## Kendall Hunt’s Illustrative Mathematics

##### v1.5
###### Usability
Our Review Process

#### Additional Publication Details

Title ISBN Edition Publisher Year
Kendal Hunt's Illustrative Mathematics Grade 1 978-1-7924-6275-7 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Grade 1 978-1-7924-6289-4 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Grade 4 978-1-7924-6278-8 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Grade 4 978-1-7924-6292-4 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Grade 3 978-1-7924-6277-1 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Grade 3 978-1-7924-6291-7 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Kindergarten 978-1-7924-6274-0 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Kindergarten 978-1-7924-6287-0 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Grade 5 978-1-7924-6279-5 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Grade 5 978-1-7924-6293-1 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Grade 2 978-1-7924-6276-4 2021 Kendall Hunt Publishing Company 2021
Kendal Hunt's Illustrative Mathematics Grade 2 978-1-7924-6290-0 2021 Kendall Hunt Publishing Company 2021
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## Report for 2nd Grade

### Overall Summary

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and meet expectations for practice-content connections.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

##### Indicator {{'1a' | indicatorName}}

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum is divided into nine units and each unit contains a written End-of-Unit Assessment for individual student completion. The Unit 9 Assessment is an End-of-Course Assessment and it includes problems from across the grade. Examples from End-of-Unit Assessments include:

• Unit 3, Measuring Length, End-of-Unit Assessment, Problem 3, “Here are the heights of some dogs, measured in inches: 20, 13, 16, 25, 20, 19, 20, 14, 16, a. Label the line plot with numbers. b. Use the dog heights to complete the line plot.” (2.MD.9)

• Unit 5, Numbers to 1,000, End-of-Unit Assessment, Problem 5, “Fill in each blank with <, =, or > to make a true statement. a. 51 ___151, b. 497+100+100___703, c. 138___118+10+10.” (2.NBT.3, 2.NBT.4)

• Unit 6, Geometry, Time, and Measurement, End-of-Unit Assessment, Problem 4, “a. Split the circle into 4 equal parts. b. Explain why 4 fourths of the circle is the whole circle.” An image of a circle is provided. (2.G.3)

• Unit 7, Adding and Subtracting within 1,000, End-of-Unit Assessment, Problem 6, “Find the value of each difference. Show your thinking. Use base-ten blocks if it helps. a. 528-315, b. 471-124, c. 600-594.” (2.NBT.7)

• Unit 9, Putting It All Together, End-of-Course Assessment, Problem 8, “Diego has 34 cents. Mai has 19 more cents than Diego. How many cents do Mai and Diego have together? Explain or show your reasoning.” (2.NBT.5, 2.OA.1)

##### Indicator {{'1b' | indicatorName}}

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials provide extensive work in Grade 2 as students engage with all CCSSM standards within a consistent daily lesson structure, including a Warm Up, one to three Instructional Activities, a Lesson Synthesis, and a Cool-Down. Examples of extensive work include:

• Unit 2, Adding and Subtracting Within 100, Lessons 4, 5, and 6 engage students in extensive work with 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction). Lesson 4, Center Day 1, Warm-up: Number Talk, students use the addition and subtraction facts they know to develop fluency with addition and subtraction within 100, “Display one expression. ‘Give me a signal when you have an answer and can explain how you got it.’ 1 minute; quiet think time.” Student Facing, “Find the value of each expression mentally. 6-3, 66-3, 66-30, 66-33.” Lesson 5, Subtract Your Way, Activity 2, students subtract a one-digit number from a two-digit number using base-ten blocks to represent the starting number and subtract an amount that requires them to decompose a ten, “‘Diego was representing numbers using base-ten blocks. Work with a partner to follow along and see what Diego discovered. Use your blocks first to show what Diego does. Then answer any questions.’ 8 minutes: partner work time. Monitor for students who talk about ‘exchanging’ or ‘trading’ a ten for ten ones.” Lesson 6, Compare Methods for Subtraction, Activity 2, students subtract numbers within 100 with and without decomposing a ten, “Groups of 2. Give each student a copy of the recording sheet and a set of the number cards. ‘We are going to learn a new way to play Target Numbers. You and your partner will start with 99 and race to see who can get closest to 0. First, represent 99 with base-ten blocks. When it’s your turn, draw a card. Decide whether you want to subtract that many tens or that many ones. Then show the subtraction with your blocks and write an equation on your recording sheet. Take turns drawing a card and subtracting until you play 6 rounds or one player reaches 0. After 6 rounds, whoever is closest to 0 is the winner.’ As needed, demonstrate a round with a student volunteer.”

• Unit 2, Adding and Subtracting within 100, Lesson 13; Unit 3, Measuring Length, Lesson 6; Unit 4, Addition and Subtraction on the Number Line, Lesson 12; and Unit 9, Putting It All Together, Lesson 10 engage students in the extensive work with 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Unit 2, Lesson 13, Story Problems and Equations, Activity 1, students connect story problems to the equations that represent them and solve different types of story problems. Student Facing, “1. Match each story problem with an equation. Explain why the cards match. 2. Choose 2 story problems and solve them. Show your thinking.” Unit 3, Lesson 6, Compare Repite Lengths in Story Problems, Activity 1, students interpret and solve compare problems involving length. Student Facing, “1. Lin's pet lizard is 62 cm long. It is 19 cm shorter than Jada's. How long is Jada's pet lizard? a. Whose pet is longer? b. Circle the diagram that matches the story. (Four tape diagrams are displayed.) c. Solve. Show your thinking. Jada’s pet lizard is ___ cm long. 2. Diego and Mai have pet snakes. Mai’s snake is 17 cm longer than Diego’s. Mai’s snake is 71 cm. How long is Diego’s pet snake? a. Whose pet is shorter? b. Circle the diagram that matches the story. (Four tape diagrams are displayed.” c. Solve. Show your thinking. ​​Diego’s pet snake is ___cm long.” Unit 4, Lesson 12, Equations with Unknowns, Activity 1, students solve addition and subtraction problems within 100 with the unknown in all positions. Student Facing, “Solve riddles to find the mystery number. For each riddle: Write an equation that represents the riddle and write a ? for the unknown. Write the mystery number. Represent the equation on the number line. 1. I started at 15 and jumped 17 to the right. Where did I end? 2. I started at a number and jumped 20 to the left. I ended at 33. Where did I start? 3. I started on 42 and ended at 80. How far did I jump? 4. I started at 76 and jumped 27 to the left. Where did I end? 5. I started at a number and jumped 19 to the right. I ended at 67. Where did I start? 6. I started at 92 and ended at 33. How far did I jump?” Each number includes space to write the equation and the mystery number. Unit 9, Lesson 10, What’s the Question? Activity 2, students work with given numbers and use a story context to determine what question was answered. Student Facing, “Clare picked 51 apples. Lin picked 18 apples and Andre picked 19 apples. Here is some student work showing the answer to a question about the apples.” For number 1, a tape diagram showing 51, 18, 19 above and a question mark below is pictured. The equations 51+19=70 and 70+18=88 are also shown, “What’s the question? Explain how you know.” For number 2, a double tape diagram is shown with 19, 18, and ? on the top and 51 on the bottom. Equations, 19+18=37 and 51-37=14 are shown, “What’s the question? Explain how you know.“

### Usability

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports; partially meet expectations for Criterion 2, Assessment; and meet expectations for Criterion 3, Student Supports.

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Teacher Supports

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain 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; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.

##### Indicator {{'3a' | indicatorName}}

Materials provide 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.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. This is located within IM Curriculum, How to Use These Materials, and the Course Guide, Scope and Sequence. Examples include:

• IM Curriculum, How To Use These Materials, Design Principles, Coherent Progression provides an overview of the design and implementation guidance for the program, “The overarching design structure at each level is as follows: Each unit starts with an invitation to the mathematics. The first few lessons provide an accessible entry point for all students and offer teachers the opportunity to observe students’ prior understandings. Each lesson starts with a warm-up to activate prior knowledge and set up the work of the day. This is followed by instructional activities in which students are introduced to new concepts, procedures, contexts, or representations, or make connections between them. The lesson ends with a synthesis to consolidate understanding and make the learning goals of the lesson explicit, followed by a cool-down to apply what was learned. Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals. In each of the activities, care has been taken to choose contexts and numbers that support the coherent sequence of learning goals in the lesson.”

