1st Grade - Gateway 3

The materials reviewed for Everyday Mathematics 4 Grade 1 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 4, Length and Addition Fact, Lesson Organizer, Coherence, 1. MD.2, provides an overview of content and expectations for the unit. “In Kindergarten, children identified measurable attributes of objects, including length. They also used direct comparison to determine which of the two objects is longer. In Unit 5, children will be presented with more complicated paths, made up of several straight lines joined together, and will use an iteration of a single paper clip to determine the total length. In Grade 2, children will measure a single object using two different units of measure and discuss why the length measurements differed based on the chosen unit.”

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 4-11, 10 More, 10 Less, Focus: Assessment Check-In, teacher guidance supports students in identifying 10 more or less than a given number. “Observe whether children can find 10 more and 10 less than a given number while playing What’s Your Way? Expect most children to do this using a number grid. Have children who struggle discuss patterns they see as they count by 10s on a number grid. Have those who exceed expectations complete the Enrichment activity for this lesson. Children practice finding 10 more and 10 less throughout Grade 1.”

• Lesson 6-6, Introducing Making 10, Focus: Developing the Making-10 Strategy, Math Message Follow-Up, teacher guidance connects students' prior knowledge to new concepts. “DIsplay a double ten frame (Math Masters, p. TA19). Have children use their own double ten frames (Math Journal 1, Activity Sheet 3) and counters to share their thinking. Although children may represent the numbers in the Math Message in a variety of ways, emphasize filling one ten frame with ten and then representing the remaining ones on the second ten frame.”

• Lesson 8-4, Sharing Paper Squares (Day 2), Focus: Solving the Open Response Problem, Common Misconception, teacher guidance addressed common misconceptions as students decompose shapes. “Children sometimes do not understand that decomposing shapes into a larger number of equal shapes creates smaller shares. In this problem, for example, children may say that the boys get more because there are more boys (4 pieces is more than 2 pieces). As you review children’s work, plan to address this misconception through the re-engagement discussion.”

The materials reviewed for Everyday Mathematics 4 Grade 1 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 4-1, Introducing Length Measurement, Focus: Introduction Length Comparison, Professional Development, teacher guidance explains the concept of indirect comparison. “Making a direct comparison of two objects involves clearly observing and comparing the aspects of those objects. In the first part of the activity, children place the objects next to each other to compare their lengths directly. In the second part of the activity, they cannot directly compare two edges of the same box, so they use an intermediary (such as string, strips of paper, paper clips, or inches) to measure each object. Then they compare the results. This is called indirect comparison.”

• Lesson 5-11, Two-Digit Addition and Subtraction, Focus: Adding Animal Weights, Professional Development, supports teachers with concepts for work beyond the grade. “The sample strategies listed in this lesson demonstrate children’s understanding of one or more of the following: place value, properties of operations, and the relationship between addition and subtraction. Although these are not the only possible strategies, they are listed here to help you connect your class’s work to 1.NBT.4 and 1.NBT.6. Children are not expected to use these phrases.”

• Lesson 7-4, More Subtraction Fact Strategies, Focus: Comparing Counting Up and Counting Back to Subtract, Professional Development, teacher guidance explains the strategy. “Children were informally introduced to counting up as a subtraction strategy in Unit 2. It is a powerful subtraction fact strategy because it makes use of the relationship between addition and subtraction. 1.OA.4 Counting up to subtract is an accessible strategy that improves children's accuracy. It also transfers well to multi-digit computation.”

• Lesson 7-8, Finding Unknowns: “What’s My Rule?”, Focus: Introducing “What’s My Rule?”, Professional Development, teacher guidance explains a routine that works with number patterns. “The Everyday Mathematics routine, “What’s My Rule?”, provides practice with number patterns and arithmetic facts as well as a format for thinking about relationships between pairs of numbers in a function. A function machine is a diagram or metaphor that indicates the input and output numbers in “What’s My Rule?” tables are related.”

