3rd Grade - Gateway 3

The materials reviewed for Everyday Mathematics 4 Grade 3 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 assists 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 3, Operations, Organizer, Coherence, provides an overview of content and expectations for the unit. “In Unit 2, children represented multiplication number stories with arrays and recorded a number model to match. In Grade 2, children used addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. They wrote an equation to express the total as a sum of equal addends. In Unit 5, children will use helper facts, doubling, and near-squares to solve for unknown products. In Grade 4, children will use multiplicative comparison statements to interpret a multiplication equation.”

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, Number Stories, Focus: Assessment Check-In, teacher guidance supports students in writing number stories. “Expect most children to make sense of and solve Problems 1-4 and to write number models with question marks for the unknowns. For children who struggle to make sense of and solve the problems, ask the guiding questions from the lesson. If children struggle to write a number model, suggest that they use a situation diagram or draw a picture to help organize the information from the story.”

• Lesson 4-3, Exploring Measures of Distance and Comparisons of Mass, Focus: Measuring Around Objects, Math Message, teacher guidance connects students' prior knowledge to new concepts. “Have children compare their measurements with a partner and think about whether they make sense. Invite volunteers to share how they measured and how they know whether their measures make sense. Expect responses to include that the distance around someone’s head is more than the distance around someone’s wrist because a head is bigger around than a wrist. Ask: Which measuring tools did you choose and why? When might it be useful to know these measurements?”

• Lesson 7-8, (Day 2): Finding Rules for Comparing Fractions, Common Misconception, teacher guidance addresses common misconceptions as students write rules for ordering fractions. “Watch for children who assume fractions with smaller denominators are smaller in size (or that fractions with larger denominators are larger in size). Encourage them to model two fractions, such as \frac{1}{3} and \frac{1}{4} using fraction circles. Ask: Would you get more pizza if you shared a pizza with three friends or four friends? Why?”

The materials reviewed for Everyday Mathematics 4 Grade 3 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 1-4, Number Lines and Rounding, Professional Development, explains connections between rounding and estimating. “Rounding can help with estimation. This lesson introduces a common rounding method that involves rounding to the nearest 10 or 100. The traditional version of this algorithm involves rounding up if the digit to the right of the target place is 5 or greater, and rounding down if the digit is less than 5.”

• Unit 3, Operations, Unit 3 Organizer, 3.G.1, supports teachers with concepts for work beyond the grade. “Links to the Future: In Grade 4, children will solve multistep number stories using all four operations and interpret the remainders in division number stories. They will explore different estimation strategies.”

• Unit 4, Measurement and Geometry, Unit 4 Organizer, 3.OA.8, provides support with explanations and examples of the more complex grade/course-level concepts. “Links to the Past: In Grade 2, children focused on specific attributes such as the number of sides, angles, and faces. They explored parallel sides.”

• Lesson 5-1, Exploring Equal Parts, Fractions of Different Wholes, and Area, Professional Development, explains concepts for work beyond the grade. “When working with fraction circles, many children may incorrectly think that the red circle is always the whole. For example, a pink piece may be the whole with a yellow piece representing 1-half. Children worked with other pieces as the whole in Lesson 2-12, Exploration A. Flexibility with the whole is important for solving real-world problems in which the size of the whole varies. It also lays a foundation for more complicated computation in later grades.”

• Lesson 6-4, Fact Power and Beat the Calculator, Professional Development, explains connections between multiplication and fluency. “The first five units of Third Grade Everyday Mathematics include many fact strategies to help children develop fluency with multiplication facts. By now, many children will already be automatic with beginning facts, such as 2s, 5s, and 10s, and squares- that is, they are able to recall these facts from memory or use a strategy automatically and instantaneously. For the rest of the year, meaningful practice through games, activities, and fact-extensions exercises will encourage children to progress beyond fluency to automaticity with basic multiplication facts.”

• Lesson 7-1, Liquid Volume, Professional Development, supports teachers with concepts for work beyond the grade. “In Everyday Mathematics, children begin by comparing liquid volume informally, followed by estimating in liters and finally estimating and measuring using liters and milliliters. As with other forms of measurement, such as length and mass, the need for more precise measurement motivates children's use of small, standard units. This progression done interactively, helps children understand volume concretely before exploring more abstract volume concepts in later grades.”