• Course Guide, Scope and Sequence, provides an overview of content and expectations for the units, “The big ideas in grade 2 include: extending understanding of the base-ten number system, building fluency with addition and subtraction, using standard units of measure, and describing and analyzing shapes. In these materials, particularly in units that focus on addition and subtraction, teachers will find terms that refer to problem types, such as Add To, Take From, Put Together or Take Apart, Compare, Result Unknown, and so on. These problem types are based on common addition and subtraction situations, as outlined in Table 1 of the Mathematics Glossary section of the Common Core State Standards.”

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Several components focus specifically on the content of the lesson. Preparation and lesson narratives within the Warm-up, Activities, and Cool-down provide useful annotations. Examples include:

• Unit 1, Adding, Subtracting, and Working with Data, Lesson 3, Activity 1, teachers are provided context to support students finding numbers within 20 to make an equation true. Narrative states, “In this activity, students learn stage 3 of the What’s Behind My Back center. In this new stage, called 20 cubes, students work with 20 cubes, organized into two towers of 10 cubes. One partner snaps the tower and puts one part behind their back and shows the other part to their partner. The other partner figures out how many cubes are behind their partner’s back. Students record an addition equation with a blank to represent the missing cubes. Students may write equations with the blank as the first or second addend. Ask students to explain what each number and blank in the equation represents in the context of the center activity (MP2).” Launch states, “Groups of 2. Give each group 20 connecting cubes and a recording sheet. ‘We are going to play What’s Behind My Back, this time with 20 cubes. How did you figure out how many connecting cubes were behind your partner’s back last time? (I thought about an addition expression that would make 10. I subtracted what they showed me from 10.) Let’s play a round with 20.’ Show students 2 towers of 10 cubes. Put the towers behind your back. Break off and display 8 of the cubes. ‘This time when you play, you are going to record an addition equation with a blank to represent the missing cubes, before you figure out how many are behind your partner’s back. What equation should we record? ($$8+$$___$$=20$$).’ 30 seconds: quiet think time. Share responses. ‘How many cubes are behind my back? How do you know? (12 because 2 more makes 10 and then here’s another tower of 10.)’ 30 seconds: quiet think time. 30 seconds: partner discussion. ‘Play with your partner. Don’t forget to record an equation each round.’” Activity Synthesis states, “Display 9 cubes. ‘What’s an addition equation I can write to represent the number of cubes you know and the number of cubes you need to figure out? ($$9+$$___$$=20$$). Tell your partner how you can figure out how many cubes are missing.’ Monitor for students who talk about making a 10 and knowing there is one more 10. Share responses.”

• Unit 5, Numbers to 1000, Lesson 2, Warm-Up, provides information to the teacher about the importance of students being able to count by 10, as a precursor to counting by larger numbers. Narrative states, “The purpose of this Choral Count is for students to practice counting by 10 beyond 120 and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to recognize multiples of 100 written as numerals and make connections between groups of 10 tens and hundreds.”

##### Indicator {{'3b' | indicatorName}}

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject.

Within the Teacher’s Guide, IM Curriculum, About These Materials, there are sections entitled “Further Reading” that consistently link research to pedagogy. There are adult-level explanations, including examples of the more complex grade-level concepts and concepts beyond the grade, so that teachers can improve their own understanding of the content. Professional articles support teachers with learning opportunities about topics such as ensuring mathematical success for all, early understanding of equality, and repeating patterns. Additionally, each lesson provides teachers with a lesson narrative, including adult-level explanations and examples of the more complex grade/course-level concepts. Examples include:

• Unit 1, Adding, Subtracting, and Working with Data, Lesson 16, Preparation, Lesson Narrative states, “The number choices in the Compare problems in this lesson encourage students to use methods based on place value to find the unknown value. Students may look for ways to compose a ten or subtract multiples of ten when finding unknown values within 100. Students will subtract numbers other than multiples of ten within 100 in future lessons. Encourage students to use a tape diagram to make sense of the problem if it is helpful.”

• IM K-5 Math Teacher Guide, About These Materials, Unit 4, “To learn more about the essential nature of the number line (which is introduced in this unit) in mathematics beyond grade 2, see: The Nuances of Understanding a Fraction as a Number. In this blog post, Gray discusses the role the number line plays in student understanding of fractions as numbers. Why is 3–5=3+(-5)? In this blog post, McCallum discusses the use of the number line in introducing negative numbers.”

• Unit 7, Adding and Subtracting Within 1000, Lesson 2, Preparation, Lesson Narrative states, “In grade 1, students added and subtracted multiples of 10 within 100. In a previous unit, students represented three-digit numbers with base-ten blocks, drawings, and words. Students used equations to represent three-digit numbers as sums of the value of hundreds, tens, and ones using the number and name of each unit (235 = 2 hundreds + 3 tens + 5 ones) and using expanded form (235=200+30+5). In this lesson, students add and subtract three-digit numbers and multiples of 10 and 100 using what they know about tens and hundreds. Students compare representations such as base-ten blocks, base-ten diagrams, and equations to understand that when adding or subtracting multiples of 10, the tens place changes and when adding or subtracting multiples of 100 the hundreds place changes (MP7, MP8).”

• IM K-5 Math Teacher Guide, About These Materials, Unit 8, “What is Multiplication? In this blog post, McCallum discusses multiplication beyond repeated addition—as equal groups. The foundation of this understanding is laid in this unit of grade 2.”

##### Indicator {{'3c' | indicatorName}}

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level/series and can be found in several places, including the curriculum course guide, within unit resources, and within each lesson. Examples include:

• Grade 2, Course Guide, Lesson Standards includes a table with each grade-level lesson (in columns) and aligned grade-level standards (in rows). Teachers can search any lesson for the grade and identify the standard(s) that are addressed within.

• Grade 2, Course Guide, Lesson Standards, includes all Grade 2 standards and the units and lessons each standard appears in. Teachers can search a standard for the grade and identify the lesson(s) where it appears within materials.

• Unit 5, Resources, Teacher Guide, outlines standards, learning targets and the lesson where they appear. This is present for all units and allows teachers to identify targeted standards for any lesson.

• Unit 7, Adding and Subtracting within 1,000, Lesson 1, the Core Standards are identified as 2.NBT.A.2, 2.NBT.B.7, and 2.NBT.B.3. Lessons contain a consistent structure: a Warm-up that includes Narrative, Launch, Activity, Activity Synthesis; Activity 1, 2, or 3 that includes Narrative, Launch, Activity; an Activity Synthesis; a Lesson Synthesis; and a Cool-down that includes Responding to Student Thinking and Next Day Supports. This provides an additional place to reference standards, and language of the standard, within each lesson.

Each unit includes an overview outlining the content standards addressed within as well as a narrative describing relevant prior and future content connections. Examples include:

• Grade 2, Course Guide, Scope and Sequence, Unit 3: Measuring Length, Unit Learning Goals, includes an overview of how the math of this module builds from previous work in math, “This unit introduces students to standard units of lengths in the metric and customary systems. In grade 1, students expressed the lengths of objects in terms of a whole number of copies of a shorter object laid without gaps or overlaps. The length of the shorter object serves as the unit of measurement. Here, students learn about standard units of length: centimeters, meters, inches, and feet. They examine how different measuring tools represent length units, learn how to use the tools, and gain experience in measuring and estimating the lengths of objects. Along the way, students notice that the length of the same object can be described with different measurements and relate this to differences in the size of the unit used to measure.”

