## Alignment: Overall Summary

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for alignment to the Common Core State Standards (CCSS). ​The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor. The materials meet expectations for meaningfully connecting the Standards for Mathematical Content and the Cluster Standards for Mathematical Practice (MPs).

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## Gateway 1:

### Focus & Coherence

0
7
12
14
14
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
17
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

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## Gateway 3:

### Usability

0
22
31
38
34
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

### Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

​The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades.

### Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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Indicator Rating Details

The instructional materials for  HMH Into Math Grade 3 meet expectations for assessing grade-level content. An Assessment Guide, included in the materials, contains two parallel versions of each module assessment, and the assessments include a variety of question types. In addition, there is a Performance Task for each unit, and there are Beginning, Middle, and End-of-Year assessments.

Examples of assessment items aligned to grade-level standards include:

• Module 4, Form A, Question 9, students “write a multiplication expression to complete the equation   _____$$\times$$_____ = 18”. (3.OA.4)
• Unit 5, Performance Task, students draw a picture graph to represent the drinks sold at a coffee shop. “Mario collects information about the drinks sold today. Use the data to make a picture graph. Include a key.” (3.MD.3)
• Module 9, Form A, students solve, “Roman has 293 snap blocks. He uses 69 of the snap blocks to make an airplane and 32 to make a car. About how many snap blocks does Roman have left?” (3.NBT.1)
• Module 16, Form B, Question 4, students identify equivalent fractions by matching pairs of differently-partitioned and shaded rectangles. (3.NF.3a.)

### Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade.

### Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for spending a majority of instructional time on major work of the grade.

• The number of modules devoted to major work of the grade is 14 out of 20, which is approximately 70%.
• The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 72 out of 100, which is approximately 72%.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 118 out of 170 days, which is approximately 69%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work and is not dependent on pacing suggestions. As a result, approximately 72% of the instructional materials focus on major work of the grade.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
8/8
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

### Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Examples of how the materials connect supporting standards to the major work of the grade include:

• Lesson 10.6, Check Understanding, Question 1, 3.NBT.2 supports the major work of 3.OA.8 when students solve two-step word problems using the four operations. “Kai has 65 stamps. He buys 7 more stamps. He uses all of the stamps to fill 9 equal pages. How many stamps are on each page? Write two equations to model the problem.”
• Lesson 13.2, On Your Own, Question 8, 3.G.2 supports the major work of 3.NF.1 when students partition shapes into parts with equal areas and represent those parts as fractional values. Question 8, “Write a fraction to name the part of the whole or the part of the group that is blue”. A square divided into two parts is given.
• Lesson 14.1, Teacher’s Manual, Question 3, 3.G.2 supports 3.MD.5. Students are asked to examine a rectangle divided into 4 shaded parts and determine if the parts are the same shape. Then students determine if the shapes have the same area by counting unit squares.
• Lesson 14.3, Check Understanding, Question 2, 3.G.2 supports the major work of 3.NF.A.1. Students partition shapes into parts with equal areas and represent those parts as fractional values. “Divide the shape into 3 equal areas. What unit fraction names each equal part of the shape?”
• Teacher’s Manual, Lessons 18.1-4, align to 3.MD.3 and 3.OA.3.Lesson 2, Question 1, students choose a scale amount for their picture graph. They then divide the quantities in the data table by their chosen scale amount to determine how many representative pictures to draw. Students use subtraction to solve the remaining questions.

### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet expectations that the amount of content designated for one grade level is viable for one year. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 170 days, 121 days for lessons and 49 days for assessments.

• The Planning and Pacing Guide and Planning pages at the beginning of each module in the Teacher Edition provide the same pacing information.
• Grade 3 has 6 units with 20 modules that contain 100 lessons.
• The Planning and Pacing Guide designates 15 lessons as 2-day lessons and 85 as 1-day lessons, leading to a total of 115 days. The materials do not define the number of minutes in a lesson or instructional day.
• Each unit includes a Unit Opener, there are 6 unit openers for Grade 3 (6 days).
• Each lesson includes a variety of supplemental instruction, such as reteaching lessons, flipbook lessons, etc. However, there is no guidance around building in days for differentiation; therefore, no additional days were added.
• There are a total of 121 lesson days.

