to Numerals: One partner chooses a number card and the other shows that many fingers or creates a set of that many connecting cubes or other objects. The child showing the card counts the fingers or objects to make sure the set matches the number on the card. Partners switch roles until all the cards have been used.”

Materials attend to the specialized language of mathematics in connection to grade-level content. Examples include:

• Lesson 2-3, Getting to Know Triangles, Focus: Getting To Know Triangles, students use the specialized language of math when they are introduced to shapes and their names. “Display the large poster board triangle you created and ask children to repeat the name of the shape: triangle. Place the triangle where children can look at it and have them draw your triangle in the air with large arm motions, saying side, vertex, side, vertex, side, vertex as they draw. Ask children to describe the triangle. If needed, prompt them with these questions: How many sides does this triangle have? How many vertices (corners) does it have? Are the sides straight or curved? Emphasize that triangles have three straight sides and three vertices (corners).”

• Lesson 9-9, Measuring Time in Seconds, Focus: Measuring in Seconds, students use the specialized language of mathematics when telling time. “Ask children if they know the name of a unit that the stopwatch can measure. Introduce the word second by explaining that it is the unit of time used by people around the world; explain that a second means the same length of time no matter where you live or what tool you use to measure it, so using seconds allows us to measure time in a way that everyone understands. (Remind them of Lesson 8-3 and mention that a second is about as long as saying ‘one Mississippi.”) With the class, brainstorm activities that take about one second, such as standing up or snapping your fingers once.”

• Independent Problem Solving 4b, “to be used after Lesson 4-13”, Problem 1, students draw objects to represent objects with measurable attributes. “a) Look around the room. Draw and label something that is very long. b) Draw or write something that is longer than that object. c) Draw or write something that is shorter than that object.”

While the materials do attend to precision and the specialized language of mathematics, there are several instances of mathematical language that are not precise or grade level appropriate. Examples include:

• Lesson 8-12, Function Machines, Focus: Using Function Machine, “Show and explain the function machine you created. Highlight the in, out, and rule features of the machine. Explain that when a number goes in the machine, something happens to it, and a new number comes out of the machine. The rule tells what will happen to each in number in the machine.”

• Lesson 9-2, Subtraction Top-It, Practice: Reviewing Function Machines, “Use your function machine box to review how to apply a given rule, such as ‘subtract 2’ or ‘-2’.” Students work in “My First Math Book” p.25. The materials state, “Each child thinks of a rule and writes it in the function machine in his or her own book. Each child also fills in the in numbers. Children then trade books with a partner. Partner must write out the numbers.”

• Lesson 9-3, “What’s My Rule?” with Numbers, Focus: Playing “What’s My Rule?”, “Show children the function machine box from lesson 8-12 and display an In and Out Chart (Math Masters, page TA64). Point out that the rule is missing from the front of the box. Explain that children will use in and out numbers to figure out the rule.”

##### Indicator {{'2i' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten 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.

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice).

Materials provide intentional development of MP7 to meet its full intent in connection to grade-level content. Students look for and make use of structure throughout the sections as they describe, and make use of patterns within problem-solving as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 4-8, Building Numbers, Focus: Decomposing Numbers, students look for patterns or structures as they compose and decompose numbers using connecting cubes. “Direct them to build the number in as many ways as they can using the two colors and to record each combination on their sheets. Afterward ask: What do you notice? Do you see any patterns?

• Lesson 7-13, Mystery Block, Focus: Playing Mystery Block, students look for and explain the structure within mathematical representation using shape attributes to correctly guess the mystery block. “After children ask a question, have them remove blocks according to the response. For example, if the answer to ‘Is it thick?’ is yes, then the child who asked the question removes all the blocks except the thick blocks. After children remove blocks, follow up with questions such as: Why did you take away all the thin blocks? Why didn’t you need to ask whether it was thin? What rule were you following? Have children think strategically about the questions that will be most helpful for figuring out the mystery block given the blocks that remain.”

• Independent Problem Solving 9a, “to be used after Lesson 9-6”, Problem 1, students make use of structure by solving a problem in 3 different ways. “Bria loves sports. She plays softball, basketball, and soccer. She has 8 trophies that she wants to arrange on 2 shelves. Show 3 different ways she could arrange them. Write a number sentence that fits each way.”

Materials provide intentional development of MP8 to meet its full intent in connection to grade-level content. Students look for and express regularity in repeated reasoning throughout the sections to make generalizations and build a deeper understanding of grade level math concepts as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 2-7, Introduction to Sorting, Focus: Solving the Open Response, students sort and classify objects in different ways. “Explain that pairs of children will sort a collection of objects in a way that makes sense to them and that others can understand. Remind them that all objects in a group must share one or more attributes, or be the same in one or more ways. Give each pair a sorting mat and a collection of objects (or send groups of children to their first sorting station). As children work, circulate and provide support and guidance for sharing objects and working together, as well as for sorting. What is your rule for sorting your objects?”

• Lesson 4-1, Attribute Blocks, Assessment Check-In, students evaluate the reasonableness of their answers and thinking to sort and classify objects based on their attributes. “Use this lesson to assess whether children can identify and describe multiple attributes of objects and sort and classify objects by those attributes. Expect most children to be able to describe a single block using at least two attributes, such as color and shape, and to sort attribute blocks by color. Many children will be able to sort by other attributes. For children who struggle, provide more chances to work with attribute blocks; reduce the number of variables initially (for example, by removing all the thick blocks).”

• Lesson 5-12, Number Scrolls, Focus: Making Number Scrolls, students notice repeated calculations as they use number patterns to fill in a blank number scroll. “Distribute blank number scrolls to children and support them as they begin to write numbers. As you circulate, note how children fill in their scrolls. Do they write the numbers in order? Do they use patterns to complete the scroll (for example, filling in all the numbers in one column)?”

### Usability

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports; partially meet expectations for Criterion 2, Assessment; and meet expectations for Criterion 3, Student Supports.

##### Gateway 3
Meets Expectations

#### 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 Everyday Mathematics 4 Kindergarten 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' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten 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.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• Teacher’s Lesson Guide, Welcome to Everyday Mathematics, explains how the program is presented. “Throughout the Kindergarten program, emphasis is placed on building from and connecting with children's informal, everyday experiences with mathematics; problem solving in everyday situations and mathematical contexts; an instructional design that revisits topics regularly to ensure depth of knowledge and long-term learning; distributed practice through routines, games, and other activities; teaching that supports ‘productive struggle’ and maintains high cognitive demand; and playful lessons and activities that engage all children and make mathematics fun!”

