Kindergarten - Gateway 3

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.”

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.”

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.”

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.

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.”

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)

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.”

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 ___.’”

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.”

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.

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.”