Assessments included:

• The Planning and Pacing Guide indicates a Beginning, Middle, and End-of-Year Interim Growth assessment that would require 1 day each (3 days).
• Each unit includes a Performance Task which indicates an expected time frame ranging from 25-45 minutes. There are 6 performance tasks for Grade 3 (6 days).
• Each module has both a review and an assessment. There are 20 modules (40 days).
• Based on this, 49 assessment days can be added.

### Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet expectations for the materials being consistent with the progressions in the Standards. The materials identify content from prior and future grade-levels, relate grade-level concepts explicitly to prior knowledge from earlier grades, and attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems.

The introduction for every module in the Teacher Edition includes Mathematical Progressions, which identifies standards from Prior Learning, for Current Development, and makes Future Connections, as well as clarifying student learning statements in these categories. For example, before Lesson 3.1, Multiply with 2 and 4, Prior Learning is identified as “counted objects by 2’s, write equations to represent the sum of equal addends.” (2.OA.3 and 2.OA.4) Future Connections identify “will solve multi-step word problems” and “will write equations with one variable to represent multi-step word problems.” (4.OA.3) Additional features of the materials further support the progressions of the Standards. These include:

• The beginning of each module includes a diagnostic assessment, Are You Ready?, that explicitly identifies prior knowledge needed for the current module. For example, Module 4 links prior learning to Grade 2, Lesson 2.3, Count Equal Groups. (2.OA.4)
• In each lesson the standard of focus is explicitly connected to future work. For example, Lesson 6.1 states the lesson focuses on standard 3.OA.3. This work will continue in Grade 4 with a focus on standards 4.OA.2 and 4.NBT.6 during Lesson 6.1-6.6 and 7.1-7.4.

The materials give all students extensive work with grade-level problems. The lesson structure includes Spark Your Learning, Build Understanding, and Step It Out where “students connect important processes and procedures to mathematical concepts, Independent Practice, and Math Center Activities. For example:

• Lesson 2.3, Build Understanding, students relate area to addition and multiplication. (3.MD.7a) Students find the area of a card two ways using both multiplication and addition. During Step It Out and On Your Own, students complete problems to “Find the area of the figure. Show repeated addition. Show multiplication.”
• Lesson 7, Build Understanding, students relate multiplication and division. (3.OA.6.) Question 1 states: “Jackson plants pepper plants in 3 equal rows. He plants 18 plants. How many plants are in each row?” Students write both multiplication and division equations for the problem and explain how the equations are the same and different.
• Lesson 15.3, Build Understanding, has students compare fractions with the same numerator  using drawings, number lines, and by reasoning about the number and size of the parts. (3.NF.3d)

The materials explicitly relate grade-level concepts to prior knowledge from earlier grades in the Mathematical Progressions Across the Grade which links explicitly to standards. In addition, the materials include options for the lesson warm-ups to Activate Prior Knowledge to “Use these activities to quickly assess and activate prior knowledge…”; however, no standards are identified for these activities. For example:

• Lesson 3.3, Multiply with 3 and 6, Activate Prior Knowledge, Problem of the Day: “April and 5 of her friends each made 5 friendship bracelets. Write an equation to show the total number of friendship bracelets April and her friends made.” Based on student responses, teachers can use an Interactive Reteach from Lesson 3.2 or complete a prerequisite skills activity such as “Brienne has 7 bags of shells. There are 5 shells in each bag. How many shells does Brienne have?”
• Lesson 6.2 Separate Objects into Equal Groups, Activate Prior Knowledge, Problem of the Day: “Draw Arrays: Use 12 tiles. Make as many different arrays as you can using all 12 tiles.” Based on student responses, teachers can use an Interactive Reteach from Grade 3, Lesson 1.3, or complete an additional Prerequisite Skills Activity.
• Lesson 13.2 builds on this knowledge to introduce fractions as partitioned areas of a shape. For example, question 1 asks students to draw a model of a fence that is divided into fourths where one of the fourths is painted. It then asks students to identify how many equal parts in the whole fence, how many parts are being counted, and relates that to writing a fraction as $$\frac{1}{4}$$. (3.G.2)

### Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives that are visibly shaped by CCSSM cluster headings. Examples include:

• Lesson 2.3, the learning objective “Relate finding area to using an array to find a product,”  is shaped by 3.MD.3, geometric measurement: understand concepts of area and relate area to multiplication and addition.
• Lesson 8.4, the learning objective states “Develop strategies and use reasoning to represent and solve two-step word problems” which is shaped by 3.OA.4: “Solve problems involving the four operations and identify and explain patterns in arithmetic.”
• Lesson 10.2, the learning objective states “Use place value strategies to add 2- and 3- digit numbers” which is shaped by 3.NBT.1: “Use place value understanding and properties of operations to perform multi-digit arithmetic.”
• Lesson 12.1, the learning objective states “Read, write, and tell time on analog and digital clocks to the nearest minute” which is shaped by 3.MD.1: “Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.”

The materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. Examples include:

• Lesson 2.3 identifies and connects the following Mathematical Standards in the Lesson Focus and Coherence: “Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
• Lesson 4.4 connects 3.OA.1 with 3.OA.3 as students multiply with 7’s. Students use multiplication to solve word problems and fluently multiply within 100.
• Lesson 18.1 connects 3.NBT.2 with 3.MD.3 as students use scaled graphs to answer questions about how many more and how many less and fluently adding and subtracting within 1000.

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

### Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

### Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions that develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Throughout the materials, there are sections that emphasize introducing concepts and developing understanding such as Build Understanding and Spark Your Learning. Students have the opportunity to independently demonstrate their understanding in the Check Understanding and On Your Own problems at the end of each lesson. Evidence includes the following:

• Lesson 1.2, Spark Your Learning states “Ling is at a fair with her friends Jimmy and Pablo. At a game booth, they each get 4 balls. How many balls do Ling and her friends get?” Show more than one way to find the number of balls. (3.OA.1)
• Lesson 6.2, Spark Your Learning states “Annie wants to arrange 20 photographs in equal groups in a book. She wants to make equal groups. Write questions that can be asked about Annie's photographs. Draw equal groups to show how Annie's photographs can be arranged.” (3.OA.1)
• Lesson 13.1, Build Understanding, students compare pictures of flags to determine which are divided into equal parts and which are not. They are asked to use this knowledge to draw both types of flags and then they name equal parts using words like fourths and eighths. (3.NF.1)
• Lesson 13.3, On My Own, Question 4, students shade four equal parts of a hexagon, then write the fraction in words and numbers. (3.NF.1)
• Lesson 13.6, Practice and Homework Journal, Question 7 states “The shape represents $$\frac{1}{2}$$ of a whole. To make an amount that is greater than 1, how many shapes will you need? Draw your shapes. Write the mixed number that represents the amount you drew.” (3.NF.1)
• Lesson 15.3, Practice and Homework Journal, Question 8, Math on the Spot, states “James ate $$\frac{4}{8}$$ of his pancake. David ate $$\frac{4}{6}$$ of his pancake. Who ate more of his pancake? James said he knows he ate more because eight is greater than six. Does his answer make sense?” (3.NF.3d)

### Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The materials include problems and questions that develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. Procedural skills and fluencies are intentionally built on conceptual understanding.

This is primarily found in two areas of the materials:

• In the On Your Own section, students work through activities to practice procedural skill and fluency.
• In the More Practice/Homework section, students can find additional fluency practice.

Students have numerous opportunities to develop and independently demonstrate procedural skill and fluency, especially where called for by Standard 3.OA.7. Examples include but are not limited to:

• Lesson 4.6, Multiply by 9’s, On Your Own, Problem 5: $$9 \times 1 =$$ __. Problem 6: $$4 \times 9 =$$ __. Problem 7: ___ $$=9 \times 7$$. (3.OA.7)
• Lessons 7.3 and 7.4 provide students practice with multiplication and division with 2, 4, 5, 8, and 10.  Different representations are presented for each operation. (3.OA.7)
• In Lesson 7.7 students practice skip counting by 2, 3, and 4. Students circle the numbers that are the same in each set. (3.OA.7)
• Lesson 9.2 asks students to use mental math to find the sum or difference. “Problem 5, 46 + 24 + ____. Problem 6, 639 - 425 = ___.”
• Lesson 10.2 asks students to estimate and find the sum of two multi-digit numbers. Problem 7, “612 + 75”; Problem 8, “548 + 56”; Problem 9: “324 + 119”. (All problems are presented vertically). (3.OA.7)
• In Lesson 10.4 students find the difference using place value and regrouping. (3.NBT.2)

### Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade-level. Students also have opportunities to independently demonstrate the use of mathematics flexibly in a variety of contexts. Application contexts are used throughout the curriculum to build conceptual understanding. During Spark your Learning, Independent Practice, On Your Own, students engage with problems that include real-world context and present opportunities for application. For example:

• Lesson 1.3, On Your Own, STEM problem, students use multiplication and division within 100 to solve word problems. “Solar cells on a solar panel collect sunlight which is changed into electricity. Solar cells are arranged in equal rows on a frame to make a solar panel. Describe one way you could arrange 24 solar cells in an array to make a panel.”  (3.OA.3)
• Lesson 1.4, Spark Your Learning, students use multiplication and division within 100 to solve word problems in situations. “Andy designed the game board shown (picture provided of a flow chart). The game will have 21 squares The squares need to be in equal rows. Show two different game board designs.” (3.OA.3)
• Lesson 3.3, On My Own, Problem 4: “Michael buys 2 packages of hamburger buns. Each package has the number of buns shown. How many hamburger buns are in 2 packages? Show the equal groups. Write a multiplication equation for the problem.” (3.OA.3)
• Lesson 5.4, More Practice/Homework, Problem 9: students solve two-step word problems using the four operations. “Ava's class buys 8 packages of balloons for the class celebration. Each package has 50 balloons. If 21 balloons are left over, how many balloons are used for the party?” (3.OA.D.8)
• Lesson 8.4, On Your Own, Problem 11, students write two equations with letters representing the unknown to solve the problems. “Jamie’s plant grows 3 inches each week for three weeks. During the fourth week, it growth 5 inches. How much does Jamie’s plant grow over the four weeks?” (3.OA.D.8)
• Lesson 10.6, On Your Own, Problem 8: “Write a two-step word problem with an unknown number. Write equations to model the problem. Then solve.” (3.OA.8)

Each unit has a Performance Task that involves real world applications of the mathematics from that unit. For example, the Unit 3 Performance Task has students follow one child, a baseball card collector, throughout his day. Students estimate the number of baseball cards he has at the end of the day (3.NBT.1), tell the time of his various stops throughout the day (3.MD.1), determine the perimeter of his baseball card display (3.MD.8), and how many coins he has (not counting money) (3.OA.3).

### Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. In general, two, or all three, of the aspects are interwoven throughout each module. The module planning pages include a progression diagram showing the first few lessons focused on understanding and connecting concepts and skills and the last lessons focused on applying and practicing.

All three aspects of rigor are present independently throughout the program materials.

• Lesson 16.1 builds conceptual understanding of equivalent fractions. Students draw visual models and use number lines to show fraction equivalence. (3.NF.3b)
• In Modules 4, 7, 9 and 10, students develop procedural skill and fluency as students find products, work with related facts, division, as well as implementing estimation and mental math to support the addition and subtraction for the grade level. (3.OA.7 and 3.NBT.2)
• Lesson 8.4, On Your Own, Problem 8, students engage in application as they “Write a two-step word problem that can be solved using two equations with different operations.” (3.OA.8)

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Evidence includes:

• Lesson 7.6, Check for Understanding, Problem 4, students solve: “The 28 students in Van’s class are on a field trip to a cave. They are divided into groups of 7 for a tour of the cave. How many groups are there?” (3.OA.5).
• The Unit 4 Performance Task attends to conceptual understanding and application. Students create number lines to visually see equal parts and then use it to solve real-world problems. Item 2, “Ava makes a white cake and a strawberry cake that are the same size. She cuts the white cake into fourths and the strawberry cake into eighths. Yoshi puts $$\frac{1}{4}$$ of the white cake on a plate. He wants to put an equal amount of the strawberry cake on the plate. How many pieces of each cake should Yoski put on the plate? Use the number line to show what fraction of each cake Yoshi should put on the plate.” (3.NF.1, 3.NF.2, 3.NF.3, and 3.MD.4.)
• Lesson 13.6, Spark Your Learning, attends to conceptual understanding and application. “Emilio cuts his pizzas into slices. Each slice is a fourth of a whole pizza. Emilio has 9 slices to sell. Show all the different amounts of pizza that Emilio can sell. Name each fraction that you show.” (3.NF.1 and 3.NF.2)

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and clearly labeled throughout the materials, and the instructional materials support the standards’ emphasis on mathematical reasoning.

