2nd Grade - Gateway 3

The materials reviewed for Everyday Mathematics 4 Grade 2 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 Everyday Mathematics, emphasis is placed on 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 games and other daily activities; teaching that supports “productive struggle” and maintains high cognitive demand; and 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 7, Whole Number Operations and Measurement and Data, Lesson Organizer, Coherence, 2.NBT.6, provides an overview of content and expectations for the unit. “In Grade 1, children applied their knowledge of addition strategies to solve number stories involving three whole numbers whose sum is less than 20. In Unit 9, children will choose at least three items to purchase for $100. In Grade 3, children will add and subtract numbers using strategies and algorithms.”

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 1-6, Equivalent Names for Numbers, Focus: Assessment Check-in, teacher guidance supports students to find equivalent number names. “Expect that most children will find at least one equivalent name each for Problems 1-5 on journal page 4. Some children may find more than one name for each; others may use more than one operation. For children who struggle to find one name for each problem, have them count out the number of counters that is the same as the ‘show’ number, divide the counters into two groups, and write an addition number model to represent the groups. Be sure that the number model does not contain the number of the broken key.”

• Lesson 4-7, Playing Target, Focus: Making Exchanges, Adjusting the Activity, teacher guidance supports struggling students. “For children who struggle to remember the values of the base-10 blocks, provide a card showing pictures of the base-10 blocks and their values.”

• Lesson 8-10, Playing Array Concentration, Focus: Math Message Follow-Up, teacher guidance connects students' prior knowledge to new concepts. “Remind children that when they arrange things in equal rows, they are making arrays. Ask volunteers to share their arrays and number models. If children wrote multiplication number models, ask them to suggest addition models as well.”

The materials reviewed for Everyday Mathematics 4 Grade 2 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 1-9, Even and Odd Number Patterns, Focus: Identifying Even and Odd Numbers, Professional Development, teacher guidance clarifies the pairing strategy for even numbers. “The pairing definition for even numbers does not apply to the number 0 because 0 objects cannot be paired. In later grades, children will learn that a number is even if dividing it by 2 yields a remainder of 0. Using this definition, 0 is an even number because 0\div2 has a remainder of 0.”

• Lesson 4-9, The Inch, Focus: Sharing Strategies, Professional Development, teacher guidance explains the transition from iterating units to standard measurement. “The 12-inch (foot-long) ruler is introduced in this lesson. Some children may not yet see the ruler as composed of a series of inch-long intervals. The activities in this lesson are designed to show children that the length of an object must be the same number of inches, whether it is measured with 1-inch long blocks or with a ruler-a potentially unfamiliar concept to children.”

• Lesson 5-8, Change-to-More Number Stories, Focus: Introducing the Change Diagram, Professional Development, teacher guidance explains how number models are used beyond the grade. “In Everyday Mathematics, children use number models to represent situations and summarize relationships among quantities. In first through fifth grade, number models are used to clarify the quantitative relationships in a problem. Writing number models may help some children decide how to solve a problem, but more importantly, doing so helps them learn the mathematical-symbol system. Translating a word problem into a number model that can be manipulated to find an answer comes later when children begin to learn formal algebra.”

• Lesson 6-3, Interpreting Number Stories, Focus: Sharing Strategies, Professional Development, explains the connection between previous lessons and this lesson. “Until now, lessons have focused on one type of number story at a time. For example, all the problems in Lesson 6-2 were comparison stories, and the comparison diagram was the only diagram used. In this lesson, children are asked to categorize addition and subtraction number stories and then solve them. Do not force any number story into a particular mold. There may be several ways to interpret a problem.”

• Lesson 8-7, Partitioning Rectangles, Part 2, Focus: Partitioning Strategies, Professional Development, supports teachers with concepts for work beyond the grade. “Work with partitioning in Grade 2 lays the foundation for area measurement in Grade 3. In Grade 2 children develop the ability to visualize a rectangle as a collection of squares arranged in a row-by-column structure. This structure is important because it allows children to see the one-to-one correspondence between the number of squares in a row or a column and the number of units of measurement in the rectangle’s sides.”

• Lesson 9-10, Connecting Doubles Facts, Even Numbers, and Equal Groups, Focus: Connecting Doubles and Equal Groups, Professional Development, supports teachers with concepts for work beyond the grade. “This lesson focuses on finding the total number of objects in two equal groups and expressing an even number of objects as the sum of the number of objects in two equal groups. These are expectations for second grade but also build an understanding of how doubles addition facts relate to multiplying by 2. Children are exposed to multiplication number models in this lesson to build readiness for solving 2s multiplication facts early in third grade.”