• Grade 2, Course Guide, Scope and Sequence, Unit 6: Geometry, Time, and Money, Unit Learning Goals, includes an overview of how the math of this module builds from previous work in math, “In this unit, students transition from place value and numbers to geometry, time, and money. In grade 1, students distinguished between defining and non-defining attributes of shapes, including triangles, rectangles, trapezoids, and circles. Here, they continue to look at attributes of a variety of shapes and see that shapes can be identified by the number of sides and vertices (corners). Students then study three-dimensional (solid) shapes, and identify the two-dimensional (flat) shapes that make up the faces of these solid shapes. Next, students look at ways to partition shapes and create equal shares. They extend their knowledge of halves and fourths (or quarters) from grade 1 to now include thirds. Students compose larger shapes from smaller equal-size shapes and partition shapes into two, three, and four equal pieces. As they develop the language of fractions, students also recognize that a whole can be described as 2 halves, 3 thirds, or 4 fourths, and that equal-size pieces of the same whole need not have the same shape. Which circles are not examples of circles partitioned into halves, thirds, or fourths? Later, students use their understanding of halves and fourths (or quarters) to tell time. In grade 1, they learned to tell time to the half hour. Here, they relate a quarter of a circle to the features of an analog clock. They use ‘quarter past’ and ‘quarter till’ to describe time, and skip-count to tell time in 5-minute intervals. They also learn to associate the notation ‘a.m.’ and ‘p.m.’ with their daily activities. To continue to build fluency with addition and subtraction within 100, students conclude the unit with a money context. They skip-count, count on from the largest value, and group like coins, and then add or subtract to find the value of a set of coins. Students also solve one- and two-step story problems involving sets of dollars and different coins, and use the symbols \$ and ¢.”

##### Indicator {{'3d' | indicatorName}}

Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

Each unit has corresponding Family Support Materials, in English and Spanish, that provide a variety of supports for families. Each unit includes a narrative for stakeholders, describing what students will learn within each section. Additionally, Try it at home! includes suggestions for at home activities and questions families can ask, all geared towards supporting the mathematical ideas in the unit. Examples include:

• For Families, Grade 2, Unit 2, Adding and Subtracting within 100, Family Support Materials, “In this unit, students add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction. They then use what they know to solve story problems. Section A: Add and Subtract. This section allows students to use methods that make sense to them to help them solve addition and subtraction problems. They can draw diagrams and use connecting cubes to show their thinking. For example, students would be exposed to the following situation: Make trains with cubes. Find the total number of cubes you and your partner used. Show your thinking. Find the difference between the number of cubes you and your partner used. Show your thinking. As the lessons progress, students analyze the structure of base-ten blocks and use them to support place-value reasoning. Unlike connecting cubes, base-ten blocks cannot be pulled apart. Students begin to think about two-digit numbers in terms of tens and ones. To add using base-ten blocks, they group the tens and the ones, and then count to find the sum.”

• For Families, Grade 2, Unit 5, Numbers to 1,000, Family Support Materials, Try it at home!, “Near the end of the unit, ask your student to think about the number 593 and complete the following tasks: Write the number as a number name and in expanded form. Draw an amount of base-ten blocks that has the same value. Create a number line from 500 to 600 and place the number on a number line. Compare the number to 539 using either <, >, or =. Questions that may be helpful as they work: What pieces of information were helpful? Can you explain to me how you solved the problem? Could you have drawn a different amount of base-ten blocks?”

• For Families, Grade 2, Unit 6, Geometry, Time and Money, Family Support Materials, “In this unit, students reason with shapes and their attributes and partition shapes into equal pieces. This work helps to build their foundation for fractions. Students also use their understanding of fourths, quarters, and skip-counting by 5 to tell time, and solve story problems involving money. Section A: Attributes of Shapes, In this section, students extend their understanding of geometry from previous grades to identify and draw triangles, quadrilaterals, pentagons, and hexagons. Students learn to count the sides to determine the name of a shape and come to see that any shape has the same number of corners as the number of sides. For example, students are familiar with the hexagon shape from the frequent use of pattern blocks in previous grades. They expand their understanding to realize that hexagons include any shape with six sides and six corners, and may look different from the pattern block they worked with in the past.At the end of the section, students use their understanding of two-dimensional shapes to identify three-dimensional (solid) shapes. They recognize that two-dimensional shapes make up the faces of solid shapes, and use the names of two-dimensional shapes to describe solid shapes. For example, students learn to describe a cube as a solid shape that has 6 equal-sized square faces.”

##### Indicator {{'3e' | indicatorName}}

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

The IM K-5 Math Teacher Guide, Design Principles, outlines the instructional approaches of the program, “It is our intent to create a problem-based curriculum that fosters the development of mathematics learning communities in classrooms, gives students access to the mathematics through a coherent progression, and provides teachers the opportunity to deepen their knowledge of mathematics, student thinking, and their own teaching practice. In order to design curriculum and professional learning materials that support student and teacher learning, we need to be explicit about the principles that guide our understanding of mathematics teaching and learning. This document outlines how the components of the curriculum are designed to support teaching and learning aligning with this belief.” Examples of the design principles include:

• IM K-5 Math Teacher Guide, Design Principles, All Students are Capable Learners of Mathematics, “All students, each with unique knowledge and needs, enter the mathematics learning community as capable learners of meaningful mathematics. Mathematics instruction that supports students in viewing themselves as capable and competent must leverage and build upon the funds of knowledge they bring to the classroom. In order to do this, instruction must be grounded in equitable structures and practices that provide all students with access to grade-level content and provide teachers with necessary guidance to listen to, learn from, and support each student. The curriculum materials include classroom structures that support students in taking risks, engaging in mathematical discourse, productively struggling through problems, and participating in ways that make their ideas visible. It is through these classroom structures that teachers will have daily opportunities to learn about and leverage their students’ understandings and experiences and how to position each student as a capable learner of mathematics.”

• IM K-5 Teacher Guide, Design Principles, Coherent Progression, “Each unit starts with an invitation to the mathematics. The first few lessons provide an accessible entry point for all students and offer teachers the opportunity to observe students’ prior understandings. Each lesson starts with a warm-up to activate prior knowledge and set up the work of the day. This is followed by instructional activities in which students are introduced to new concepts, procedures, contexts, or representations, or make connections between them. The lesson ends with a synthesis to consolidate understanding and make the learning goals of the lesson explicit, followed by a cool-down to apply what was learned. Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals. In each of the activities, care has been taken to choose contexts and numbers that support the coherent sequence of learning goals in the lesson.”

• IM K-5 Teacher Guide, Design Principles, Learning Mathematics by Doing Mathematics, “Students learn mathematics by doing mathematics, rather than by watching someone else do mathematics or being told what needs to be done. Doing mathematics can be defined as learning mathematical concepts and procedures while engaging in the mathematical practices—making sense of problems, reasoning abstractly and quantitatively, making arguments and critiquing the reasoning of others, modeling with mathematics, making appropriate use of tools, attending to precision in their use of language, looking for and making use of structure, and expressing regularity in repeated reasoning. By engaging in the mathematical practices with their peers, students have the opportunity to see themselves as mathematical thinkers with worthwhile ideas and perspectives. ‘Students learn mathematics as a result of solving problems. Mathematical ideas are the outcomes of the problem-solving experience rather than the elements that must be taught before problem solving’ (Hiebert et al., 1996). A problem-based instructional framework supports teachers in structuring lessons so students are the ones doing the problem solving to learn the mathematics. The activities and routines are designed to give teachers opportunities to see what students already know and what they can notice and figure out before having concepts and procedures explained to them.”

Research-based strategies are cited and described within the IM Curriculum and can be found in various sections of the IM K-5 Math Teacher Guide. Examples of research-based strategies include:

• IM Certified, Blog, Making Sense of Story Problems, Deborah Peart, How can we support “sense-making” of stories in math class?, “The mission of Illustrative Mathematics is to create a world where learners know, use, and enjoy mathematics. By using stories to help students see math in the world around them and recognize the ways in which using math is a part of their daily lives, word problems can become an enjoyable part of math learning. This starts with calling word problems ‘story problems’ in the early grades. From there, other supports embedded in the curriculum include: providing relevant contexts and images with which students can engage, supporting reading comprehension with routines and instructional practices, like Act it Out and Three Reads, encouraging students to use visual representations to support sense-making, inviting students to write their own math stories and ask questions that can be answered by them.”

• IM K-5 Math Teacher Guide, Design Principles, Using the 5 Practices for Orchestrating Productive Discussions, “Promoting productive and meaningful conversations between students and teachers is essential to success in a problem-based classroom. The Instructional Routines section of the teacher course guide describes the framework presented in 5 Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011) and points teachers to the book for further reading. In all lessons, teachers are supported in the practices of anticipating, monitoring, and selecting student work to share during whole-group discussions. In lessons in which there are opportunities for students to make connections between representations, strategies, concepts, and procedures, the lesson and activity narratives provide support for teachers to also use the practices of sequencing and connecting, and the lesson is tagged so teachers can easily identify these opportunities. Teachers have opportunities in curriculum workshops and PLCs to practice and reflect on their own enactment of the 5 Practices.”