• Lesson 8-2, Halves, Focus: Naming Shares, Note, supports teachers with concepts for work beyond the grade. “Although it may come up in discussion, avoid using formal fraction notation, such as \frac{1}{2}, to name one or all of the shares. The focus in Grade 1 is using words and pictures to describe equal shares. Fractional notation will be introduced in later grades.”

• Lesson 9-5, Vending Machine Addition and Subtraction, Focus: Adding 2-Digit Vending Machine Prices, Professional Development, teacher guidance clarifies sample strategies. “The sample strategies listed in this lesson demonstrate children’s understanding of one or more of the following: place value, properties of operations, and the relationship between addition and subtraction. These are not the only possible strategies. They are listed as they are to help you connect your class’s work to 1.NBT.4 and 1.NBT.6. Do not expect children to use these phrases.”

The materials reviewed for Everyday Mathematics 4 Grade 1 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 1 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, 1.OA.4, “First Quarter: Understand that some addition strategies can be used to solve subtraction problems. For example, think ‘What do I need to add to 7 in order to get 10?’ Second Quarter: Understand that a difference can be found with both subtraction and addition. Third Quarter: Understand subtraction as an unknown addend problem. For example, subtract 10-8 by finding the number that makes 10 when added to 8. Fourth Quarter: Ongoing practice and application.”

• Lesson 2-7, Labeling Counts, standards identified in the Focus and Practice are identified as 1.OA.5, 1.NBT.1. 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 1, Counting, Unit 1 Organizer, Coherence, 1.NBT.3, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “In Kindergarten, children learned to compare numbers less than or equal to 10 when expressed in numeral form. In Grade 2, children will use their understanding of place value to compare numbers up to 1000.”

• Unit 5, Place Value Comparisons, Unit 5 Organizer, Coherence, 1.NBT.4, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “In Kindergarten, children developed an understanding of teen numbers as 10 ones and some further ones. In Grade 2, they will expand upon those strategies to make sense of addition and subtraction within 1000.”

• Unit 9, Two-Digit Addition and Subtraction and Review, Unit 9 Organizer, Coherence, 1.MD.2, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “In Unit 5, children used iteration of a single paper clip to determine lengths of pathways. This work built upon Kindergarten experiences identifying measurable attributes of objects, including length. In Grade 2, children will learn to use tools such as yardsticks and measuring tapes to measure lengths with standard units.”

The materials reviewed for Everyday Mathematics 4 Grade 1 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 children using other programs. They develop powerful, life-long habits of mind such as perseverance, creative thinking, and the ability to express and defend their reasoning.”

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

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

• Teacher’s Lesson Guide, Everyday Mathematics in Your Classroom, The Everyday Mathematics Lesson, outlines the design of lessons. “Lessons are designed to help teachers facilitate instruction and engineered to accommodate flexible group models. 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 1 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 First 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 4, Length and Addition Facts, Unit 4 Organizer, Unit 4 Materials, each lesson has materials under the following categories: Math Masters, Activity Cards, Manipulative Kit, and Other Materials. For example, Lesson 4-8, materials listed, Math Masters: “pp.28 (optional); 111-113; G26 (optional); G27”, Activity Card: “50”, Manipulative Kit; “Quick Look Cards 60, 64, 69, 84, 86, 88, 90, 92, 93; Ten Frame; per partnership; 2 dot dice, 10 pennies, 10 counters”, Other Materials: “slate; Ten Frame; timer or stopwatch; per partnership; plastic cup.”

• Lesson 5-11, Two-Digit Addition and Subtraction, Overview, Materials: Math Message, “number line, number grid base-10 blocks, counters (optional).”

• Lesson 7-5, Attributes of Shapes, Math Message, “Choose a block. Record everything you notice about your block.” Note: “Place a set of attribute blocks in a box or basket near the Math Message. Because of the differences among attribute block sets, the activities in this lesson are generic. Adapt the activities to the blocks that you are using.”