• Implementation Guide, Guiding Principles for the Design and Development of Everyday Mathematics, explains the foundational principles. “The foundational principles that guide Everyday Mathematics development address what children know when they come to school, how they learn best, what they should learn, and the role of problem-solving and assessment in the curriculum.”

• Unit 5, Exploring Teen Numbers, Organizer, Coherence, K.OA.4, provides an overview of content and expectations for the unit. “Earlier in Kindergarten, children explored number pairs that add to 10 through ten-frame activities and games like Ten-Bean Spill. Children’s fingers provided a natural context for these explorations in Pre-K and early Kindergarten as well. In Section 5, children compose and decompose numbers 11 through 19 on double ten frames and with partners using two pairs of hands. In Sections 7 and 8, they record these types of decompositions with drawings and equations. In Grade 1, children will apply this concept as they extend their understanding of place value to include all 2-digit numbers.”

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Examples include:

• Implementation Guide, Everyday Mathematics Instructional Design, “Lesson Structure and Features include; Lesson Opener, Mental Math and Fluency, Daily Routines, Math Message, Math Message Follow-Up, Assessment Check-In, Summarize, Practice, Math Boxes, and Home-Links.”

• Lesson 2-2, Top-It with Dot Cards, Focus: Assessment Check-In, teacher guidance supports students in identifying and comparing quantities. “As children play Top-It with Dot Cards, observe whether they can correctly identify how many dots are on the cards and which card has more dots. Expect most children to be able to count and compare quantities for representations (both arranged and scattered) of at least 1 through 5 dots; many children will be able to compare larger sets. Children will continue to practice comparing sets in the sorting and graphing activities in Lessons 2-7, 2-10, and 3-1, as well as in later lessons.”

• Lesson 4-11, Counting by 10s, Focus: Counting by 10s, Professional Development, teacher guidance enhances instruction by explaining the importance of how to introduce groups of 10. “Counting concrete groups of 10 develops foundational place-value concepts. Delay using manipulatives (such as base-10 rods) that are already connected into groups of ten and cannot be broken apart into ones. Instead, have children count and group sets of ten discrete objects, such as fingers or straws to promote understanding that 1 ten is the same as 10 ones.”

• Lesson 8-2, Marshmallow and Toothpick Shapes, Focus: Assessment Check-in, teacher guidance supports students with modeling 2- and 3-dimensional shapes. “Expect most children to model basic 2-dimensional shapes with toothpicks and marshmallows, not all will be able to model 3-dimensional shapes without help. Also expect children to identify, name, and describe basic 2- and 3-dimensional shapes in their own or other children’s work.”

##### Indicator {{'3b' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten meet expectations for containing 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.

Each Unit Organizer Coherence table provides adult-level explanations and examples of complex grade/course-level concepts so teachers can improve their content knowledge. Professional Development side notes within Lessons support teachers in building knowledge of key mathematical concepts. Examples include:

• Lesson 1-12, Describing Shapes, Professional Development, supports teachers with concepts for work beyond the grade. “This lesson focuses on describing shapes. The emphasis is not yet on formal shape terminology (such as vertex or parallel), but hearing these terms helps children build them into their vocabulary. Gesturing can be a powerful teaching tool. When two shapes have straight sides, gesture along that side on each shape to highlight the common feature. Later, gestures such as these can help children learn new words such as vertex and angle.”

• Lesson 2-13, More Number Stories, Focus: Exploring More Number Stories, Professional Development, teacher guidance explains the different problem-solving situations. “Exposing children to a variety of problem types encourages them to think flexibly about the meanings and solutions of problems, instead of carrying out rote operations with the numbers. Generally, children find end-unknown problems the easiest to solve and start-unknown problems the most challenging.”

• Lesson 3-7, Comparing Representations, Focus: Solving the Open Response Problem, Professional Development, teacher guidance explains the different representations for the same number. “During this task, children create a variety of representations for the same number, which develops their quantitative reasoning in a variety of ways. First, they must think about what can change from one representation to the next (the objects, arrangement, grouping, and format) and what cannot change (the quantity). Then they must apply this knowledge to their own representations.”

• Lesson 6-7, Tall Enough to Ride?, Professional Development, supports teachers with concepts for work beyond the grade. “This lesson gives children an opportunity to explore using same-size units as a tool to measure and compare heights. Children engage with the idea that effective measurement requires iterating, or repeating, units without gaps or overlaps. They also share and make sense of their results in order to solve a problem. This early problem-solving experience lays the foundation for measurement lessons in later grades, when children learn about standard measurement units (such as inches, centimeters, milliliters, minutes, and grams) and tools (such as rulers, clocks, and scales).”

• Lesson 7-12, Dice Addition, Focus: Playing Dice Addition, Professional Development, teacher guidance explains how students develop fluency. “Dice Addition helps children develop fluency for sums that total 5 or less. To avoid having children view addition as simply a rote process, emphasize understanding before focusing on speed. With practice and encouragement, children will develop efficiency and fluency.”

• Lesson 9-10, Doubles on Double Ten Frames, Focus: Working with Doubles, Professional Development, teacher guidance explains how students will use doubles in future grades. “In this lesson, children begin learning small doubles facts using Quick Looks. In Grades 1 and 2, children will use their knowledge of doubles, which are among the easiest additional facts to learn, to derive more challenging addition and subtraction facts.”

##### Indicator {{'3c' | indicatorName}}

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level/series and can be found in several places, including the Correlations to the Standards for Mathematics, Unit Organizers, Pathway to Mastery, and within each lesson. Examples include:

• Kindergarten Math, Correlation to the Standards for Mathematics Chart includes a table with each lesson and aligned grade-level standards. Teachers can easily identify a lesson when each grade-level standard will be addressed.

• Mastery Expectations, K.CC.5, “First Quarter: Count arranged and scattered sets of up to 10 objects. Second Quarter: Count arranged sets of up to 20 objects. Count scattered sets of up to 10 objects. Count out up to 10 objects. Third Quarter: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. Fourth Quarter: Ongoing practice and application.”