• IM K-5 Math Teacher Guide, Key Structures in This Course, Student Journal Prompts, “Writing can be a useful catalyst in learning mathematics because it not only supplies students with an opportunity to describe their feelings, thinking, and ideas clearly, but it also serves as a means of communicating with other people (Baxter, Woodward, Olson, & Robyns, 2002; Liedtke & Sales, 2001; NCTM, 2000). NCTM (1989) suggests that writing about mathematics can help students clarify their ideas and develop a deeper understanding of the mathematics at hand.”

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Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

The Course Guide includes a section titled “Required Materials” that includes a breakdown of materials needed for each unit and for each lesson. Additionally, specific lessons outline materials to support the instructional activities and these can be found on the “Preparation” tab in a section called “Required Materials.” Examples include:

• Course Guide, Required Materials for Grade 2, Materials Needed for Unit 1, Lesson 4, teachers need, “Connecting cubes, Number cards 0–10, How Close? Stage 1 Recording Sheet (groups of 1).”

• Unit 2, Adding and Subtracting within 100, Lesson 7, Activity 1, Required Materials, “Base-ten blocks, Connecting cubes.” Launch states, “Groups of 2. Give students access to connecting cubes and base-ten blocks.” Activity states, “‘Find the value of each difference and share your method and solution with your partner.’ 7 minutes: independent work time. MLR8 Discussion Supports ‘After your partner shares their method, repeat back what they told you.’ Display the sentence frames: I heard you say . . . . Our methods are alike because . . . . Our methods are different because . . . . 5 minutes: partner discussion. Monitor for students who use base-ten blocks to show decomposing a ten.”

• Unit 4, Addition and Subtraction on the Number Line, Lesson 5, Activity 2, Required Materials, “Chart paper, Markers. Materials to Copy: Order Numbers on the Number Line Cards.” Launch states, “Groups of 3. Give each group chart paper, markers, and a set of number cards.” Activity states, “‘You will be working with your group to arrange the number cards on the number line. Take turns picking a card and placing it near its spot on the number line. Explain how you decided where to place your card. If you think you need to rearrange other cards, explain why. When you agree that you have placed all the numbers in the right spots, mark each of the numbers on your cards with a point on the number line. Label each point with the number it represents.’ 10 minutes: small-group work time.”

• Course Guide, Required Materials for Grade 2, Materials Needed for Unit 8, Lesson 6, teachers need, “Dry erase markers, Materials from previous centers, Sheet protectors, Write the Number Stage 4 Gameboard (groups of 2).”

##### Indicator {{'3g' | indicatorName}}

This is not an assessed indicator in Mathematics.

##### Indicator {{'3h' | indicatorName}}

This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 partially meet expectations for Assessment. The materials identify the standards and the mathematical practices assessed in formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but do not provide suggestions for follow-up. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.

##### Indicator {{'3i' | indicatorName}}

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

End-of-Unit Assessments and the End-of-Course Assessments consistently and accurately identify grade-level content standards. Content standards can be found in each Unit Assessment Teacher Guide. Examples from formal assessments include:

• Unit 6, Geometry, Time, and Money, End-of-Unit Assessment, Assessment Teacher Guide denotes standards addressed for each problem. Problem 5, 2.MD.7, “a. Jada gets up in the morning at 6:45. Show the time on the clock face. Then circle a.m. or p.m. b. Jada goes to bed at the time on the clock. Write the time and circle a.m. or p.m.”

• Unit 8, Equal Groups, End-of-Unit Assessment, Assessment Teacher Guide denotes standards addressed for each problem. Problem 5, 2.OA.3, “For each number, decide whether the number is even or odd. Write each even number as the sum of 2 equal addends. a. 6   b. 11  c. 14.”

• Unit 9, Putting it All Together, End-of-Course Assessment, Assessment Teacher Guide denotes standards addressed for each problem. Problem 9, 2.NBT.7, “Find the value of each expression. Show your thinking. a. 347+583. b. 612-174.”

Guidance is provided within materials for assessing progress of the Mathematical Practices. According to IM K-5 Math Teacher Guide, How to Use These Materials, “Because using the mathematical practices is part of a process for engaging with mathematical content, we suggest assessing the Mathematical Practices formatively. For example, if you notice that most students do not use appropriate tools strategically (MP5), plan in future lessons to select and highlight work from students who have chosen different tools.” For each grade, there is a chart outlining a handful of lessons in each unit that showcase certain mathematical practices. There is also guidance provided for tracking progress against “I can” statements aligned to each practice, “Since the Mathematical Practices in action can take many forms, a list of learning targets for each Mathematical Practice is provided to support teachers and students in recognizing when engagement with a particular Mathematical Practice is happening. The intent of the list is not that students check off every item on the list. Rather, the ‘I can’ statements are examples of the types of actions students could do if they are engaging with a particular Mathematical Practice.” Examples include:

• IM K-5 Math Teacher Guide, How to Use These Materials, Standards for Mathematical Practices Chart, Grade 2, MP3 is found in Unit 3, Lessons 4, 8, 9, 12, and 16.

• IM K-5 Math Teacher Guide, How to Use These Materials, Standard for Mathematical Practices Chart, Grade 2, MP8 is found in Unit 6, Lessons 9, 12, and 16.

• IM K-5 Math Teacher Guide, How to Use These Materials, Standards for Mathematical Practice Student Facing Learning Targets, “MP6 I Can Attend to Precision. I can use units or labels appropriately. I can communicate my reasoning using mathematical vocabulary and symbols. I can explain carefully so that others understand my thinking. I can decide if an answer makes sense for a problem.”

• IM K-5 Math Teacher Guide, How to Use These Materials, Standards for Mathematical Practice Student Facing Learning Targets, “MP7 I Can Look for and Make Use of Structure. I can identify connections between problems I have already solved and new problems. I can compose and decompose numbers, expressions, and figures to make sense of the parts and of the whole. I can make connections between multiple mathematical representations. I can make use of patterns to help me solve a problem.”

##### Indicator {{'3j' | indicatorName}}

Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 partially meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Each End-of-Unit Assessment and End-of-Course Assessment provides guidance to teachers for interpreting student performance, with an answer key and standard alignment. According to the Teacher Guide, Summative Assessments, “All summative assessment problems include a complete solution and standard alignment. Multiple choice and multiple response problems often include a reason for each potential error a student might make.” Examples from the assessment system include:

• Unit 4, Addition and Subtraction on the Number Line, End-of-Unit Assessment, Problem 1, “Select 3 true statements about the numbers on the number line. A. P+18=Q. B. Q+18=P. C. P=Q-18. D. Q=P-18 E. $$Q-P=18$$.” The Assessment Teacher Guide states, “Students interpret equations relating numbers given on a number line. Students who select B or fail to select A, or who select D or fail to select C, need further practice with interpreting the operations of addition and subtraction on the number line. Students may fail to select E if they do not accurately calculate the difference between P and Q but the other responses should provide support in this direction.” The answer key aligns this problem to 2.MD.6.

• Unit 5, Numbers to 1,000, End-of-Unit Assessment, Problem 1, “Label the tick marks on the number line.” A number line is shown with 15 tick marks with 0 and 10 labeled. The Assessment Teacher Guide states, “Students label the tick marks on a number line starting at 0 where the tick marks represent tens. This is a version of skip counting by 10 where the students record the count as labels on the number line. This gives an opportunity to make sure students know how to skip count by 10 and that they appropriately label the tenth tick mark as 100.” The answer key aligns this problem to 2.NBT.1 and 2.NBT.2.

• Unit 9, Putting It All Together, End-of-Course Assessment, Problem 6, “Clare made a necklace that is 74 cm long. She made a bracelet that is 28 cm long. How many centimeters longer is the necklace than the bracelet? Show your thinking using drawings, numbers, or words.” The Assessment Teacher Guide states, “Students solve a compare story problem about lengths. They may draw a number line, a base-ten representation, or use equations as in the provided solution. Students may misread the question and add 74 and 28. These students may need more practice interpreting stories.” The answer key aligns this problem to 2.MD.5 and 2.OA.1.

