5th Grade - Gateway 3

The materials reviewed for Everyday Mathematics 4 Grade 5 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 students 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 2, Whole Number Place Value and Operations, Organizer, Coherence, provides an overview of content and expectations for the unit. “In Grade 4, students used partial-products multiplication and lattice multiplication to solve multi-digit multiplication problems. Through Grade 5, students will use U.S. traditional multiplication to solve multiplication problems in mathematical and rich, real-world contexts. In Grade 6, students will use U.S.traditional multiplication to solve multi-digit decimal multiplication problems.”

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 2-5, U.S. Traditional Multiplication, Part 2, Focus: Assessment Check-In, teacher guidance supports students in solving multiplication problems. “Expect most students to be able to solve 423\star3, which does not involve writing any digits above the line, using U.S. traditional multiplication. Some may also be able to solve 2,681\star5, which does involve writing digits above the line and remembering to add them.”

• Lesson 4-3, Representing Decimals in Expanded Form, Focus: Introducing Expanded Form for Decimals, Math Message Follow-Up, teacher guidance connects students' prior knowledge to new concepts. “Ask: What did you notice as you added different colors of shading to your grid? Display a shaded grid for the Math Message problem. Ask: What number do the first 3 columns of shading represent? What number does the 1 square in the second color represent? What number do the 2 tiny rectangles shaded in the third color represent? Point out that the shading shows how 0.3, 0.01, and 0.002 combine to make 0.312. Ask: What operation is used to show combining or putting together? Display the number sentence 0.312=0.3+0.01+0.002. Remind students that this way of writing a number is called expanded form. Highlight how expanded form shows the number broken apart by place value and shows the sum of the value of each digit.”

• Lesson 7-3, Multiplication of Mixed Numbers, Part 2, Common Misconception, teacher guidance addresses common misconceptions as students use tiling to differentiate square foot. “Students may confuse \frac{1}{2} of square foot, as shown in Figure 1, with a \frac{1}{2} foot square (a square that is \frac{1}{2} foot by \frac{1}{2} foot), as shown in Figure 2. When speaking, be sure to differentiate between fractions of a square area and squares with fractional side lengths.”

The materials reviewed for Everyday Mathematics 4 Grade 5 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, Two Formulas for Volume, Professional Development, explains finding the volume of rectangular prisms. “Counting the cubes that fit into the bottom of a rectangular prism and finding the area of the base of the prism result in the same numerical value, but they are two different measurements. The number of cubes that pack the first layer of a prism is the volume of the first layer, which is a 3-dimensional measurement, while the area of the base is a 2-dimensional measurement. They have the same numerical value because, to find the volume, the area is multiplied by 1 to account for the height of the layer. Multiplying by 1 does not change the numerical value, but it does change the unit of measurement from square units to cubic units, thereby making it a different measurement.”

• Lesson 2-4, U.S. Traditional Multiplication, Part 1, Professional Development, explains the traditional multiplication algorithm. “Everyday Mathematics calls the algorithm introduced in this lesson U.S. traditional multiplication because it is not the standard algorithm in other parts of the world. The Grade 5 standards require students to fluently multiply multi-digit whole numbers using U.S. traditional multiplication, so it is the focus of Fifth Grade Everyday Mathematics lessons. Students should learn this method, but if they prefer a different multiplication strategy, they should be allowed to use it to solve multiplication problems.”

• Unit 3, Fraction Concepts, Addition, and Subtraction, Unit 3 Organizer, 5.NF.5, provides support with explanations and examples of the more complex grade/course-level concepts. “Links to the Past: In Grade 4, students used visual fraction models and other strategies to solve number stories involving multiplication of a fraction by a whole number.”