The materials reviewed for Everyday Mathematics 4 Grade 2 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:

• Grade 2 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, 2.NBT.2, “First Quarter: Count by 1s to at least 120; skip count by 5s using a calculator, and skip count by 10s to at least 200. Second Quarter: Count by 1s within 500; skip count by 5s and 10s past 200; count by 100 to 900. Third Quarter: Count within 1000; skip-count by 5s, 10s, and 100s. Fourth Quarter; Ongoing practice and application.”

• Lesson 3-6, -0 and -1 Fact Strategies and Subtraction Top-It, standards identified in the Focus are 2.OA.2, 2.NBT.5, 2.NBT.9, and standards identified in the Practice are 2.OA.2, 2.NBT.3, and 2.NBT.5. Lessons contain a consistent structure that includes an Overview, Before You Begin, Vocabulary, Warm-Up, Focus, Assessment Check-In, Practice, Math Boxes, and Home-Link. This provides an additional place to reference 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 4, Place Value Measurement, Unit 4 Organizer, Coherence, 2.NBT.1a, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “In Grade 1, children used base-10 blocks to learn about place value of 2-digit numbers through a variety of hands-on activities. In Grade 3, children will use place value understanding to round whole numbers to the nearest 10 or 100.”

• Unit 6, Whole Number Operations and Number Stories, Unit 6 Organizer, Coherence, 2.OA.1, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. In Grade 1, children modeled and solved number stories within 20 of all different types, with the position of the unknown varying. In Grade 3, children will solve one-and two-step number stories using all operations.”

• Unit 8, Geometry and Arrays, Unit 8 Organizer, Coherence, 2.G.1, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “In Grade 1, children began to differentiate between defining and non-defining attributes as they sorted attribute blocks and defined a rectangle by its attributes. Such work extended informal Kindergarten discussions of attributes and activities that involved building and drawing shapes. In Grade 3, children will compare and classify polygons based on attributes and will explore the relationships between categories of quadrilaterals.”

The materials reviewed for Everyday Mathematics 4 Grade 2 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 the five areas of the Everyday Mathematics 4 classroom. “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 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 students 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. The three-part, activity-driven lesson structure helps you easily incorporate research-based instructional methods into your daily instruction. 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 Grade 2 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 Second Grade Everyday Mathematics.” Each unit 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 2-1, Grouping by 10s, Overview, Materials, Math Message, “Math Masters, pp. G11-G13; scissors; envelope, paper clip, or rubber band”

• Lesson 4-1, Clocks and Telling Time, Focus: Math Message, “Display two clock faces as shown in the margin. Which clock shows 4:30? Explain to a partner how you know. Use the words minute hand and hour hand.”

• Unit 5, Addition and Subtraction, Unit 5 Organizer, Unit 5 Materials, each lesson has materials under the following categories: Math Master, Activity Cards, Manipulative Kit, and Other Materials. For example, Lesson 5-3, materials listed, Math Masters: “pp.121; 123-125”, Activity Card: “66-67”, Manipulative Kit; “toolkit coins; per group: 4 each of number cards 0-10; per partnership: two 6-sided dice”, Other Materials: “slate; scissors.” 

• Unit 7, Whole Number Operations and Measurement and Data, Unit 7 Organizer, Unit 7 Materials, each lesson has materials under the following categories: Math Master, Activity Cards, Manipulative Kit, and Other Materials. For example, Lesson 7-8, materials listed, Math Masters: “pp.155 (1 copy per partnership); 202-206”, Activity Card: “94-95”, Manipulative Kit; “tape measure; per partnership; on 6-sided die”, Other Materials: “slate; stick-on notes; stick-on notes from Math Message.”