While assessments provide guidance to teachers for interpreting student performance, suggestions for following-up with students are either minimal or absent. Cool-Downs, at the end of each lesson, include some suggestions. According to IM Curriculum, Cool-Downs, “The cool-down (also known as an exit slip or exit ticket) is to be given to students at the end of the lesson. This activity serves as a brief check-in to determine whether students understood the main concepts of that lesson. Teachers can use this as a formative assessment to plan further instruction. When appropriate, guidance for unfinished learning, evidenced by the cool-down, is provided in two categories: next-day support and prior-unit support. This guidance is meant to provide teachers ways in which to continue grade-level content while also giving students the additional support they may need.” An example includes:

• Unit 1, Adding, Subtracting, and Working with Data, Lesson 4, Cool-down, Student Facing states, “Find the value of each expression. Show your thinking using drawings, numbers, or words. 1. 8+6; 2. 13-5; 3. 16-4.” Responding to Student Thinking states, “Students show evidence in their explanations or drawings that they count on by ones to find the value of sums and differences within 20.” Next Day Supports states, “Encourage students to use connecting cubes in towers of 10 and singles.” This problem aligns to 2.OA.2.

##### Indicator {{'3k' | indicatorName}}

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

Formative assessment opportunities include some end of lesson cool-downs, interviews, and Checkpoint Assessments for each section. Summative assessments include End-of-Unit Assessments and the End-of-Course Assessment. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, multiple response, short answer, restricted constructed response, and extended response. Examples from summative assessments include:

• Unit 5, Numbers to 1,000, End-of-Unit Assessment develops the full intent of 2.NBT.3 (Read and write numbers to 1000 using base-ten numerals, number names, and expanded form). For example, Problem 3 states, “Select 2 ways to represent the number 518. A. 500+10+8 B. 5+1+8 C. 5 hundreds and 18 tens D. 51 tens and 8 ones E. 4 hundreds and 11 tens.”

• Unit 6, Geometry, Time, and Money, End-of-Unit Assessment develops the full intent of 2.G.1 (Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Sizes are compared directly or visually, not compared by measuring. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes). For example, Problem 1 states, “Draw a quadrilateral with one square corner and two equal sides.”

• Unit 8, Equal Groups, End-of-Unit Assessment supports the full intent of MP3 (Construct viable arguments and critique the reasoning of others) as students reason about a situation involving sharing. For example, Problem 6 states, “​​Here are some pattern blocks that Jada and Diego want to share. (There are images of some pattern blocks shown.) a. Explain why there are an even number of trapezoids. b. Jada says that she and Diego can share the pattern blocks so they each have 9 pattern blocks. Explain why Jada is correct. c. Can Jada and Diego share all of the pattern blocks so that they each have the same set of pattern block shapes? Explain or show your reasoning.”

• Unit 9, Putting It All Together, End-of-Course Assessment supports the full intent of MP2 (Reason abstractly and quantitatively) as students compare numbers within 1,000. For example, Problem 2 states, “Fill in each blank with <, =, or > to make the statements true. a. 675 ___ 576 b. 98 ___ 205 c. 500+40+3___$$543$$ d. 675___$$600+70+1$$.”

##### Indicator {{'3l' | indicatorName}}

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment. These suggestions are provided within the Teacher Guide in a section called “Universal Design for Learning and Access for Students with Disabilities.” As such, they are included at the program level and not specific to each assessment.

Examples of accommodations include:

• IM K-5 Teacher Guide, How to Assess Progress, Summative Assessment Opportunity, “In K–2, the assessment may be read aloud to students, as needed.”

• IM K-5 Teacher Guide, UDL Strategies to Enhance Access states, “Present content using multiple modalities: Act it out, think aloud, use gestures, use a picture, show a video, demonstrate with objects or manipulatives. Annotate displays with specific language, different colors, shading, arrows, labels, notes, diagrams, or drawings. Provide appropriate reading accommodations. Highlight connections between representations to make patterns and properties explicit. Present problems or contexts in multiple ways, with diagrams, drawings, pictures, media, tables, graphs, or other mathematical representations. Use translations, descriptions, movement, and images to support unfamiliar words or phrases.”

• IM K-5 Teacher Guide, UDL Strategies to Enhance Access states, “It is important for teachers to understand that students with visual impairments are likely to need help accessing images in lesson activities and assessments, and prepare appropriate accommodations. Be aware that mathematical diagrams are provided as scalable vector graphics (SVG format), because this format can be magnified without loss of resolution. Accessibility experts who reviewed this curriculum recommended that students who would benefit should have access to a Braille version of the curriculum materials, because a verbal description of many of the complex mathematical diagrams would be inadequate for supporting their learning. All diagrams are provided in the SVG file type so that they can be rendered in Braille format.”

• IM K-5 Teacher Guide, UDL Strategies to Enhance Access states, “Develop Expression and Communication, Offer flexibility and choice with the ways students demonstrate and communicate their understanding. Invite students to explain their thinking verbally or nonverbally with manipulatives, drawings, diagrams. Support fluency with graduated levels of support or practice. Apply and gradually release scaffolds to support independent learning. Support discourse with sentence frames or visible language displays.”

#### Criterion 3.3: Student Supports

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

##### Indicator {{'3m' | indicatorName}}

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics as suggestions are outlined within each lesson and parts of each lesson. According to the IM K-5 Teacher Guide, Universal Design for Learning and Access for Students with Disabilities, “These materials empower all students with activities that capitalize on their existing strengths and abilities to ensure that all learners can participate meaningfully in rigorous mathematical content. Lessons support a flexible approach to instruction and provide teachers with options for additional support to address the needs of a diverse group of students, positioning all learners as competent, valued contributors. When planning to support access, teachers should consider the strengths and needs of their particular students. The following areas of cognitive functioning are integral to learning mathematics (Addressing Accessibility Project, Brodesky et al., 2002). Conceptual Processing includes perceptual reasoning, problem solving, and metacognition. Language includes auditory and visual language processing and expression. Visual-Spatial Processing includes processing visual information and understanding relation in space of visual mathematical representations and geometric concepts. Organization includes organizational skills, attention, and focus. Memory includes working memory and short-term memory. Attention includes paying attention to details, maintaining focus, and filtering out extraneous information. Social-Emotional Functioning includes interpersonal skills and the cognitive comfort and safety required in order to take risks and make mistakes. Fine-motor Skills include tasks that require small muscle movement and coordination such as manipulating objects (graphing, cutting with scissors, writing).”

Examples of supports for special populations include:

• Unit 1, Adding, Subtracting, and Working with Data, Lesson 3, Activity 1, Narrative, Access for Students with Disabilities, “Representation: Internalize Comprehension. Synthesis: Invite students to identify which details were important or most useful to pay attention to. Display the sentence frame, ‘To figure out how many cubes are behind my partner’s back, I can . . . .’ Supports accessibility for: Visual-Spatial Processing.

• Unit 3, Measuring Length, Lesson 5, Activity 2, Narrative, Access for Students with Disabilities, “Engagement: Provide Access by Recruiting Interest. Synthesis: Optimize meaning and value. Invite students to share people they know or specific jobs they recognize that may use the measuring tools they have been exposed to. ‘When and why might someone use these measuring tools?’ Supports accessibility for: Conceptual Processing.

• Unit 6, Geometry, Time, and Money, Lesson 8, Activity 2, Narrative, Access for Students with Disabilities, “Representation: Develop Language and Symbols. Synthesis: Maintain a visible display to record images of ways to make thirds (also add fourths and halves) to reiterate that fractions have equal parts and can be made in certain ways. Invite students to suggest details (words or pictures) that will help them remember the meaning of the fractions. Supports accessibility for: Memory, Language, Organization.

• Unit 7, Adding and Subtracting within 1,000, Lesson 6, Activity 2, Narrative, Access for Students with Disabilities, “Action and Expression: Develop Expression and Communication. Synthesis. Identify connections between strategies that result in the same outcomes but use differing approaches. Supports accessibility for: Conceptual Processing.”