• Unit 8, Geometry, Unit 8 Organizer, Unit 8 Materials, each lesson has materials under the following categories: Math Masters, Activity Cards, Manipulative Kit, and Other Materials. For example, Lesson 8-6, materials listed, Math Masters: “pp.240-241; TA4; TA40; G58 (optional)”, Activity Card: “99”, Manipulative Kit; “base-10 blocks; 3-dimensional blocks; pattern blocks”, Other Materials: “slate; ball; can; box; everyday objects; paper bag, scissors, glue.”

The materials reviewed for Everyday Mathematics 4 Grade 1 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 1, Counting, Unit Assessment, denotes standards and mathematical practices addressed for each problem. Problem 2, “How many spotted dogs are there? ___spotted dogs. How many dogs are there in all? ___dogs.” 5 dogs are pictured. (1.NBT.1, SMP2)

• Unit 3, Number Stories, Open Response Assessment, denotes standards addressed for the open response. “Use the number line to help you solve the story. You are collecting leaves. You have 3 leaves in your pocket. You pick up some more leaves. Now you have 10 leaves. How many leaves did you pick up? Write how you solved it.” (1.OA.1, 1.OA.6) 

• Unit 4, Length and Addition Fact, Cumulative Assessment, denotes mathematical practices addressed for each problem. Problem 4, “Fill in the missing numbers. Rule: Count up by 5s. 5, 10, ___, ___, ___, ___. How did you know which numbers to put in the empty frames?” (SMP7)

• Mid-Year Assessment, denotes standards addressed for each problem. Problem 10, “Look for three things in the room that are longer than a crayon. Name them from shortest to longest.” (1.MD.1)

• End-of-Year Assessment, denotes the mathematical practice addressed for each problem. Problem 17, “Alex knows that 13+8=21. He says, ‘That means that 8+13=21.’ Is Alex correct? Explain.” (SMP3)

The materials reviewed for Everyday Mathematics 4 Grade 1 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 2, Introducing Addition, Cumulative Assessment, develops the full intent of MP2, reason abstractly and quantitatively as students understand the relationships between problem scenarios and mathematical representations. Problem 1, “How many tally marks? (12 tally marks are shown.) ___ tally marks.”

• Mid-Year Assessment, supports the full intent of MP1, make sense of problems and persevere in solving them as students determine who is taller by using comparison statements. Problem 11, “Anna and Mark are comparing how tall they are. Mark says, “I am taller than Anna. But I am shorter than my friend Lisa.” Who is taller, Anna or Lisa? Explain how you know.” 

• Unit 5, Place Value and Comparisons, Unit Assessment, develops the full intent of 1.NBT.2, understand that the two digits of a two-digit number represent amounts of tens and ones. Problem 5, “What is the value of 2 in 23? ___ What is the value of 3 in 23? ____”

• End-of-Year Assessment, develops the full intent of 1.OA.7, understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. Problem 6, “Write True or False. 8 = 8 ___. 6+6=14. 10=7+3+1. 9-6=8-5.”

The materials reviewed for Everyday Mathematics 4 Grade 1 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 7, Subtraction Fact Strategies and Attributes of Shapes, Lesson 7, include:

• Readiness, “To provide additional experience with attributes of shapes, have children use the Shape Sorting Cards prepared from Math Masters, page 203. Ask children to find three shapes that have one or more attributes in common. Then have them determine a rule that tells the commonality. Then have children choose three more shapes with at least one attribute in common and suggest a rule that tells what those shapes have in common. Repeat as time permits.”

• Enrichment, “To extend children's understandings of defining and nondefining attributes, have them build composite polygons with pattern blocks. Children discuss the attributes of polygons and composite polygons. They determine whether shapes are the same after being rotated.”

• Extra Practice, “To provide practice comparing attributes, have children play Attribute Train. For detailed instructions, see Lesson 7-6. Observe: Which children change only one attribute when placing the next shape? Discuss: Which attribute did you change when you chose this shape? What can you do if you do not know what shape to play next?”