The materials reviewed for Everyday Mathematics 4 Grade 3 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:

• 3rd Grade 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. 

• 3rd Grade Math, Unit 2, Number Stories and Arrays, Organizer, Contents Lesson Map outlines lessons, aligned standards, and the lesson overview for each lesson. This is present for all units and allows teachers to identify targeted standards for any lesson.

• Lesson 6-3, Taking Inventory of Known Fact Strategies, Core Standards identified are 3.OA.1, 3.OA.5, and 3.OA.7. Lessons contain a consistent structure that includes an Overview, Before You Begin, Vocabulary, Warm-Up, Focus, Assessment Check-In, Practice, Minute Math, Math Boxes, and Home-Link. This provides an additional place to reference standards, and language of the standard, within each lesson.

• Mastery Expectations, 3.OA.1, “First Quarter: Represent multiplication as equal groups with concrete objects and drawings. Second Quarter: Represent multiplication as equal groups with arrays. Third Quarter: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. Fourth Quarter: Ongoing practice and application.” Mastery is expected in the Third Quarter. 

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, Math Tools, Time, and Multiplication, Organizer, Coherence, includes an overview of how the content in 3rd grade builds from previous grades and extends to future grades. “In Grade 2, children partitioned shapes into equal shares and described the whole as two-halves, three-thirds, or four-fourths. In Grade 4, children will extend the use of equal-sharing strategies to help develop an understanding of fraction equivalence. In Grade 5, children will interpret fraction and mixed-number quotients of whole numbers and will solve number stories that lead to quotients in the form of fractions or mixed numbers.” 

• Unit 4, Measurement and Geometry, Organizer, Coherence, includes an overview of how the content in 3rd grade builds from previous grades and extends to future grades. “In Grade 2, children focused on specific attributes such as the number of sides, angles, and faces. They explored parallel sides. In Grade 4, children will begin more formal geometry work with angles.”

• Unit 9, Multidigit Operations, Organizer, Coherence includes an overview of how the content in 3rd grade builds from previous grades and extends to future grades. “In Grade 2, children used Commutative and Associative properties of operations to add and subtract. In Grade 4, children will solve larger whole-number problems using strategies based on place value and the properties of operations.”

The materials reviewed for Everyday Mathematics 4 Grade 3 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, a distributed practice through 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 students 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 student can and should learn challenging, interesting, and useful mathematics. The program is designed to ensure that each of your students 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:

  • A Study to Explore How Gardner’s Multiple Intelligences Are Represented in Fourth Grade Everyday Mathematics Curriculum in the State of Texas.

  • 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.

  • Achievement Results for Second and Third Graders Using the Standards-Based Curriculum Everyday Mathematics.

  • The Relationship between Third and Fourth Grade Everyday Mathematics Assessment and Performance on the New Jersey Assessment of Skills and Knowledge in Fourth Grade (NJASK/4).

  • The Impact of a Reform-Based Elementary Mathematics Textbook on Students’ Fractional Number Sense.

  • A Study of the Effects of Everyday Mathematics on Student Achievement of Third, Fourth, and Fifth-grade students in a Large North Texas Urban School District.

The materials reviewed for Everyday Mathematics 4 Grade 3 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 Third 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:

• Unit 3, Operations, Unit 3 Organizer, Unit 3 Materials, teachers need, “pattern blocks; 25 centimeter cubes; number cards 1-9 (4 of each), slate; 1-foot square cardboard templates; colored paper; scissors; straightedge (optional); masking tape (optional); collection of objects (optional) in lesson 7.” 

• Lesson 5-5, Multiplication Facts Strategies, Doubling, Part 1, Overview, Materials, “Math Masters, p. TA19; centimeter cubes (50 per partnership); rectangles; Class Data Pad; slate; Math Journal 2, pp. 164-165; Minute Math; Math Journal 2, p. 167; Math Masters, p. 167.” Math Message, “Use centimeter cubes and grid paper to show your thinking.”