##### Indicator {{'3n' | indicatorName}}

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

While there are no instances where advanced students do more assignments than classmates, materials do provide multiple opportunities for students to investigate grade-level content at a higher level of complexity. These are found in a section titled “Exploration Problems” within lessons where appropriate. According to the IM K-5 Teacher Guide, How To Use The Materials, Exploration Problems, “Each practice problem set also includes exploration questions that provide an opportunity for differentiation for students ready for more of a challenge. There are two types of exploration questions. One type is a hands-on activity directly related to the material of the unit that students can do either in class if they have free time, or at home. The second type of exploration is more open-ended and challenging. These problems go deeper into grade-level mathematics. They are not routine or procedural, and they are not just the same thing again but with harder numbers. Exploration questions are intended to be used on an opt-in basis by students if they finish a main class activity early or want to do more mathematics on their own. It is not expected that an entire class engages in exploration problems, and it is not expected that any student works on all of them. Exploration problems may also be good fodder for a Problem of the Week or similar structure.” Examples include:

• Unit 1, Adding, Subtracting, and Working with Data, Section A: Add and Subtract Within 20, Problem 10, Exploration, “Clare has a set of cards numbered 1, 2, 3, 4, 5, 6, 7, 8, 9. She picks out seven of the cards. Clare was NOT able to make 20 with 3 of her 7 cards. Which cards do you think she picked out if she was NOT able to make 20?”

• Unit 2, Adding and Subtracting within 100, Section A: Add and Subtract, Problem 7, Exploration, “Jada added 3 different numbers between 1 and 9 and got 20. What could Jada’s numbers be? Give three different examples. If Jada used 6, what are the other two numbers? Explain your reasoning.”

• Unit 4, Addition and Subtraction on the Number Line, Section B: Add and Subtract on a Number Line, Problem 8, Exploration, “Using addition or subtraction, how many equations can you make with these three numbers: 20, 13, 7? Draw number lines to match each of the equations you wrote. How are the number lines the same? How are they different?”

• Unit 8, Equal Groups, Section B: Rectangular Arrays, Problem 10, Exploration, “What are some things in the classroom that you know there are an even number of without counting them? Explain your reasoning.”

##### Indicator {{'3o' | indicatorName}}

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 provide various approaches to learning tasks over time and variety in how students are expected to demonstrate their learning, but do not provide opportunities for students to monitor their learning.

Students engage with problem-solving in a variety of ways within each lesson: Warm-up, Instructional Activities, Cool-down, and Centers. According to the IM K-5 Teacher Guide, A Typical IM Lesson, “After the warm-up, lessons consist of a sequence of one to three instructional activities. The activities are the heart of the mathematical experience and make up the majority of the time spent in class. An activity can serve one or more of many purposes. Provide experience with a new context. Introduce a new concept and associated language. Introduce a new representation. Formalize a definition of a term for an idea previously encountered informally. Identify and resolve common mistakes and misconceptions that people make. Practice using mathematical language. Work toward mastery of a concept or procedure. Provide an opportunity to apply mathematics to a modeling or other application problem. The purpose of each activity is described in its narrative. Read more about how activities serve these different purposes in the section on design principles.” Examples of varied approaches include:

• Unit 1, Adding, Subtracting, and Working with Data, Lesson 4, Activity 1, students use cards to make a target number. Launch states, “Give each group a set of cards. Have them remove the number 10 cards. Display the digit cards at the top of the student page. ‘We are going to play a game called How Close. Let’s play 1 round together. Look at the 5 cards. Think about which 3 cards you would choose to add together to get close to 20.’ Share responses. ‘After you choose your 3 cards, you will write an equation showing the sum.’ Demonstrate writing an equation to show the sum of the 3 cards that get closest to 20. ‘When you have your equation written, compare it with your partner’s to see who found a sum closer to 20. Then you will replace the cards you used and play again.’”

• Unit 2, Adding and Subtracting Within 100, Lesson 14, Warm-up, students add expressions mentally. Student Facing states, “Find the value of each expression mentally. 5+9+5, 25+9+5, 25+15+19, 25+30+15+19.”

• Unit 3, Measuring Length, Lesson 1, Activity 2, students use connecting blocks to measure the length of a string. Activity states, “‘Your job is to use these cubes to measure the length of the string.’ 5 minutes: small-group work time. 5 minutes: small-group discussion.”  Student Facing states, “Use the cubes to measure Priya’s string. 1. Priya’s iguana is ___cubes long. 2. Compare your measurement with another group.”

• Center, How Are They the Same? (1–5), Stage 2: Grade 2 Shapes, students find shapes that have shared attributes. Narrative states, “Students lay six shape cards face up. One student picks two cards that have an attribute in common. All students draw a shape that has a shared attribute with the two shapes. Students get a point if they draw a shape that no other student drew. It is possible that students will draw a shape with a different shared attribute than what the original student chose. This can be an interesting discussion for students to have.”

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 provide opportunities for teachers to use a variety of grouping strategies. Suggestions are consistently provided for teachers within the facilitation notes of lesson activities and include guidance for a variety of groupings, including whole group, small group, pairs, or individual. Examples include:

• Unit 2, Adding and Subtracting Within 100, Lesson 14, Activity 2, students work in groups of three using strategies to solve one- and two-step problems. Launch states, “Groups of 3, Give students access to base-ten blocks.” Activity states, “‘Read the problems together. Each person in your group must solve one problem on their own. Decide together who will solve each problem. Be ready to share your thinking with your group. After everyone shares and you agree on how many seeds each character has, complete the story and solve the problem together.’ 4 minutes: independent work time. 5 minutes: small-group discussion.”

• Unit 3, Measuring Length, Lesson 5, Activity 1, students work in groups of three or four to measure larger objects that require longer length units and measuring tools. Launch states, “Groups of 3–4. Give students access to centimeter rulers and base-ten blocks. Display the reptile images. ‘In previous lessons, we measured different kinds of smaller reptiles. What do you know about some of these larger reptiles? Let’s imagine we are zookeepers who need to measure the lengths of these reptiles. Some of these reptiles would be too dangerous to bring in the classroom to measure. I’ve placed strips of tape on the floor to represent their lengths. Look at the strips of tape on the floor. Choose anything we’ve used so far to measure each of the strips A through D with your group. You can use centimeter cubes, 10-centimeter tools, the rulers you made, or the centimeter rulers.’” Activity states, “‘Record the length of these four reptiles in centimeters.’ 10 minutes: small-group work time. Monitor for different ways students use their tools to measure the komodo dragon: iterating 10-centimeter tools, iterating rulers, iterating a combination of tools.”

• Unit 4, Addition and Subtraction on the Number Line, Lesson 5, Activity 2, students work in small groups to locate numbers on a number line. Launch states, “Groups of 3. Give each group chart paper, markers, and a set of number cards.” Activity states, “‘You will be working with your group to arrange the number cards on the number line. Take turns picking a card and placing it near its spot on the number line. Explain how you decided where to place your card. If you think you need to rearrange other cards, explain why. When you agree that you have placed all the numbers in the right spots, mark each of the numbers on your cards with a point on the number line. Label each point with the number it represents.’ 10 minutes: small-group work time. Consider asking: Why did you place your card there? Where would you draw a point to represent this number? Which cards did you choose to place first? Why?”

• Unit 8, Equal Groups, Lesson 8, Activity 1, students work in pairs to create arrays with a variety of counters available. Launch states, “Groups of 2. Give each group 3 sets of counters with 6, 7, and 9. Display A from the warm-up or arrange counters. (Counters are arranged in rows with 4, 2, 4, and 2)  ‘The red counters are arranged in rows, but it is not an array. How could we rearrange the counters to make an array like image B?’ (We could move the bottom two counters to the middle row. We could move one from the top row to the next row. We could move 1 from the third row to the bottom row.) 1 minute: quiet think time. 1 minute: partner discussion. Share responses.” Activity states, “‘Arrange each of your sets of counters into an array. Your arrays should have the same number of counters in each row with no extra counters. Be prepared to explain how you made an array out of each set. If you have time, try to figure out a different way to make an array out of each set of counters.’ 12 minutes: partner work time.”