• Lesson 4-7, Playing Hidden Treasure, Professional Development, supports teachers with concepts for work beyond the grade. “There are two common ways to look at distances in the coordinate plane. One type of distance is practical distance. On a coordinate grid, the practical distance between two points is along horizontal and vertical grid lines. Practical distance is sometimes called taxicab distance because it measures the distance along a route a taxicab might take. The other type of distance is straight line distance. On a coordinate plane, the straight-line distance between two points is the length of the line segment that connects the points. In Grade 5 students explore practical distance only. They will explore straight-line distance in later grades.”

• Lesson 5-13, Fraction Division, Part 1, Professional Development, supports teachers with concepts for work beyond the grade. “Lessons 5-13 and 5-14 build conceptual understanding of fraction division. According to the standards (5.NF.7), fraction division problems in Grade 5 are limited to the division of unit fractions by whole numbers and vice versa. Students are expected to use visual models and informal reasoning to solve them. They are not expected to use a generalized method of fraction division. Students will be introduced to an algorithm for fraction division in Grade 6. To build a conceptual understanding of division, students are asked to write multiple number models. The initial number model with a variable is intended to help students identify problems as division situations. The number models for the summary division sentence and multiplication check are designed to emphasize the relationship between division and multiplication as described in 5.NF.7a.”

• Unit 6, Investigations in Measurement: Decimal Multiplication and Division, Unit 6 Organizer, 5.MD.1, supports teachers with concepts for work beyond the grade. “Links to the Future: In Grade 6, students will use ratio reasoning to convert measurement units.”

The materials reviewed for Everyday Mathematics 4 Grade 5 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:

• 5th 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. 

• 5th Grade Math, Unit 1, Area and Volume, 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 8-4, Extending Line Symmetry, Core Standards identified are 5.NBT.2, 5.MD.3, 5.MD.5, and 5.MD.5b. 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, 5.NBT.4, “First Quarter: No expectations for mastery at this point. Second Quarter: Use grids, number lines, or a rounding shortcut to round decimals to the nearest tenth or hundredth in cases when rounding only affects one digit. Third Quarter: Use place value understanding to round decimals to any place. 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 2, Fraction Concepts, Addition, and Subtraction, Organizer, Coherence, includes an overview of how the content in 5th grade builds from previous grades and extends to future grades. “In Grade 4, students worked with place-value concepts in whole numbers through 1,000,000. In Grade 6, students will extend their understanding of place value by applying their reasoning to make sense of decimal computation.” 

• Unit 5, Operations with Fractions, Organizer, Coherence, includes an overview of how the content in 5th grade builds from previous grades and extends to future grades. “In Grade 4, students explored and explained a multiplication rule for producing equivalent fractions. In Grade 6, students will consider the sizes of dividends and divisors to help them make sense of the size of quotients when they divide fractions.”

• Unit 6, Investigations in Measurement: Decimal Multiplication and Division, Organizer, Coherence includes an overview of how the content in 5th grade builds from previous grades and extends to future grades. “In Grade 4, students made line plots to display fractional measurement data and answered questions about that data. In Grade 6, students will collect and display data using dot plots, histograms, and box plots.”

The materials reviewed for Everyday Mathematics 4 Grade 5 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 5 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 Fifth 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 3-2, Connecting Fractions and Division, Part 2, Overview, Materials, “slate; fraction circles; Math Journal 1, pp. 74-75; Student Reference Book p. 318; per partnership: Math Masters p. G11; two 6-sided dice; Math Journal 1, p. 76; Math Masters, p. 82.” Math Message, “Use your fraction circle pieces to help you.”

• Unit 5, Operations with Fractions, Unit 5 Organizer, Unit 5 Materials, teachers need, “fraction circles; per partnership: cards 0-10 (4 of each), 4 counters; slate; per partnership: calculator (optional); coin (optional) in lesson 1.” 

• Unit 7, Multiplication of Mixed Numbers; Geometry; Graphs, Unit 7 Organizer, Unit 7 Materials, teachers need, “fraction circles (optional); per partnership: number cards 1-8 (4 of each); Fraction Number Lines Poster; per group: Math Journal 2, Activity Sheet 19 (Spoon Scramble cards); scissors; 3 spoons in lesson 2.” 