• Unit 7, Fractions, Unit 7 Organizer, Unit 7 Materials, teachers need, “Quick Look Cards 164, 165, 174; fraction circles; Class Fraction Number-Line Poster; fraction strips; straightedge; Fact Strategy Logs (optional); slate; fraction cards; comparison-symbol cards; paper (optional); scissors (optional); The Area and Perimeter Game Action Deck, Deck B. in lesson 10.” 

• Lesson 7-10, Justifying Fraction Comparisons, Math Message, “Use your fraction circles to solve this problem.” Focus: Modeling Fraction Comparisons, “Have children use their fraction strips and the Fraction Number-Line Post on journal page 229 (or the Class Fraction Number-Line Poster) to show that \frac{1}{6}>\frac{1}{8} with other tools.”

The materials reviewed for Everyday Mathematics 4 Grade 3 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 include:

• Unit 2, Number Stories and Arrays, Unit Assessment, denotes standards addressed for each problem. Problem 5, “Maria swam a total of 56 minutes over the weekend. She swam for 20 minutes on Saturday. How many minutes did she swim on Sunday?” (3.OA.3) 

• Unit 3, Operations, Open Response Assessment, denotes mathematical practices for the open response. Open Response, “Mia wants to solve this problem: 552-153=? She begins by making an estimate. Estimate: 550-150=400. Then she uses the expand-and-trade subtraction to find an exact answer, but her answer is not close to her estimate. ‘Oops,’ said Mia, ‘I didn’t cross out 500 and write 400.’ Explain why not changing 500 to 400 is a mistake.” (SMP3)

• Mid-Year Assessment, denotes standards addressed for each problem. Problem 2, “A brown bear has a mass of about 318 kilograms. A grizzly bear has a mass of about 363 kilograms. About how much more mass does the grizzly bear have than the brown bear? Solve. Show your work.” (3.MD.2)

• Unit 6, More Operations, Cumulative Assessment, denotes mathematical practices addressed for each problem. Problem 7, “Draw a picture and use words to explain why 2\times8=8\times2.” (SMP8)

• End-of-Year Assessment, denotes standards addressed for each problem. Problem 9, “A collection of 6 movie tickets is shared equally among 3 families. How many tickets does each family get? What fractions of the collection of movie tickets does each family get?” (3.NF.1)

The materials reviewed for Everyday Mathematics 4 Grade 3 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:

• Unit 1, Math Tools, Time, and Multiplication, Open Response Assessment, supports the full intent of MP4, model with mathematics, as students use addition and subtraction strategies to figure out time. Problem 2, “Carols leaves for school at 8:00 A.M. Cheryl leaves 5 minutes later. a. Who gets to school first? b. Explain how you figured it out.” 

• Mid-Year Assessment, develops the full intent of standard 3.OA.1, interpret products of whole numbers. Problem 1, “Explain how 2\times9=18 matches the array. Payton wants to use 2\times9=18 as a helper fact to solve 3\times9=? Use the helper fact and the above array to help Payton. Explain your thinking.” 

• Unit 7, Fractions, Unit Assessment, problems support the full intent of MP2, reason abstractly and quantitatively, as students make sense of quantities and their relationships as they partition a number line with increments of \frac{1}{4}. Problem 6, “Partition the number line into fourths and label each tick mark. You may use the fraction strip to help.” A fraction strip shows \frac{0}{4} to \frac{?}{4} on a number line. 

• End-of-Year Assessment, develops the full intent of 3.G,1, understand that shapes in different categories), and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Problem 21, “Circle all the rectangles, mark an X on all squares, and sade all the rhombuses. Explain why the shapes you circled are rectangles. Draw another quadrilateral that is not a rectangle, a square, or a rhombus.”

The materials reviewed for Everyday Mathematics 4 Grade 3 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 6, More Operations, Lesson 4, include:

• Readiness, “To prepare children for playing Beat the Calculator, have them use calculators to solve missing-factor problems. As needed, remind children how to enter numbers and clear calculators. Pose problems verbally or display them in a table. Explain that they should use multiplication to find the answers. For example: Start with 3. Change to 6. How? Start with 5. Change to 30. How? Allow children to experiment with their calculators to find the missing factors, including using guess-and-check. If needed, rephrase and display problems as 3 times what equals 6? 3\times ___ = 6? Have children explain their thinking to the group.”