##### Indicator {{'3q' | indicatorName}}

Materials provide 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 materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Guidance is consistently provided for teachers to support students who read, write, and/or speak in a language other than English, providing scaffolds for them to meet or exceed grade-level standards. According to the IM K-5 Math Teacher Guide, Mathematical Language Development and Access for English Learners, “In a problem-based mathematics classroom, sense-making and language are interwoven. Mathematics classrooms are language-rich, and therefore language demanding learning environments for every student. The linguistic demands of doing mathematics include reading, writing, speaking, listening, conversing, and representing (Aguirre & Bunch, 2012). Students are expected to say or write mathematical explanations, state assumptions, make conjectures, construct mathematical arguments, and listen to and respond to the ideas of others. In an effort to advance the mathematics and language learning of all students, the materials purposefully engage students in sense-making and using language to negotiate meaning with their peers. To support students who are learning English in their development of language, this curriculum includes instruction devoted to fostering language development alongside mathematics learning, fostering language-rich environments where there is space for all students to participate.” The series provides the following principles that promote mathematical language use and development:

• “Principle 1. Support sense-making: Scaffold tasks and amplify language so students can make their own meaning.

• Principle 2. Optimize output: Strengthen opportunities for students to describe their mathematical thinking to others, orally, visually, and in writing.

• Principle 3. Cultivate conversation: Strengthen opportunities for constructive mathematical conversations.

• Principle 4. Maximize meta-awareness: Strengthen the meta-connections and distinctions between mathematical ideas, reasoning, and language.”

The series also provides Mathematical Language Routines in each lesson. According to the IM K-5 Math Teacher Guide, Mathematical Language Development and Access for English Learners, “Mathematical Language Routines (MLRs) are instructional routines that provide structured but adaptable formats for amplifying, assessing, and developing students' language. MLRs are included in select activities in each unit to provide all students with explicit opportunities to develop mathematical and academic language proficiency. These “embedded” MLRs are described in the teacher notes for the lessons in which they appear.” Examples include:

• Unit 1, Adding, Subtracting, and Working with Data, Lesson 2, Activity 1, Teaching notes, Access for English Learners, “MLR8 Discussion Supports. Provide all students with an opportunity for verbal output. Invite students to read each expression they create to their partner. Amplify words and phrases such as: add, addition, sum, take away, difference, value, and expression. Advances: Speaking, Listening, Representing.”

• Unit 2, Adding and Subtracting within 100, Lesson 12, Activity 1, Activity, “MLR6 Three Reads, Display only the problem stem for the first problem, without revealing the question. ‘We are going to read this problem 3 times.’ 1st Read: ‘Clare captured 54 seeds. Han captured 16 fewer seeds. What is this story about?’ 1 minute: partner discussion. Listen for and clarify any questions about the context. 2nd Read: ‘Clare captured 54 seeds. Han captured 16 fewer seeds. What are all the things we can count in this story?’ (Clare’s seeds. Han’s seeds. The difference between their seeds.) 30 seconds: quiet think time. 1 minute: partner discussion. Share and record all quantities. Reveal the question. 3rd Read: Read the entire problem, including the question aloud. Ask students to open their books. ‘Which of the diagrams shows a way we could represent this problem?’ (See Student Responses for the first problem). 30 seconds: quiet think time. 1–2 minutes: partner discussion. Share responses. ‘Read each story with your partner. Then choose a diagram that matches on your own. When you have both selected a match, compare your choices and explain why the diagram matches the story or why other diagrams do not match the story.’ 5 minutes: partner work time.”

• Unit 7, Adding and Subtracting within 1,000, Lesson 13, Activity 1, Teaching Notes, Access for English Learners, “MLR5 Co-Craft Questions. Keep books or devices closed. Display only the images, without revealing the question, and ask students to write down possible mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the task. Ask, ‘What do these questions have in common? How are they different?’ Reveal the intended questions for this task and invite additional connections. Advances: Reading, Writing.”

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 provide a balance of images or information about people, representing various demographic and physical characteristics.

Images of characters are included in the student facing materials when they connect to the problem tasks. These images represent different races and portray people from many ethnicities in a positive, respectful manner, with no demographic bias for who achieves success based on the grade-level mathematics and problem circumstances. Names include multi-cultural references such as Han, Andre, Kiran, and Priya and problem settings vary from rural, to urban, and international locations. Additionally, lessons include a variety of problem contexts to interest students of various demographic and personal characteristics.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 partially provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The student materials are available in Spanish. Directions for teachers are in English with prompts for students available in Spanish. The student materials including warm ups, activities, cool-downs, centers, and assessments are in Spanish for students.

The IM K-5 Teacher Guide includes a section titled “Mathematical Language Development and Access for English Learners” which outlines the program’s approach towards language development in conjunction with the problem-based approach to learning mathematics, which includes the regular use of Mathematical Language Routines, “The MLRs included in this curriculum were selected because they simultaneously support students’ learning of mathematical practices, content, and language. They are particularly well-suited to meet the needs of linguistically and culturally diverse students who are learning mathematics while simultaneously acquiring English.” While Mathematical Language Routines (MLRs) are regularly embedded within lessons and support mathematical language development, they do not include specific suggestions for drawing on a student’s home language.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 provide some guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Spanish materials are consistently accessible for a variety of stakeholders within the Family Support Materials for each unit. Within lessons, cultural connections are included within the context of problem solving, picture book centers, or games. Examples include:

• Unit 2, Adding and Subtracting within 100, Lesson 12, Warm-up, students are introduced to the game of Mancala. Activity synthesis states, “The picture shows a type of a game called Mancala. It is one of the world’s oldest games. Mancala was created in Africa. The game has over 800 different names and can be played in many different ways. Most games are played with a board that has different pits or holes in it. Each player uses a certain amount of seeds that they place on their side of the board. Players might use real seeds or they may use shells, rocks, or beads. Each player takes turns placing their seeds on the board. In most games, you try to ‘capture’ more seeds than the other player. In Ghana and the Caribbean, one popular mancala game is called Oware. The board has 12 pits, 6 for each player, and the game uses 32 seeds. In Sudan, one popular mancala game is called Bao. The board for Bao has 28 pits, 14 pits for each player, and the game uses 64 seeds. The largest mancala game is called En Gehé and is played in Tanzania. The board can have up to 50 pits and the players use 400 seeds! Mancala is played all over the world. This board shows a game played in India called Pallanguzhi. The board has 14 pits and uses 70 seeds. What math questions could we ask about this image? (How many seeds are there in all? How many seeds are in the holes? How many more seeds are on the top than on the bottom?)”

• Unit 3, Measuring Length, Lesson 12, Activity 1, students measure different pieces of ribbon to solve problems where friendship bracelets are being made. The lesson title, Saree Silk Stories: Friendship Bracelets, refers to the previous lesson where the discussion of sarees was held. When the saree is no longer worn, ribbons are made of it. Launch states, “Groups of 2. Give each group access to base-ten blocks. ‘The students in Priya’s class are sharing ribbons to make necklaces and bracelets for their friends and family members.’” Activity states, “Display both parts of the story, but only the problem stems, without revealing the questions. ‘We are going to read this problem 3 times.’ 1st Read: ‘Lin found a piece of ribbon that is 92 cm long. She gave Noah a piece that is 35 cm. Then, Lin gave Jada 28 cm of ribbon. What is this story about?’ 1 minute: partner discussion. Listen for and clarify any questions about the context. 2nd Read: ‘Lin found a piece of ribbon that is 92 cm long. She gave Noah a piece that is 35 cm. Then, Lin cut off 28 cm of ribbon for Jada. Which lengths of ribbon are important to pay attention to in the story?’ (length of ribbon Lin started with, length of ribbon given to Noah, length of ribbon given to Jada, length of ribbon Lin has in the end) 30 seconds: quiet think time. 1–2 minutes: partner discussion. Share and record all quantities. Reveal the questions. 3rd Read: Read the entire problem, including the questions, aloud. ‘What are different ways we could represent this problem?’ (tape diagram, equations) 30 seconds: quiet think time. 1–2 minutes: partner discussion.”

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 provide some supports for different reading levels to ensure accessibility for students.