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Beginning-of-Year Assessment, Unit Assessments, Open Response Assessments, Cumulative Assessments, 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:

• Unit 3, More Fact Strategies, Unit Assessment, denotes standards and mathematical practices addressed for each problem. Problem 6, “Martin made a 10 to figure out the sum for 8 + 4. Explain Martin’s thinking.” (2.OA.2, SMP6)

• Unit 5, Addition and Subtraction, Open Response Assessment, denotes standards addressed for the open response. “Carlos wants to buy chocolate milk from the vending machine. The milk cost 75 cents. Carlos has 2 quarters, 5 dimes, and 5 nickels. Show at least four possible coin combinations Carolos could use to pay for the milk. Use N, D, and Q to record your answers.” (2.MD.8) 

• Mid-Year Assessment, denotes the aligned grade-level standard and mathematical practices. Problem 13, “Farid says the clock at the right reads 9:15. Yasmin says the clock reads 3:45. Who is correct? How do you know? Explain the other child’s mistake.” (2.MD.7, SMP3)

• Unit 8 Cumulative Assessment, denotes standards and mathematical practices addressed for each problem. Problem 3, “Solve. Try to make friendly numbers. 23+17+10+12= __, 16+31+14+19= ____ Pick one of the problems above. Explain how you added the numbers.” (2.NBT.6, 2.NBT.9, SMP6)

• End-of-Year Assessment, denotes the aligned mathematical practice. Problem 3, “Shawn has 24 crayons. His teacher gave him 24 more. Then he lost 8 crayons. How many crayons does he have now? Number model(s): ___.” (SMP4)

The materials reviewed for Everyday Mathematics 4 Grade 2  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 Preview Math Boxes. Summative Assessments include Mid-Year Assessment, End-of-Year Assessment, Unit Assessments, Open Response Assessment/Cumulative Assessments. All assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types: multiple choice, short answer, and constructed response. Examples include:

• Mid-Year Assessment, develops the full intent of standard 2.OA.2, fluently add and subtract within 20 using mental strategies. Problems 1, “a. 1 + 5 = ___. b. 9 + ___= 10. c. 4 - 1 = ___. d. 7 - ___ = 6.” Problem 2, “a. 7 + 7 = ___. b. 2 + 9 = ___. c. 10 + ___ = 20. d. 8 + 8 = ___. e. For problems 2a-2d, which fact does not fit the pattern? How is it different?”

• Unit 5, Addition and Subtraction, Unit Assessment, develops the full intent of 2.MD.6, represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. Problem 6, “Use an open number line to help you solve the story. Mrs. Peters had 22 pencils to give to her students. She bought 35 more. How many does she have now? ___ pencils.” (An open number line is pictured below the problem.)

• Unit 7, Whole Number Operations and Measurement and Data, Open Response Assessment, develops the full intent of MP2, reason abstractly and quantitatively as students determine if two sets of base-10 blocks represent the same number. Problems 1 and 2 “1.) Maria represented the number 349 like this (three flats, four longs, and nine units). Bill represented the number 349 like this (two flats, thirteen longs, and nineteen units). Write whether Maria, Bill, or both of them represented the number 349. 2) Explain your answer. You may include drawings.”

• End-of-Year Assessment, develops the full intent of MP3, construct viable arguments and critique the reasoning of others as students explain their strategy. Problem 10g, “Below, Marsha explained how she solved Problem 10d. I counted up from 178 to 200. I knew that was 22. I know that from 200 to 256 is 56 so I added 22 and 56 and got 78. Does Marha’s strategy work? ___ Explain.”

The materials reviewed for Everyday Mathematics 4 Grade 2 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 Unit 1, Establishing Routines, Lesson 1, include:

• Readiness, “For experience reading and comparing numbers, children put number cards in order. Write a sequence of numbers (such as 0-10) on index cards. Children work together to put the cards in order.”

• Enrichment, “To explore whole numbers represented as lengths from 0 on a number line, children complete number-line puzzles.”

• Extra Practice, “For additional practice with counting, children fill in missing numbers on a number line. Depending on children’s ability to read and order numbers, write one or more 1-, 2-, or 3-digit numbers on the number lines on Math Masters, page 3. Children review their work with a partner and explain how they found the missing numbers.”

• English Language Learner, Beginning ELL, “The Total Physical Response (TPR) technique allows beginning English language learners to participate in lesson activities even with minimal English language proficiency. To teach children actions they can use to demonstrate understanding, display a number line and then model actions as you say the following: Point to the number that comes before 5. Circle the number that comes after 6. Use your finger to hop on the number line from 7 to 10. After demonstrating several times with other numbers, have children respond to the same directions without your modeling.”