• Lesson 4-1, Attribute Blocks, core standards are identified for the Focus: K.CC.5, K.CC.6, K.MD.1, K.MD.3, K.G.2, and the Practice: K.CC.3, K.CC.5. Lessons contain a structure that includes Before You Begin, Terms to Use, Materials, Daily Routines, Focus, Practice, Assessment Check-in, and Home Link. This provides an additional place to reference the standards within each lesson.

Each Unit Organizer Coherence table includes an overview of content standards addressed within the unit as well as a narrative outlining relevant prior and future content connections for teachers. Examples include:

• Unit 1, Foundational Counting Principles and Skills, Unit 1 Organizer, Coherence, K.G.2, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “In PreK, Children explored mostly 2-dimensional shapes in various sizes and orientations through tactile, kinesthetic, and visual activities. In Grades 1 and 2 they will further these understandings by thinking about defining and non-defining attributes of particular shape categories and by identifying additional shape categories, such as quadrilaterals.”

• Unit 3, Reading, Writing, and Using Numbers; Making Comparisons, Unit 3 Organizer, Coherence, K.CC.6, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “In Kindergarten Sections 1 and 2, children used visual, counting and matching strategies to compare small sets during sorting and graphing activities and games. Children had similar experiences in PreK, starting with even smaller sets. This will lead to comparisons of numerals later in Kindergarten and into Grade 1, when children will order and compare numbers using the number line and will be formally introduced to inequality symbols.”

• Unit 7, Addition and Subtraction Strategies; Expanding Number Sense, Unit 7 Organizer, Coherence, K.OA.2, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “Since the beginning of Kindergarten, children have solved addition and subtraction word problems. They have also practiced addition and subtraction in games and activities using dominoes and dice. They began by adding and subtracting within 5, and increased the range to within 10, beginning in Section 5. In Grade 1, children will model and solve problems involving addition or subtraction of two numbers within 20.”

##### Indicator {{'3d' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten 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.

Home Connection Handbooks can be shared with stakeholders through digital or print copies. The Implementation guide suggests, “These handbooks outline articles, explanatory material about Everyday Mathematics philosophy and program, and provide suggestions for parents regarding how to become involved in their children’s mathematics education.” Several lessons within each unit contain a corresponding Family Letter available in both English and Spanish, providing a variety of support for families including the core focus for each unit, ideas for practice at home, key vocabulary terms, building skills through games, and solutions to the. Examples include:

• Lesson 1-3, Gotcha: A Counting Game, Home Link, Family Note, “Children enjoy counting things. Look for opportunities to practice this skill. You will be pleasantly surprised how counting things brings about many playful and productive mathematics activities. Counting hops, skips, jumps, and sidesteps helps children develop counting skills as well as coordination. When you count with your child, help him or her say one number word for each item counted and reinforce that the last number he or she says tells the total number of things counted.”

• Lesson 3-5, Longer or Shorter? Home Link, Family Note, “Your child is learning about length measurement by comparing objects and describing them as longer and shorter than other objects. In Kindergarten we focus on direct comparisons of length to prepare children to use measuring tools later. Help your child line up the end of his or her arm (at the longest finger) with the end of the object being compared. This technique will be helpful later when your child learns to line up objects with the end of a ruler or other measuring tool.”

##### Indicator {{'3e' | indicatorName}}

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Instructional approaches to the program are described within the Teacher’s Lesson Guide. Examples include:

• Teacher’s Lesson Guide, Welcome to Everyday Mathematics, The University of Chicago School Mathematics Project (UCSMP) describes areas of the Everyday Mathematics 4 classroom. “Building from and connecting with children’s informal, everyday experiences with mathematics; problem-solving in everyday situations and mathematical contexts; an instructional design that revisits topics regularly to ensure depth of knowledge and long-term learning; distributed practice through routines, games, and other activities; teaching that supports ‘productive struggle’ and maintains high cognitive demand; and playful lessons and activities that engage all children and make mathematics fun!”

• Teacher’s Lesson Guide, About Everyday Mathematics, An Investment in How Your Children Learn, The Everyday Mathematics Difference, includes the mission of the program as well as a description of the core beliefs. “Decades of research show that children who use Everyday Mathematics develop deeper conceptual understanding and greater depth of knowledge than children using other programs. They develop powerful, life-long habits of mind such as perseverance, creative thinking, and the ability to express and defend their reasoning.”

• Teacher’s Lesson Guide, About Everyday Mathematics, A Commitment to Educational Equality, outlines the student learning experience. “Everyday Mathematics was founded on the principle that every child can and should learn challenging, interesting, and useful mathematics. The program is designed to ensure that each of your children develops positive attitudes about math and powerful habits of mind that will carry them through college, career, and beyond. Provide Multiple Pathways to Learning, Create a System for Differentiation in Your Classroom, Access Quality Materials, Use Data to Drive Your Instruction, and Build and Maintain Strong Home-School Connections.”

• Teacher’s Lesson Guide, About Everyday Mathematics, Problem-based Instruction, approach to teaching skills helps to outline how to teach a lesson. “Everyday Mathematics builds problem solving into every lesson. Problem solving is in everything they do. Warm-up Activity: Lessons begin with a quick, scaffolded Mental Math and Fluency exercise. Daily Routines: Reinforce and apply concepts and skills with daily activities. Math Message: Engage in high cognitive demand problem-solving activities that encourage productive struggle. Focus Activities: Introduce new content with group problem solving activities and classroom discussion. Summarize: Discuss and make connections to the themes of the focus activity. Practice Activities: Lessons end with a spiraled review of content from past lessons.”

• Teacher’s Lesson Guide, Everyday Mathematics in Your Classroom, The Everyday Mathematics Lesson, outlines the design of lessons. “Lessons are designed to help teachers facilitate instruction and engineered to accommodate flexible group models. Embedded Rigor and Spiraled Instruction: Each lesson weaves new content with the practice of content introduced in earlier lessons. The structure of the lessons ensures that your instruction includes all elements of rigor in equal measure with problem solving at the heart of everything you do.”

Preparing for the Module provides a Research into Practice section citing and describing research-based strategies in each unit. Examples include:

• Implementation Guide, Everyday Mathematics & the Common Core State Standards, 1.1.1 Rigor, “The Publishers’ Criteria, a companion document to the Common Core State Standards, defines rigor as the pursuit, with equal intensity, of conceptual understanding, procedural skill and fluency, and applications (National Governors Association [NGA] Center for Best Practices & Council of Chief State School Officers [CCSSO], 2013, p. 3).