According to the IM K-5 Teacher's Guide, the Three Reads routine supports reading and interpreting mathematical tasks, “Use this routine to ensure that students know what they are being asked to do, create opportunities for students to reflect on the ways mathematical questions are presented, and equip students with tools used to actively make sense of mathematical situations and information (Kelemanik, Lucenta, & Creighton, 2016). This routine supports reading comprehension, sense-making, and meta-awareness of mathematical language. In this routine, students are supported in reading and interpreting a mathematical text, situation, diagram, or graph three times, each with a particular focus. Optional: At times, the intended question or main prompt may be intentionally withheld until the third read so that students can concentrate on making sense of what is happening before rushing to find a solution or method. Read #1: ‘What is this situation about?’ After a shared reading, students describe the situation or context. This is the time to identify and resolve any challenges with any non-mathematical vocabulary. (1 minute) Read #2: ‘What can be counted or measured?’ After the second read, students list all quantities, focusing on naming what is countable or measurable in the situation. Examples: ‘number of people in a room’ rather than ‘people,’ ‘number of blocks remaining’ instead of ‘blocks.’ Record the quantities as a reference to use when solving the problem after the third read. (3–5 minutes) Read #3: ‘What are different ways or strategies we can use to solve this problem?’ Students discuss possible strategies. It may be helpful for students to create diagrams to represent the relationships among quantities identified in the second read, or to represent the situation with a picture (Asturias, 2014). (1–2 minutes).” Additional reading supports include those connected to making sense of problems (MP1) and examining precision in mathematical language (MP6) within problem contexts. These support sense-making and accessibility for students. Examples include:

• Unit 4, Addition and Subtraction on the Number Line, Lesson 4, Activity 1, Access for Students with Disabilities, “Engagement: Provide Access by Recruiting Interest. Give students a context to relate the number line to. For example, a frog jumping on lily pads, or a rabbit hopping. The counters can represent the animal hopping along the number line. Supports accessibility for: Conceptual Processing, Attention.”

• Unit 5, Numbers to 1,000, Lesson 3, Activity 1, Activity states, “MLR7 Compare and Connect. “‘Create a visual display to show the total value of the blocks. Include details such as diagrams, labels, and numbers to help others understand your thinking.’ 2–5 minutes: group work time. ‘As you look at other groups’ representations, look for different ways groups show the value. Which ways are the same as your group’s representation? Which ways are different? How do you know they represent the same value?’ 5 minutes: gallery walk. ‘Discuss any revisions you would like to make to your representations with your group.’ 1–2 minutes: small-group work time. Monitor for students who: create a base-ten diagram with the fewest amount of blocks represented.”

• Unit 7, Adding and Subtracting within 1,000, Lesson 10, Activity 1, Access for Students with Disabilities, “Action and Expression: Internalize Executive Functions. Check for understanding by inviting students to rephrase directions in their own words. Allow students to check off each task as it is completed. Supports accessibility for: Memory, Organization.

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 meet expectations for providing manipulatives, physical but not virtual, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Suggestions and/or links to manipulatives are consistently included within materials, often in the Launch portion of lessons, to support the understanding of grade-level math concepts. Examples include:

• Unit 3, Measuring Length, Lesson 9, Activity 1, references inch tiles, rulers, and tape to introduce students to measurement units and tools. Launch states, “Give each student an inch ruler and access to inch tiles. ‘You have measured the length of objects and the sides of shapes using inches. If you are measuring longer objects, like the fish in the warm-up, you might want to use a different unit. A foot is a longer length unit in the U.S. Customary Measurement System. A foot is the same length as 12 inches. When we measure a length that starts at 0 on the ruler and ends at the 12, we can say the length is 12 inches or we can say the length is 1 foot. What are some things you see around the classroom that are about 1 foot long?’"

• Unit 5, Numbers to 1,000, Lesson 11, Activity 2, identifies number cards 0-10 to support students’ reasoning about place value and the greatest possible digit. Launch states, “Give each group a set of number cards and each student a recording sheet. ‘Now you will be playing the Greatest of Them All center with your partner. You will try to make the greatest three-digit number you can.’ Display spinner and recording sheet. Demonstrate spinning. ‘If I spin a (2), I need to decide whether I want to put it in the hundreds, tens, or ones place to make the largest three-digit number. Where do you think I should put it? (I think it should go in the ones place because it is a low number. In the hundreds place, it would only be 200.) At the same time, my partner is spinning and building a number, too. Take turns using the spinner and writing each digit in a space. Read your comparison aloud to your partner.’”

• Unit 7, Adding and Subtracting within 1,000, Lesson 2, Activity 1, base-ten blocks and numbers cubes are identified to support adding and subtracting three-digit numbers. Launch states, “Groups of 2. Give each group base-ten blocks and a number cube.” Activity states, “‘Work with your partner to show each number with base-ten blocks. Take turns rolling the number cube to see how many tens or hundreds to add or subtract.’ 10 minutes: partner work time. Monitor for students to share their equations for the number of hundreds they subtract from 805.”

• Unit 9, Putting It All Together, Lesson 8, Activity 1, references number cards to play a game called Heads Up, practicing addition and subtraction within 100. Launch states, “Give students number cards.” Activity states, “‘We are going to play a game called Heads Up.’ Demonstrate with 2 students. ‘Players A and B pick a card and put it on their foreheads without looking at it. I am Player C. My job is to find the value of the sum and tell my group. Players A and B use the other player’s number and the value of the sum to determine what number is on their head. Finally, each player writes the equation that represents what they did.’ Demonstrate writing an equation for each of the players. After each round switch roles and play again.”

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards. The materials do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic. The materials do not provide teacher guidance for the use of embedded technology to support and enhance student learning.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

According to the IM K-5 Teacher Guide, About These Materials, “Teachers can access the teacher materials either in print or in a browser as a digital PDF. When possible, lesson materials should be projected so all students can see them.” While this format is provided, the materials are not interactive.

According to the IM K-5 Teacher Guide, Key Structures in This Course, “Across lessons and units, students are systematically introduced to representations and encouraged to use representations that make sense to them. As their learning progresses, students are given opportunities to make connections between different representations and the concepts and procedures they represent. Over time, they will see and understand more efficient methods of representing and solving problems, which support the development of procedural fluency. In general, more concrete representations are introduced before those that are more abstract.” While physical manipulatives are referenced throughout lessons and across the materials, they are not virtual or interactive.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

According to IM K-5 Teacher Guide, Key Structures in this Course, “Classroom environments that foster a sense of community that allows students to express their mathematical ideas—together with norms that expect students to communicate their mathematical thinking to their peers and teacher, both orally and in writing, using the language of mathematics—positively affect participation and engagement among all students(Principles to Action, NCTM).” While the materials embed opportunities for mathematical community building through student task structures, discourse opportunities, and journal and reflection prompts, these opportunities do not reference digital technology.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design within units and lessons that supports student understanding of the mathematics. According to the IM K-5 Teacher Guide, Design Principles, “Each unit, lesson, and activity has the same overarching design structure: the learning begins with an invitation to the mathematics, is followed by a deep study of concepts and procedures, and concludes with an opportunity to consolidate understanding of mathematical ideas.” Examples from materials include:

• Each lesson follows a common format with the following components: Warm-up, one to three Activities, Lesson Synthesis, and Cool-Down, when included in lessons. The consistent structure includes a layout that is user-friendly as each component is included in order from top to bottom on the page.

• Student materials, in printed consumable format, include appropriate font size, amount and placement of directions, and space on the page for students to show their mathematical thinking.

• Teacher digital format is easy to navigate and engaging. There is ample space in the printable Student Task Statements, Assessment PDFs, and workbooks for students to capture calculations and write answers.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Grade 2 do not provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

While the IM K-5 Teacher Guide provides guidance for teachers about using the “Launch, Work Synthesize” structure of each lesson, including guidance for Warm-ups, Activities, and Cool-Downs, there is no embedded technology.

## Report Overview

### Summary of Alignment & Usability for Kendall Hunt’s Illustrative Mathematics | Math

#### Math K-2

The materials reviewed for Illustrative Mathematics Kendall Hunt Grades K-2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for usability including Teacher Supports and Student Supports; the materials partially meet expectations for Assessment.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

The materials reviewed for Illustrative Mathematics Kendall Hunt Grades 3-5 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for usability including Teacher Supports and Student Supports; the materials partially meet expectations for Assessment.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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### Overall Summary

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###### Usability
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