• English Language Learner, Beginning ELL, “Prepare children for discussing shapes by looking at examples. Display pairs of shapes with one differing attribute. Ask yes/no questions about color, shape, and size to identify how the shapes are the same and different. For example: Are all the shapes squares? Are all the shapes the same color? Are they the same shape? Use the terms in common and same to summarize answers. Repeat with the words different and not the same.”

The materials reviewed for Everyday Mathematics 4 Grade 1 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 6, Addition Fact Strategies, Challenge, “Fill the name-collection box for 11 using these rules: The names must use either addition or subtraction. Each Name can only use two numbers between 1 and 20. For example, 1+10=11 and 12-1=11. 1+10 and 12-1 are already in the box. With these rules, there are nineteen different names for the number 11. Finish writing ALL nineteen names for 11 in the name-collection box below.”

• Lesson 7-1, Fact Families, Focus: Writing Fact Families, Enrichment, “To further explore finding unknowns in number sentences and recording fact families, have children write facts and complete their partners’ fact families.”

• Lesson 9-1, Review: Measurement, Focus: Measuring with Rulers, Adjusting the Activity, “Children who are already familiar with standard rulers may choose to write the numerals where units meet on their paper-clip rulers. Connect this representation to a number line by making sure that they write 1 at the end (rather than the beginning) of the first unit.”

The materials reviewed for Everyday Mathematics 4 Grade 1 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 1-5, 1 More, 1 Less, Differentiation Options, English Language Learner, Beginning ELL, “Show a picture of a bunny and demonstrate how it hops. Tell children that a bunny is a baby rabbit and that in English many animals have different names for their babies. Mention other examples such as dogs/puppies and cats/kittens. Encourage children to use the new words for their own number stories.”

• Lesson 4-9, More Combinations of 10, Differentiation Options, English Language Learner, Beginning ELL, “Children may associate fishing with catching real fish. They should learn that this word can also apply to asking for something or trying to get something. Display a common object, such as a card, and say: May I have that card? I want that card. I would like that card. I am fishing for that card. This will help children understand the word fishing in the context of asking for something. Have them use sentence frames, such as ‘I am fishing for ___’ to practice asking for objects, and later, for numbers.”

• Lesson 8-1, Building shapes with Defining Attributes, Differentiation Options, English Language Learner, Beginning ELL, “To review defining attributes, have children play a guessing game with yes or no questions. One child secretly puts an attribute block inside a bag. The guesser asks questions, such as: Does it have vertices? Does it have three sides? Is it a ___? The first player may reach into the bag to touch the block while answering questions. Demonstrate one round with a child, with you as the guesser. Then reverse roles so children can practice using the terms to ask questions. You may wish to play as a class or form partnerships.”

• 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 1 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 4-5, Exploring Data, Shapes, and Base-10 Blocks, Focus: Exploration B: Geoboard Shapes with Defining Attributes, materials reference use of geoboards. “Children make shapes with specified attributes using rubber bands on a geoboard. They record their shapes on Math Masters, page TA16 or TA17.”

• Lesson 5-1, Introducing Place Value, Focus: Naming Numbers with Base-10 Blocks, materials reference use of base-10 blocks. “Explain that today children will learn more about tens and ones. Provide each child with a Tens-and-Ones Math (Math Journal 1, Activity Sheet 4) and display a demonstration Tens-and-Ones Math (Math Masters, page TA20). Have the class use base-10 blocks to represent numbers.”

• Lesson 8-6, 3-Dimensional Shapes, Focus: Describing 3-Dimensional Shapes, materials reference use of solid shapes. “Divide children into 6 groups, one group for each of the following shapes: cube, non-cube rectangular prism, sphere cylinder, pyramid, and cone. Provide each group with blocks or everyday objects of their shape. After children examine the 3-dimensional shapes, encourage them to match their objects to representations on journal page 170.”