• Implementation Guide, Differentiating Instruction with Everyday Mathematics, Differentiation Strategies in Everyday Mathematics, 10.3.3, Effective Differentiation Maintains the Cognitive Demand of the Mathematics, “Researchers broadly categorize mathematical tasks into two categories;  low cognitive demand tasks, and high cognitive demand tasks. While the discussion of cognitive demand in mathematics lessons is discussed widely, see Sten, M.K., Grover, B.W. & Henningsen, M. (1996) for an introduction to the concept of high and low cognitive demand tasks.”

• Implementation Guide, Open Response and Re-Engagement, 6.1 Overview, “Research conducted by the Mathematics Assessment Collaborative has demonstrated that the use of complex open response problems “significantly enhances student achievement both on standardized multiple-choice achievement tests and on more complex performance-based assessments” (Paek & Foster, 2012, p. 11).”

• The University of Chicago School Mathematics Project provides Efficient Research on third-party studies. For example:

• Use of Student Constructed Number Stories in a Reform-Based Curriculum.

• An Action-Based Research Study on How Using Manipulatives Will Increase Student’s Achievement in Mathematics.

• Differentiating Instruction to Close the Achievement Gap for Special Education Students Using Everyday Math.

• Implementing a Curriculum Innovation with Sustainability: A Case Study from Upstate New York.

• Mental Computation of Students in a Reform-Based Mathematics Curriculum.

• ARC Center Tri-State Achievement Study.

• Teacher-Initiated Differentiation.

• The Impact of Two Standards-Based Mathematics Curricula on Student Achievement in Massachusetts.

##### Indicator {{'3f' | indicatorName}}

Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

A year-long list of materials needed is provided in the Teacher’s Lesson Guide, Getting to Know Your Classroom Resource Package, Manipulative Kits, and eToolkit. “The table below lists the materials that are used on a regular basis throughout Kindergarten Everyday Mathematics.” Each section includes a Materials Overview section outlining supplies needed for each lesson within the unit. Additionally, specific lessons include notes about supplies needed to support instructional activities, found in the overview of the lesson under Materials. Examples include:

• Lesson 3-8, Spin a Number, Materials, “Focus: walk-on gameboard and Spin a Number Gameboards and spinners (see Before You Begin); game markers Practice: Math Masters pp. 43-44; crayons or markers Home Link: Math Masters p. 51.”

• Section 4, Advanced Counting; Composing/Decomposing Numbers and Shapes; Measurable Attributes, Section 4 Organizer, Section 4 Materials, each lesson has materials listed under the following categories: Math Masters My First Math Book, Activity Cards, Manipulative Kit, Other Materials, and Literacy Suggestions. For example, Lesson 4-1, listed materials, My First Math Book: “MM, p.55-56”, Activity Card: “30”, Manipulative Kit; “attribute blocks”, Other Materials: “prepared Number Cards -10, Literacy Suggestions: “3 Little Firefighters, “The Button Story” (Frog and Toad Are Friends).”

• Lesson 7-5, Count and Skip Count with Calculators, Materials, “Focus: calculators Practice: Math Masters p. TA12 (optional); bear counters (10 per pair); plastic cups (1 per pair); slates Home Link: Math Masters, p.96.”

• Section 9, Measurement and Spatial Thinking, Section 9 Organizer, Section 9 Materials, each lesson has materials listed under the following categories: Math Masters My First Math Book, Activity Cards, Manipulative Kit, Other Materials, and Literacy Suggestions. For example, Lesson 9-7, listed materials, My First Math Book: “MM, p.TA11”, Activity Card: “84”, Manipulative Kit; “counters, dice”, Other Materials: “materials for a model of the classroom; large paper; camera (optional); children’s work from Day 1; prepared Car Race gameboards (Lesson 8-8)”, Literacy Suggestions: “books about maps.”

##### Indicator {{'3g' | indicatorName}}

This is not an assessed indicator in Mathematics.

##### Indicator {{'3h' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten partially meet expectations for Assessment. The materials identify the standards and the mathematical practices assessed in formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but do not provide suggestions for follow-up. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.

##### Indicator {{'3i' | indicatorName}}

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Beginning-of-Year Assessment, Mid-Year Assessment, and End-of-Year Assessment consistently and accurately identify grade-level content standards along with the mathematical practices within each Unit. Examples from formal assessments include:

• Beginning-of-Year Assessment, denotes the aligned grade-level standards and mathematical practices. Problem 5a, “Place 7 connecting cubes in a row. Ask: How many cubes are there? Note whether children: count with number names in the standard order, pair each cube with only one number name (one-to-one correspondence), and recognize that the last number that they counted tells how many cubes (cardinal principle). Counts with the correct count sequence (yes or no). Counts with one-to-one correspondence (yes or no).” (K.CC.4a, SMP6)

• Mid-Year Assessment, denotes the aligned grade-level standards and mathematical practices. Problem 1b, “Prompt children to count by 10s. Stop them when they reach 100 or when their counting becomes erratic. Look for children to count by 10s through 50. Counts by 10s to ____ (50).” (K.CC.1, SMP6, SMP7)

• End-of-Year Assessment, denotes the aligned grade-level standards and mathematical practices. Problem 11, “Give children a blank name-collection box for the number 9. Prompt them to use drawings or equations (or both) to show at least three different ways to combine numbers to make 9. Look for children to show at least three different combinations for 9. Shows at least three combinations for (decomposition of) 9: Yes or No.” (K.OA.3, SMP1, SMP2, SMP5)

##### Indicator {{'3j' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten partially 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.

In the Everyday Mathematics 4 materials, the assessment system consists of Ongoing and Periodic Assessments. Ongoing Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up through Assessment Check-Ins. Periodic Assessments provide sufficient guidance to teachers for interpreting student performance; however, they do not provide suggestions to teachers for follow-up with students.

Summative Assessments, such as Beginning-of-Year Assessment, Mid-Year Assessment, and End-of-Year Assessment, provide a rubric with aligned standards. While some scoring guidance is included within the materials, there is no guidance or suggestions for teachers to follow up with students. Examples include:

• Beginning-of-Year Assessment, Problem 1, “Ask children to count aloud as high as they can, starting at 1. Stop them when their counting becomes erratic. If they stop on their own, ask if they can go higher. Note the highest number children reach before they stop or their counting becomes erratic.” Student version, “Counts by 1s to ____.” This question is aligned to K.CC.1.