The materials reviewed for Everyday Mathematics 4 Grade 2 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 opposite the Lesson Opener Everyday Mathematics lessons incorporate varied grouping configurations which enables the kind of flexibility that is helpful when advanced learners in heterogeneous classrooms. Progress Check lessons include suggestions for extending assessment items for advanced learners and additional Challenge problems.” The 2-day Open Response and Re-Engagement lesson rubrics provide guidance for students in Exceeding Expectations. Examples include:

• Lesson 3-5, Subtraction Strategies: Counting Up and Counting Back, Enrichment, “To extend their understanding of subtraction, partners find differences between two 2-digit numbers by playing The Number-Grid Difference Game. On each turn, players mark two numbers on a number grid with counters and then find the difference.”

• Unit 4, Place Value and Measurement, Challenge, Problem 2, an analog clock is pictured with the time 12:10,“Simon thinks the time says 2:00. Is he correct? Explain how you know.”

• Lesson 7-2, Four or More Addends (Day 1), Focus: Solving the Open Response Problem, Adjusting the Activity, “If children quickly solve the problem and write a complete explanation, ask them to check their work by using a second strategy to solve the problem.”

The materials reviewed for Everyday Mathematics 4 Grade 2 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 Implementation Guide, English Language Learners, Everyday Mathematics addresses the needs of three groups of ELL based on their English language proficiency (beginning, emerging, and advanced), “Beginning English language learners fall into Entering (level 1) and Emerging (level 2) proficiencies. This group is typically within the first year of learning English; students' basic communication skills with everyday language are in their early development. These students require the most intensive language-related accommodations in order to access the mathematics in most lessons. Intermediate and Advanced English learners represent Levels 3, 4, and 5 (Developing, Expanding, and Bridging) in the English language proficiencies identified above. Students in this category are typically in their second to fourth year of learning English. They may be proficient with basic communications skills in English and able to carry on everyday conversations, but they are still developing proficiency with more cognitively demanding academic language of the mathematics class.” The ConnectED Teacher Center offers extended suggestions for working with diverse learners including English Language Learners. The Teacher’s Lesson Guide provides supplementary activities for beginning English Language Learners, Intermediate, and Advanced English Language Learners. In every lesson, there are Differentiation Support suggestions, English Language Learner for Beginning ELL located on the Differentiation Options Page and Focus section. Examples include:

• Lesson 1-4, Class Number Scroll, Differentiation Options, English Language Learner, Beginning ELL, “Introduce the work pattern by showing examples of simple patterns and examples that are not patterns, using materials such as pattern blocks, classroom objects, and strings of numbers. Point to examples of a pattern and say: This is a pattern. Point to the non-examples and say: This is not a pattern. As you point to examples and non-examples, ask yes/no questions. For example: Is this a pattern?”

• Lesson 6-6, Recording Addition Strategies, Differentiation Options, English Language Learner, Beginning ELL, “The expression ballpark estimate is a familiar usage in American English. Provide context for this term for English language learners by displaying visuals of a ballpark. Introduce the expressions in the ballpark and out of the ballpark. Gesture to one of the visuals to demonstrate what happens when a home run is hit out of the ballpark. Connect that to an estimate that is far away from the actual answer, or out of the ballpark. Estimates close to the actual answer are in the ballpark (such as a ground ball hit in the infield) and are therefore called ballpark estimates.”

• Lesson 9-7, Expand-and-Trade Subtractions, Part 2, Differentiation Options, English Language Learner, Beginning ELL, “Use role play to review the term trade. Give a child 10 pennies and place a dime in front of you on the table. Say: I need to trade. Please give me your 10 pennies, and I will give you my dime. Have children practice with equivalent amounts in pennies, nickels and dimes. As they trade, encourage them to use sentence frames like the following: I need to trade. Please give me ___, and I will give you ____.”

• 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 Grade 2 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 4-4, Numeration and Place Value, Focus: Matching Numbers to Base-10 Block Representations, materials reference use of base-10 blocks. “Display 200 + 40 + 8. Ask children to show the number using base-10 blocks.”

• Lesson 8-5, Attributes of 3-Dimensional Shapes, Focus: Describing Cubes, materials reference use of 3-Dimensional shapes. “Distribute a centimeter cube to each partnership. Have children share with their partners what they notice about the cube. After a few minutes, bring the class together to discuss children’s observations.”

• Lesson 9-1, Creating and Naming Equal Parts, Focus: Math Message, materials reference use of fraction squares. “Take 8 paper squares. Two children want to share a sandwich equally. Fold a paper square to show how to divide the sandwich into 2 equal shares. Draw a line on the fold. Talk with a partner. Did you both fold the square the same way?”