• Lesson 7-2, Multiplication of Mixed Numbers, Part 2, Math Message, “You may use fraction circle pieces or the Fraction Number Lines Poster to help you.”

The materials reviewed for Everyday Mathematics 4 Grade 5 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, Fraction Concepts, Addition, and Subtraction, Unit Assessment, denotes standards addressed for each problem. Problem 2, “Three families live in the same apartment building. They decided to share a giant 220-ounce of laundry detergent. If the families split the detergent equally, how many ounces of laundry detergent will each family get?” (5.NBT.6)

• Mid-Year Assessment, denotes standards addressed for each problem. Problem 2, “___ = 180\div{13+17}.” (5.OA.1)

• Unit 5, Operations with Fractions, Open Response Assessment, denotes mathematical practices for the open response. “Fred’s Restaurant is famous for its fresh fruit smoothies. Fred’s recipe calls for \frac{1}{3} of an apple, \frac{1}{4} of a lemon, and \frac{2}{3} of a peach to make a single smoothie. A family of 6 arrives at Fred’s restaurant. How much of each fruit does Fred need to make smoothies for the entire family? Use drawings, numbers, or other models to show your work. Be sure to use units in your answer.” (SMP4)

• Unit 8, Application of Measurement, Computation, and Graphing, Cumulative Assessment, denotes mathematical practices addressed for each problem. Problem 6, “Explain how you solve Problem 5 ($$88.4\div2.6$$).” (SMP6)

• End-of-Year Assessment, denotes standards addressed for each problem. Problem 10, Gary walked 2\fra{1}{3}miles on Monday, 3\frac{1}{2}miles on Tuesday, and 1\frac{3}{4}miles on Wednesday. How many miles did he walk in the three days?” (5.NF.1)

The materials reviewed for Everyday Mathematics 4 Grade 5 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, Area and Volume, Open Response Assessment, supports the full intent of MP6, attend to precision, as students explain calculate the volume of a rectangular prism and soccer balls. Problem 2, “Monica began to fill a box with the soccer balls and then took a break. The picture below shows what the box looked like when she took her break. Will all 30 soccer balls fit in this box? How do you know?” 

• Mid-Year Assessment, develops the full intent of standard 5.OA.2, write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Problem 14, “This week 6 different students paid $2.00 each in fines to the school librarian. The librarian also received a $60.00 donation from a local business. She spent $37.50 to buy books and supplies. Write an expression that shows the amount of money the librarian has at the end of the week. Do not solve the problem.” 

• Unit 5, Operations with Fractions, Unit Assessment, supports the full intent of MP7, look for and express regularity in repeated reasoning as students look for a strategy to find common denominators. Problem 2, “Describe the strategy you used to find a common denominator for \frac{3}{8} and \frac{2}{5} in problem 1b.” 

• End-of-Year Assessment, develops the full intent of 5.NBT.1, recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and \frac{1}{10} of what it represents in the place to its left. Problem 3, “a. Write the value of 2 in each of the following numbers. 32,048,671 ___. 214.9 ___. 406.972 ___. 0.028 ___. b. Look carefully at your answers to Part a. How does the value of the 2 change as it shifts one place to the left? To the right? c. Use the information in Parts a and b to write a rule about the value of any digit when it moves one place to the left or one place to the right in a number.”

The materials reviewed for Everyday Mathematics 4 Grade 5 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 3, Fraction Concepts, Addition and Subtraction, Lesson 7, include:

• Readiness, “To prepare for using benchmarks to estimate, students compare fractions to \frac{1}{2} and locate them on a number line. Have students represent fractions between 0 and 1 with fraction circles. Ask them whether each fraction is less than, equal to, or greater than \frac{1}{2} and have them explain their thinking. They record the fractions in the appropriate box on Math Masters, page 97, and then complete the problems at the bottom of the page. Discuss students’ responses.”