• Mid-Year Assessment, Problem 7, “Give children a bag with 20 connecting cubes. Say: Give me 10 cubes. Note whether children count out 10 cubes and the strategies they use to keep track of their counting. You may wish to repeat with other numbers of cubes until the task becomes too challenging. Look for children to count out a set of at least 10 cubes.” Student version, “Counts out 10 cubes: Yes or No” This question is aligned to K.CC.5.

• End-of-Year Assessment, Problem 17, “Give children a handful of attribute blocks (not a complete set) and ask them to sort the blocks by shape or by size. Have the children count the number of blocks in each group and order the groups by count from fewest to most. Look for children to sort the blocks by the given attribute, count the blocks in each group, and order the groups by count from fewest to most.” Student version, “Sorts blocks by given attribute: Yes or No” “Counts blocks in each group: Yes or No” “Orders the groups by count: Yes or No” This question is aligned to K.MD.3.

##### Indicator {{'3k' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

Formative Assessments include Beginning-of-Year Assessment and Assessment Check-Ins. Summative Assessments include Mid-Year Assessment and End-of-Year Assessment. All assessments regularly demonstrate the full intent of grade-level content and practice standards through observation, along with rubrics. Examples include:

• Lesson 6-11, Hiding Bears, Assessment Check-In, develops the full intent of K.OA.4, for any number from 1 to 9, find the number that makes 10 when added to the given number. “As children play, observe their strategies for making sense of the problem and finding the number of hidden bears. Expect most children to be able to find combinations that add to 10 using concrete strategies, such as counting on or using their fingers or a ten frame. Some children may recall combinations that add to ten.”

• Middle-of-Year Assessment, develops the full intent of K.G.1, describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. Problem 17, “Give each child a bear counter and a cup. Prompt them to model the following positions: Place the bear above the cup. Continue to prompt them to place the bear beside, in front of, next to, below, and behind the cup. You may also provide prompts using other positional words. Look for children to understand these positional terms and place the bear correctly.”

• End-of-Year Assessment, supports the full intent of MP6, attend to precision. Problem 6, “Give children a bag with 30 connecting cubes. Say: Give me 20 cubes. Note whether children count out 20 cubes and the strategies they use to keep track of their counting. Look for children to count out a set of 20 cubes.

##### Indicator {{'3l' | indicatorName}}

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for Everyday Mathematics 4 Kindergarten provide assessments that offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

According to the Assessment Handbook, Individualizing Interim Assessments, Page 6, “To maximize the information you can learn, you may need to modify or adapt the tasks according to the child or group of children you are working with at that moment. For example: If a child has difficulty with a task, simplify it slightly or engage the child in conversation about the task to better understand the root of the difficulty. If a child performs an activity with ease, add a bit of challenge to see how much farther he or she can go. Allow children to take open-ended tasks as far as they are able. Provide encouragement for children to try things, even if they think they are difficult. If they seem perplexed by a question or set of instructions, try presenting the information in a different way to see if it makes more sense to them. Children with special needs or learning differences may require specific modifications to help them best express what they know.”

#### Criterion 3.3: Student Supports

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for Everyday Mathematics 4 Kindergarten 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' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. Implementation Guide, Differentiating Instruction with Everyday Mathematics, 10.1 Differentiating Instruction in Everyday Mathematics: For Whom?, “Everyday Mathematics lessons offer specific differentiation advice for four groups of learners. Students Who Need More Scaffolding, Advance Learners, Beginning English Language Learners, and Intermediate and Advanced English Language Learners.” Differentiation Lesson Activities notes in each lesson provide extended suggestions for working with diverse learners. Supplementary Activities in each lesson include Readiness, Enrichment, Extra Practice, and English Language Learner.

For example, the supplementary activities of Section 4, Advanced Counting; Composing/ Decomposing Numbers and Shapes; Measurable Attributes, Lesson 6, include:

• Readiness, “To prepare children to count into the teens, identify a teen number on the Growing Number LIne as the counting target. Have children count to the “target” number, starting at either 1 or 10. You may wish to point, or have a child point, to each number on the Growing Number Line as children say it. Repeat for several different teen numbers.”

• Enrichment, “To extend skills from the lesson, invite children to create a movement sequence that totals the number on a ten number card. For example, a ‘12 dance’ might include 8 side steps, 2 forward steps, and 2 jumps. Have children record their sequence with symbols, pictures, or words, then repeat it multiple times to create a dance. Let them teach their teen dances to others!”

• Extra Practice, “To provide additional practice with reading and counting teen numbers, have partners or small groups take turns picking a teen number card and choosing an action to perform that many times while they count aloud, one movement per count. Alternatively, children may count out a set of objects to match the teen number on their card.”

• English Language Learner, Beginning ELL, “Use gestures to help children understand the word after. For example: Make hopping gestures, moving your hand to the right along a number line as you ask: What number comes after ___? What number comes next? Point to specific numbers, and ask the same questions. Model making corresponding statements after each example with statements such as: The number seven comes after six. Twelve comes after eleven. Encourage early-production children to respond to questions by gesturing from one number to the next on a number line and using sentence frames such as: ‘____ comes after ___.’”

##### Indicator {{'3n' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Materials provide multiple opportunities for advanced students to investigate the grade-level content at a higher level of complexity rather than doing more assignments. The Implementation Guide, Differentiation Instructions with Everyday Mathematics, 10.4 Working with Advanced Learners “Nearly all Everyday Mathematics lessons include a set of high cognitive demand tasks with mathematical challenges that can be extended. Every regular lesson includes recommended enrichment activities related to the lesson content on the Differentiation Options page at the end of the lesson. Everyday Mathematics lessons incorporate varied grouping configurations which enable the kind of flexibility that is helpful when advanced learners in heterogeneous classrooms. The 2-day Open Response and Re-Engagement lesson rubrics provide guidance for students in Exceeding Expectations. Examples include:

• Lesson 3-10, Number-Card Activities, Enrichment, “To extend the Focus activity, have children lay the cards faceup in any order or configuration. While one partner closes his or her eyes, the other partner removes a card from the set. With eyes open, the first partner tries to figure out which card is missing. Use higher number cards if children are ready.”