• Enrichment, “To apply children’s understanding of multiplication and division, have them complete two-rule Frames-and-Arrows puzzles on Math Masters, page 196. Note the rules will not always alternate ABAB. Have children color-code their arrows with crayons to distinguish one rule from another. When children finish, have them discuss their solution strategies and explain any useful patterns they identified while solving.”

• Extra Practice, “To provide additional practice with multiplication and division facts, have children generate sets of multiplication facts and compare strategies used to solve them. Some children may benefit from a small strip of tape to secure the fact wheel to their slate.”

• English Language Learner, Beginning ELL, “Use gestures to scaffold the terms Caller, Calculator, and Brain from Beat the Calculator. Point to your mouth and a multiplication fact and say: I am the Caller. I will call out a fact. I will not say the answer. Point to a child’s head and say: You are the Brain. You will solve the problem in your head. Point to the calculator and demonstrate entering the multiplication fact as you point to another child and say: You are the Calculator. You will solve the multiplication fact on the calculator.”

The materials reviewed for Everyday Mathematics 4 Grade 3 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:

• Unit 1, Math Tools, Time, and Multiplication, Challenge, Problem 2, “Don and Molly played Number-Grid Difference. The object of the game is to have the lower sum of 5 scores. Don picked 3 and 5 and made the number 35. Molly picked 8 and 5. What number should Molly make? Explain your answer.”

• Lesson 6-3, Taking Inventory of Know Fact Strategies, Enrichment, “To extend children’s application of multiplication strategies, have them choose strategies and develop rules to multiply 11 by single-digit numbers on Math Masters, page 193.”

• Lesson 7-6, Fractions on a Number Line, Part 2, Enrichment, “To apply children’s understanding of fractions greater than 1, have them locate fractions between whole numbers on a number line. Ask children to defend the placement of their fractions and make changes as needed.”

The materials reviewed for Everyday Mathematics 4 Grade 3 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 3-5, Counting-Up Subtraction, Differentiation Options, English Language Learner Beginning ELL, “Display a number line vertically, with the smaller numbers at the bottom. Demonstrate counting up as you move your hand up along the number line. Orally and with gestures, direct children to count up on a number line. For example, say, Count up from 25, gesturing to 25, then 26, 27, 28, and so on as children count. Once children can count up as you gesture, point to a number and have them count up without gestures. Provide for oral practice by asking children short-response questions, such as: ``How will you count?” 

• Lesson 6-3, Taking Inventory of Known Fact Strategies, Differentiating Lesson Activities, Analyzing Multiplication Facts Strategies, “Scaffold to help partnerships think together about the facts to identify efficient and appropriate strategies for solving them, as well as to plan for using multiple representations to communicate their thinking. Post a menu of questions and response starters. For example: Partner A: Does this fact remind you of other facts we already know? Partner B: It reminds me of ___ Do you agree? Do you think we should try the ___ strategy? Partner A: I think/don’t think that strategy would be appropriate because ___Perhaps we could ___ Partner B: Do you think it would be efficient to use the ___ strategy? Partner A: That strategy would/would not help us get the answer quickly.”

• Lesson 8-5, Playing Factor Bingo, English Language Learner Beginning ELL, “Scaffold the terms factor and product to prepare children to play Factor Bingo. Display a multiplication fact. Circle and label the factors, and then underline and label the product. Draw a square around the multiplication symbol and label it groups of, times, and multiplied by. Point to the labels as you explain the directions for the game.”

• 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 3 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 2-8, (Day 1): Picturing Division, Focus: Solving the Open Response Problem, materials reference use of counters and drawings. “Make slates, markers, and counters available so children can act out the problem, but remind them to record drawings and words that describe their thinking on paper.” 

• Lesson 5-2, Representing Fractions, Focus: Math Message, materials reference use of fraction circles. “The pink fraction circle piece is the whole. Show 1-third of the pink piece. Explain to your partner how you know it shows 1-third.”

• Lesson 7-4, Fraction Stirps, Focus: Math Message, materials reference use of fraction strips. “Cut out five fraction strips. Each strip is one whole. Fold one strip in half. What fraction names each part of the strip?”