• Enrichment, “To further develop fraction number sense and explore using benchmarks, students play Fraction Top-It (Estimation Version). In this version, they apply their knowledge of benchmarks to estimate sums and compare them.”

• Extra Practice, “For more practice using benchmarks to estimate sums and differences, students complete Math Masters, page 98. They make sense of number stories and match the stories to estimates shown on a number line.”

• English Language Learner, Beginning ELL, “Make think-aloud statements using the term scaffold student’s understanding of the term benchmark as a point of reference, or a standard according to which things are judged. For example, I will use the fraction \frac{1}{2} to help me think about the size of \frac{5}{8}. I will use \frac{1}{2} as a benchmark to help me think about the size of \frac{5}{8}. Students may benefit from seeing how benchmarks can be useful in the same way helper facts are useful for thinking about nearby facts.”

The materials reviewed for Everyday Mathematics 4 Grade 5 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 5, Operations with Fractions, Challenge, Problem 4, “What is \frac{1}{2} of \frac{2}{3} of \frac{3}{4} of 1? Explain how you found your answer.”

• Lesson 6-5, Working With Data in Line Plots, Enrichment, “To extend their work using line plots to solve problems, students create line plots showing the scores of two competitive divers. They calculate the divers’ final scores in two ways: first by using all seven judges’ scores and then by following competitive diving rules, where the two highest and two lowest scores are thrown out. Students compare results and consider why using the scoring rule makes sense.”

• Lesson 7-12, Rules, Tables, and Graphs, Part 2, Enrichment, “To extend their understanding of constructing graphs from data, students represent race results with multiple graphs. Students conduct two different types of races along a 5-meter course. They graph the results for each participant, then compare and discuss the resulting graphs.”

The materials reviewed for Everyday Mathematics 4 Grade 5 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 1-8, Measuring Volume By Iterating Layers, Differentiating Lesson Activities, Using Layers to Solve Cube-Stacking Problems, “Scaffold to help students justify their volume calculations by providing questions-and-response prompts. For example: Can you explain why you ___? If I ___ then we need to ___ because ___ What does that mean? Let me show you what I mean. To paraphrase what you just said you ___.”

• Lesson 3-9, Introduction to Adding and Subtracting Fractions and Mixed Numbers,  English Language Learner Beginning ELL, “Build on students’ understanding of the word remainder as what remains so that they make a connection between the terms remain and remainder. Display a number of objects that do not divide evenly and say: We are going to share these ____ between the 3 of us: 1 for you, 1 for you, and 1 for me…. Point to the remaining objects at the end, saying: These are left over. This is what remains. These are the remainder. Partners do the same using another set of objects, repeating the think-aloud. Ask students to point to the remainder after each round.” 

• Lesson 7-9, Collecting and Using Fractional Data, Differentiation Options, English Language Learner Beginning ELL, “In this lesson students work with the word span, which begins with the consonant cluster sp. English language learners may find it difficult to pronounce this sound in the initial position if it does not occur in that position in their home language. Students may add the vowel sound /e/ to the English pronunciation of span to make it easier to pronounce. Point out the correct pronunciation and articulate it carefully. List other words that begin with the sp sound.” 

• 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 5 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 1-7, Measuring Volume by Counting Cubes, Focus: Math Message, materials reference use of unit cubes. “Cut out and assemble Rectangular Prisms A, B, and C. Take 25 cubes. Estimate how many cubes will fit into each prism. Record your estimates in the second column of the table on Journal page 18.” 

• Lesson 3-1, Connecting Fractions and Division, Part 1, Focus: Modeling with Fraction Circle Pieces, materials reference use of fraction circles. “Make the point that fraction circle pieces are being used to model the situation.” 

• Lesson 4-14, Addition and Subtraction of Money, Focus: Introducing Spend and Save, materials reference use of coins, bills, and counters. “Then distribute one Spend and Save Record Sheet to each student and 1 coin and 1 counter to each partnership. Make play bills and coins available to students who might need them to play the game.”