• Lesson 7-5, Count and Skip Count with Calculators, Enrichment, “To extend the activity, have children use a calculator to skip count by 5s and 2s. Have them substitute 5 or 2 for 10 in the key sequences described on page 450.”

• Lesson 8-7, Birds on Wires (Day 1), Focus: Solving the Open Response Problem, Adjusting the Activity, “If children quickly find many combinations for the 10 birds, challenge them to find every solution to the problem. You may wish to have them discover how many possible combinations there are (11) or provide them with the total and ask them to find them all. Remind them that duplicate solutions do not count toward the total. Discuss how they might organize their work to know that they have found every combination without any duplicates.”

##### Indicator {{'3o' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten provide various approaches to learning tasks over time and variety in how students are expected to demonstrate their learning, and provide opportunities for students to monitor their learning.

Students engage with problem-solving in a variety of ways: My First Math Book, Math Masters, and Open Response and Re-Engagement Lessons, a key component of the program. Examples of varied approaches include:

• Lesson 2-12, Number Stories, Focus: Telling and Acting Out Number Stories, and students act out stories as the teacher tells them to the class. “Invite children to act out each story or to use counters, fingers, or drawings to model the story as you tell it.”

• Lesson 5-4, Find and Draw Shapes, Focus: Finding and Drawing Shapes, My First Math Book, students look for shapes in a picture and draw a shape in each box. “Draw four shapes you see in the picture your teacher shows.”

• Lesson 7-12, Dice Addition, Focus: Playing Dice Addition, students play a game in pairs. “As they play, circulate and observe their addition strategies and ask them to explain how they know which player’s total wins. As children seem ready, model and encourage more efficient strategies.”

Opportunities for students to monitor their learning are found in the Assessment Handbook. These reflection masters can be copied and used to analyze the work from any lesson or section. Examples include:

• Assessment Handbook, Good Work!, students reflect on work they have completed and fill out the following sheet and attach it to their work, “I have chosen this work because _______.”

• Assessment Handbook, My Work, students reflect on work they have completed and fill out the following sheet to attach to their work, “This work shows I can _______. I am still learning to ______.”

• Assessment Handbook, About Math Time, students “Draw a face or write the words that show how you feel.” There are three circles with faces, a smiley face, or “good”, a face with a straight mouth, or “OK”, and a circle with a sad face, or “Not so good.” Students reflect on 6 statements, “This Is how I feel about math, This is how I feel about working with a partner or in a group. This is how I feel about working by myself, This is how I feel about solving number stories, This is how I feel about doing Home Links with my family, and This is how I feel about finding new ways to solve problems.”

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for Everyday Mathematics 4 Kindergarten provide opportunities for teachers to use a variety of grouping strategies.

Everyday Mathematics provides suggestions for whole class, small group, partner, and independent work. Implementation Guide, 5.2.1 Collaborative Groupings, explicitly directs teachers in establishing collaborative groupings, “Because Everyday Mathematics provides activities for various groupings, teachers may want to plan seating arrangements that allow students to transition between whole-class, small-group, and independent work efficiently and with minimal disruption. Flexible grouping allows students to work with many other students in class and keep their interests high. Mixed ability, heterogenous group allows students to learn from each other by having opportunities to hear the thoughts and ideas of their peers. Homogenous groups allow the work to be differentiated to meet the needs of all in the group.” Examples include:

• Lesson 3-4, Number Books, Focus: Writing Numbers (1 and 2), students work independently to write numbers. “Introduce the Number Book pages from Math Masters, pages 34 and 35. Direct children to practice writing the number in pencil on the top part of the page. Then have them draw a corresponding number of objects in the box below.”

• Lesson 4-11, Counting by 10s, Practice: Making Rope Shapes, students work in small groups to create shapes. “Hold up the hexagon pattern block and remind children of its name. Invite children to share their observations about the shape, and ask them how many sides and vertices it has. Have small groups make a hexagon with rope. (They may need to combine groups). Repeat with the trapezoid and one of the rhombuses, as well as other shapes as time and interest permit.”

• Lesson 5-11, Growing Train, Focus: Playing Growing Train, students play a game in pairs where they roll a die marked +1, +2, and +3 and add connecting cubes to a cube train. “Have children play in pairs. As you circulate, ask children to describe their turns (I had 8 cars. I added 3 cars. Now I have 11 cars.) Model as needed. Direct the children to play until someone’s train has 20 cars (at least or exactly - you or the children can decide this detail).

##### Indicator {{'3q' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten 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.

The Teacher’s Lesson Guide and ConnectED Teacher Center include guidance for the teacher in meeting the needs of English Language Learners. There are specific suggestions for making anchor charts or explaining new vocabulary. The ConnectED Teacher Center offers extended suggestions for working with diverse learners including English Language Learners. Most lessons contain “ELL Support.” Examples include:

• Lesson 1-6, Count and Sit, Focus: Playing Count and Sit, ELL Support, “Have children recite numbers in unison, in small groups, and in pairs before asking them to recite the numbers individually.”

• Lesson 4-12, Top-It with Number Cards, Focus: Playing Top-It with Number Cards, ELL Support, “Involve children in practice rounds of Top-It using modeling and think-aloud statements and making sure children understand how to determine who takes the cards at the end of each round. Use gestures, pictures, and the number line to reinforce the terms more, less, and greater.”

• Lesson 7-11, Class Collection, Focus: Collecting Objects, ELL Support, “Help children learn that item is a general term and not the name of a specific object. Also, review the term collection (see Lesson 5-1). Show several collections of objects and pose prompts such as: How many items are in this collection? What are the names of the items in that collection? What is your favorite item in the collection?

• The online Student Center and Student Reference Book use sound to reduce language barriers to support English language learners. Students click on the audio icon, and the sound is provided. Questions are read aloud, visual models are provided, and examples and sound definitions of mathematical terms are provided.

• The Differentiation Support ebook available online contains Meeting Language Demands providing suggestions addressing student language demands for each lesson. Vocabulary for the lesson and suggested strategies for assessing English language learners’ understanding of particularly important words needed for accessing the lesson are provided.

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for Everyday Mathematics 4 Kindergarten provide a balance of images or information about people, representing various demographic and physical characteristics.