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade-level.

The MPs are identified at the unit, module and lesson level. In addition, the information in the Planning and Pacing Guide also include references to the MPs. For example:

• The Planning and Pacing Guide outlines for teachers where to look for each of the MPs. It states “MP1, MP3, and MP5 are paired with Spark Your Learning tasks. When students connect understanding they have developed with more efficient procedures, MP7 and MP8 are being attended to. This helps students explain and justify their procedures with MP4, MP2, and MP6 are attended to within lessons that ask students to apply procedures in practice.”
• Planning and Pacing Guide pages 17 -19 provide additional detail and clarity about each Mathematical Practice. These pages also include “Questions to Ask” with each MP. These questions provide support to advance students.
• MPs are clearly identified throughout the materials. For example, MP1 is identified in Lessons 2.5 and Lesson 8.2; MP2 in Lessons 4.6 and Lesson 6.2, MP3 in Lesson 9.6 and  Lesson 13.3; MP4 in Lessons 7.2 and Lesson 7.7; MP5 in Lesson 5.4 and Lesson 7.3; MP6 in Lessons 2.5 and Lesson 10.6; MP7 in Lesson 1.4 and Lesson 4.6; and MP8 in Lesson 7.7 and Lesson 8.1.
• The Planning and Pacing Guide for the teachers has a section identified as Correlations for Mathematical Practices. In this section, the 8 Mathematical Practices are listed in a table with a detailed description (from the common core documents) of the practice as well as “some examples” of where the practice is included in the text series.
• The Module Review includes a labeled question “Use Tools” in the student edition that asks students to choose a tool and explain their choice. The Teacher Edition recommends and provides additional support to have students discuss and share strategies and tools used as part of their review of the Module.

Within the Teacher Edition, in the margin under Homework & Test Prep, there is a section that describes the MPs that can be found within the Homework worksheet for the students. For example:

• Lesson 4.7, On Your Own, Problem 11, is identified as “Use structure.”
• Lesson 12.1, On Your Own, Problem 2, states “Critique Reasoning.”

For the most part, when identified, MPs are used to enrich the mathematical content of the lessons. Examples include:

• Lesson 4.4, Build Understanding, identifies MP8 as students use structure from previous work with the distributive property.
• Lesson 16.1, Build Understanding, identifies MP3 where students construct arguments about equivalent fractions.
• Lesson 10.5, On Your Own, Problem 5, has students engage in MP6 as they explain a strategy used to solve a problem.

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

The materials do not attend to the full meaning of MP4 and MP5.

Students have limited opportunity to engage with MP4 to model with mathematics. Models are often provided for the students. For example:

• Lesson 11.3, Build Understanding, Problem 3, students find the unknown side length of an irregular four sided shape when given the total perimeter. They are provided a scaffolded series of questions and prompts to complete this task. “Write an equation to find the perimeter. Use the letter n to stand for the unknown side length.” It continues, “Add the lengths of the sides you know,” and “Rewrite your original addition equation using the sum you found.”
• Lesson 18.3, On Your Own, Problems 3-7, students use a bar graph showing the number of students who like each type of game.  Students are prompted to complete this task. “If the scale showed counting by 2’s how would the bars change?”

Students have limited opportunities to choose tools strategically. The materials often tell students what tools to use, or instruct teachers on the tools students should use. For example:

• Lesson 1.5, Homework, Problem 1, students are given a visual number line to complete, “Jerome uses 4 paper clips to measure the length of a watch.  Each paper clip is 5 centimeters long. How many centimeters long is the watch?”
• Lesson 6.6, Build Understanding, Problem 1, students are given a visual of a bar model with 8 feet spanning a space to complete, “Zasha has 8 feet of yarn for a knitting project. She cuts the yarn into 4 equal pieces. How can you use a bar model to find the length of each piece of yarn?” Tools such as cubes, counters, bar model and pencil are shown in the margin prompting students what to use.
• Lesson 10.4, Spark Your Learning, students are given a visual fraction model to divide a whole number. "A nature preserve is 5 miles wide. A ranger divides the entire preserve into $$\frac{1}{3}$$ mile wide sections for different tours. how many sections does the nature preserve have for different tours?"