The characters in the student-facing materials represent different races and portray people from many ethnicities in a positive, respectful manner, with no demographic bias for who achieves success in the context of problems. Names include multi-cultural references such as Davon, Marcos, and Maya and problem settings vary from rural, urban, and international locations.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Everyday Mathematics 4 Kindergarten provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The Implementation Guide, “This edition of Everyday Mathematics incorporates a variety of strategies to increase the accessibility of the lessons to English language learners. A fundamental principle of Everyday Mathematics is that students learn mathematics best when they use it to solve problems in meaningful contexts. Similarly, languages are acquired more effectively when learned in conjunction with meaningful content and purposeful communication. Thus, instruction with Everyday Mathematics can serve two purposes for English language learners: helping them learn mathematics and helping them develop English language proficiency. English language learners enter mathematics classrooms with many similarities and differences in the language spoken at home, previous school preparation, and academic background in English as well as in their first language. Grade level does not dictate English proficiency. For example, English language learners in higher grade levels may be at beginning English proficiency levels. Conversely, students in the early grades may be at higher levels of English proficiency. Some English language learners have extensive educational backgrounds, which include the study of English. Others may have very limited formal school experiences, which may mean they lack literacy skills in their home language and English. Moreover, English proficiency does not determine mathematical proficiency.”

English Language Learner notes provide activities to support students with different English language proficiency. Examples include:

• Lesson 6-4, Solid-Shapes Museum, Focus: Creating a Solid-Shapes Museum, ELL Support, “Introduce the geometric use of face by pointing to your face and saying: This is my face. Then point to a face on a solid shape and say: This is a (shape’s name) face. Some shapes have more than one face.”

• Implementation Guide, 10.5.3 Developing and Reinforcing Vocabulary: Selected Accessibility Strategies for English Language Learners, Using Reference Materials, “Encourage English learners to use the Everyday Mathematics My Reference Book in Grades 1 and 2 and the Students Reference Books in Grades 3-6 along with other reference materials in print and online, such as encyclopedias, almanacs, and dictionaries (including bilingual dictionaries). For Spanish speakers, note that technical terms used in Everyday Mathematics may be similar to the Spanish words, which may enhance Spanish speakers’ retention of new terminology. In the appropriate context, list English and Spanish words for students to build meaning, but do not assume that students understand the meanings of that Spanish word. Some examples are: angle/angulo, circle/circulo, parallel/paralelo, interior/interior, and polygon/poligono.”

The Implementation Guide, “Increasing English language learner’s accessibility to lesson content involves a variety of strategies with the same basic principle: consider the language demands of a lesson and incorporate language-related strategies for helping students access the core mathematics of the lesson. In other words, provide students with enough language support so that their time with the lesson can focus on the mathematical ideas rather than interpreting the language.” Examples include:

• Role Playing: “An excellent way to deepen understanding of concepts is to give students the opportunity to apply what they have learned to a familiar situation. In one lesson, students simulate a shopping trip using mock Sale Posters as visual references and play with money as a manipulative to practice making change. In this example, English learners can take turns being the shopkeeper and the customer. This role play helps students learn and practice the phrases and vocabulary they need in real shopping situations while gaining familiarity with the language needed to access the mathematics content of the lesson.”

• Tapping Prior Knowledge: “English learners sometimes feel that they must rely on others to help them understand the instruction and practice in school each day. However, English learners bring unique knowledge and experience that they should be encouraged to contribute to the classroom community. For example, working with metric measurement and alternative algorithms present excellent opportunities for English learners to share their expertise with the group. Those who have gone to school outside the United States may know the metric system or other algorithms well.”

• Sheltered Instruction: “The Sheltered Instruction Observation Protocol (SIOP) Model was developed at the Center for Applied Linguistics (CAL) specifically to help teachers plan for the learning needs of English language learners. The model is based on the sheltered instruction approach, an approach for teaching content to English language learners in strategic ways that make the content comprehensible, while promoting English language development.” Components and Features of the SIOP Model include: Lesson Preparation, Building Background, Comprehensible Input, Strategies, Interaction, Practice and Application, Lesson Delivery, and Review and Assessment.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Everyday Mathematics 4 Kindergarten provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Materials include some cultural connections within the Teacher’s Lesson Guide. Examples include:

• Lesson 5-12, Number Scrolls, Practice: Connections, Art, Writing, and Dramatic Play, students examine and discuss the purpose of scrolls throughout the world. “Discuss other purposes for scrolls, such as artwork, stories, invitations, and lists. You may want to show children some examples of East Asian scroll paintings. Provide children with long sheets of paper to make into scrolls and use in dramatic play. They can use ribbon, yarn, or rubber bands to secure their scrolls. Children may make a scroll of daily events by drawing pictures to show the sequence of their activities over one or more days.”

• Lesson 8-3, Counting to Measure Time, Practice: Connections, Literacy and Social Studies, This is the Way We Go to School, students read This is the Way We Go to School and discuss the terms faster and slower. “Shows children throughout the world going to school in different ways. Talk about which ways are faster and slower than others.” Students see different cultures such as Nanjing, Venice Italy, Kenya, etc.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for Everyday Mathematics 4 Kindergarten partially provide supports for different reading levels to ensure accessibility for students.

The Home Connection Handbook provides stakeholders helpful ways for students to become comfortable with vocabulary. “Important math vocabulary is highlighted and explained in the Family Letter that your children bring home for each unit. Take a few minutes to review the vocabulary yourself. When your child is doing Home Links, ask questions that focus on the meaning of the new words. Try to use the new vocabulary as you and your child do everyday activities together. The more your children hear, see, and use new words, the more able they are to add the words to their own vocabularies.” The Academic Language Development and Professional Development in some lessons include suggestions to scaffold vocabulary or concepts to support access to the mathematics, but do not directly address accessibility for different student reading levels. Examples include:

• Lesson 2-3, Getting to Know Triangles, Focus: Getting to Know Triangles, Professional Development, “In this and other early lessons, children are likely to use familiar terms such as corner to describe shapes. Validate children’s use of these terms, but also model geometric terms such as vertex (the point at which the sides of a polygon meet). Children will learn geometric vocabulary through modeling and use.”

• Lesson 4-12, Top-It with Number cards, Focus: Playing Top-It with Number Cards, Academic Language Development, “Children may be confused by the many terms used to compare numbers, including greater, more, higher, less, lower, and fewer. Point out that these words are often used interchangeably. Orient a strip of number line vertically, with 0 at the bottom, to help children equate height with the greater number and low with the smaller number. Label the right end of your Growing Number LIne with the words greater, more, and higher. Write less, fewer, and lower at the left end of your Growing Number Line.”

• Lesson 5-10, The Addition Symbol (+), Focus: Using the Addition Symbol, Academic Language Development, “Use the words plus, add, combine, and join interchangeably. As you slide counters together, use think-aloud statements, such as I will put the counters all together. I will join (combine) the counters. I will add them. Encourage children to use these words to verbalize what they are doing.”

##### Indicator {{'3v' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten 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.

The materials consistently include suggestions and/or links, within the lesson notes, for virtual and physical manipulatives that support the understanding of grade-level math concepts. Examples include:

• Lesson 2-9, Ten Frames, Focus: Exploring Ten Frames, materials reference use of ten-frames and counters. “Remind children about representing numbers on five frames (Lesson 1-11). Explain that today they will show, or represent, numbers using a ten frame. Give each child a ten frame and 10 counters. Ask: What do you notice about this tool? Why do you think it is called a ten frame? How is a ten frame similar to a five frame? How is it different from a five frame?”

• Lesson 4-1, Attribute Blocks, Focus: Exploring Attribute Blocks, materials reference the use of attribute blocks. “Divide the class into small groups and give each group a handful of same-color blocks. (If needed, remove the thick blocks to reduce the number of variables.) Have each group identify an attribute (besides color) by which to sort their blocks.”

• Lesson 7-9, Bead Combinations, Focus: Exploring Number Combinations, materials reference use of bead counters. “Have each child take one chenille stem, put 7 to 9 same-color beads on it, and make a loop. (Children will make bead combinations that add to 10 in Lesson 8-9, Practice.) Direct them to group their beads and write number sentences for four different groupings on the My First Math Book page.”

#### 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 Everyday Mathematics 4 Kindergarten integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards. The materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic. The materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

##### Indicator {{'3w' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten 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.

Materials include a visual design that is engaging and references/integrates digital technology. Examples include:

• Materials accessible online only: eToolKit, ePresentations, Assessment Reporting Tools, Spiral Tracker, Implementation Guide, Virtual Learning Community, Home Connection Handbook, Student Learning Centers, EM Games Online, and Facts Workshop Games.

• Teacher’s Lesson Guide, “eToolkit contains online tools and virtual manipulations for dynamic instruction. ePresentations are ready-made interactive whiteboard lesson content to support daily instruction.”

• Interactive Student Journal, available for each lesson provides access to virtual manipulatives and text and drawing tools, that allow students to show work virtually. This resource includes the My First Math Book, Student Reference Book, eToolkit, Activity Cards, and other resources, which allow students to receive immediate feedback on selected problems and is available in English or Spanish.

• Digital Student Assessments, provide progress monitoring. The assessment tools create student, class, or district reports. Data is provided in real-time and allows teachers to make informed instructional decisions that include differentiating instruction.

##### Indicator {{'3x' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

Teachers can provide feedback to students through the Student Learning Center. The Implementation Guide, “If students complete their work in the Student Learning Center using a digital device, the teacher can see that work by selecting ‘Digital Activity.’ As the teacher reviews student work, he or she can select a writing tool and add feedback. When students go to the activity screen in their Student Learning Center, they see any notes from their teacher.”

Teachers can collaborate with other teachers through the Virtual Learning Community. The Implementation Guide, “Many Everyday Mathematics teachers have found support through the Virtual Learning Community, or the VLC, hosted by the University of Chicago. This online resource provides professional resources, demonstration lessons, the ability to join or form groups, and so much more. Having colleagues to share Everyday Mathematics experiences with enriches the program experience.”

##### Indicator {{'3y' | indicatorName}}

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 Everyday Mathematics 4 Kindergarten provide a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design within units and lessons that supports student understanding of the mathematics. Examples include:

• Each unit begins with an organizer that displays the content, focus, coherence, rigor, necessary materials, spiral toward mastery, and mathematical background.

• Each lesson follows a common format with the following components: Before You Begin, Terms to Use, Materials, Daily Routines, Focus, Assessment Check-In, and Practice (Math Minute, Math Boxes, and Home-Link). The layout for each lesson is user-friendly and each component is included in order from top to bottom on the page.

• The Teacher’s Lesson Guide follows a consistent format, including visuals of student-facing materials and answer keys within the lesson.

• My First Math Book pages and Home Links follow a consistent pattern and work pages provide enough space for students to record work and explain their reasoning.

• The font size, amount of text, and placement of directions and print within student materials are appropriate.

• The Student Center is engaging and houses all student resources in one area.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for Everyday Mathematics 4 Kindergarten provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The Teacher’s Lesson Guide includes a description of embedded tools, how they should be incorporated, and when they can be accessed to enhance student understanding. Examples include:

• Lesson 7-10, Class Number-Story Book, Assessment Check-In, Evaluation Quick Entry, “Go online to record children’s progress and to see trajectories toward mastery for these standards.”

• Teacher’s Lesson Guide, Getting Ready to Teach Kindergarten Everyday Mathematics, Lesson Parts, Features, and Routines, “Consider conducting routines as part of a morning meeting. Go Online to the Implementation Guide for tips on the daily routines.”

• Teacher’s Lesson Guide, Getting Ready to Teach Kindergarten Everyday Mathematics, Lesson Parts, Features, and  Differentiation Options, “Go Online to the Implementation Guide for information on differentiation.”

## Report Overview

### Summary of Alignment & Usability for Everyday Mathematics 4 | Math

#### Math K-2

The materials reviewed for Everyday Mathematics 4 K-2 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 and Student Supports; the materials partially meet expectations for Assessment.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

The materials reviewed for Everyday Mathematics 4 3-5 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 and Student Supports; the materials partially meet expectations for Assessment.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 6-8

The materials reviewed for Everyday Mathematics 4 Grade 6 partially meet expectations for Alignment to the CCSSM. In Gateway 1, the materials partially meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections.

###### Alignment
Partially Meets Expectations
Not Rated

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
{{ report.usability.label }}

### {{ gateway.title }}

##### Gateway {{ gateway.number }}
{{ gateway.status.label }}