Examples of the instructional materials attending to the full meaning of the MPs include:

• MP1: In Lesson 2.2, Spark Your Learning, “Dom plans to use either large square tiles or small square tiles to cover a wall space. Show how Dom can cover the wall space.” In Persevere, the Teacher Edition states, “If students need support, guide them by asking: How would you describe the two sizes of tiles? Which tile size would Dom need more of to cover the wall space? What other tool could you use to solve the problem? Compare using that tool with the one used in the problem. Suppose Dom wants to use the lesser number of tiles. Which tiles should he choose?”
• MP2: In Lesson 4.1, Turn and Talk, students reason abstractly and quantitatively to answer, “Does multiplying a number with 0 have the same effect as adding 0 to a number?”
• MP6: In Lesson 2.3, Build Understanding-Optimize Output, Stronger and Clearer, students share their method for finding the area of the rectangle. “As students share their methods for finding the area of a rectangle, remind them to ask questions of each other that focus on describing area clearly. Then have students refine their answers.”
• MP7: In Lesson 6.2, Spark Your Learning, students look for and make use of structure to solve. For example, “Annie wants to arrange 20 photographs in equal groups in a book. Write questions that can be asked about Annie's photographs. draw equal groups to show how Annie's photographs can be arranged.”
• MP8: In Lesson 8.1, Spark Your Learning, students look for repeated reasoning to solve. For example, “Burmese cats have about 5 kittens per litter. The number pattern shows the number of kittens in 1, 2, 3, 4, and 5 litters. Choose any number of litters from 6 to 10. Using the pattern below, how many kittens are in the number of litters you chose? Make a visual model to show the number pattern.”

### Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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### Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Student materials consistently prompt students to both construct viable arguments and analyze the arguments of others. Turn and Talk sections often require students to construct viable arguments and analyze the arguments of others. In addition, students are often asked to justify their reasoning in practice problems, especially those labeled “Critique Reasoning.”

• Lesson 7.1, On Your Own, Problem 3, students critique the reasoning of two students who have different ways to solve the same problem, one using division and the other multiplication. “Eva has 21 squash seeds. She plants groups of 3 squash seeds together in a mound. Eva says she can use division to find the number of mounds she plants. Jenna says that she can use multiplication to find the number of mounds. Who is correct? Explain your thinking.”
• Lesson 10.6, On Your Own, Problem 3, students analyze the work of others. Students are given a box labeled ‘Ed’s Work’ with two equations in it. “Ed has 8 boxes with 7 rocks in each box. Then he finds 9 more rocks. Ed writes these equations to find how many rocks he has now. Is Ed’s work correct? Explain.”
• Lesson 11.4, Turn and Talk, states, “When rectangles have the same area, how do you know which will have the greatest perimeter and the least perimeter?”.
• Lesson 13.2, Turn and Talk, states, “Compare the fractions in Task 1 and 2. How are they alike? How are they different?”
• Lesson 14.1, Turn and Talk: “What fraction of the whole playground does each hamster's play space represent?”
• Lesson 16.2, Spark your Learning, “Thea is a landscaper. According to her design, $$\frac{2}{3}$$ of the garden should contain red roses. She plants red roses in $$\frac{4}{6}$$ of her new garden. DoesThea make a mistake? Show a way to solve the problem.”
• Lesson 16.2, Build Understanding, “Coach Penny draws a diagram in which a soccer field is divided into 8 equal-sized zones. The 6 zones close to the goal are the scoring zones. Coach Ruiz divided the same field into 4 equal-sized zones with the 3 zones closest to the goal as the scoring zones.” Students write fractions for the sections of Coach Penny's portion of the field that are scoring zones, and Coach Ruiz's portion of the field. They then compare the areas of the two scoring zones and explain similarities and differences.
• Lesson 5.1, On Your Own, Problem 4, “Pam says that she can write $$8 \times 60$$ as the sum of two products. Is she correct? Explain.”
• Lesson 6.1, On Your Own, Problem 4, “Max says 20 objects can be separated into 4 equal groups. Mara says 20 objects can be separated into 5 equal groups. Who is correct? Explain. Draw to show your answer.”

### Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Many of the lesson tasks are designed for students to collaborate, with teacher prompts to promote explaining their reasoning to each other. Independent problems provided throughout the lessons also have teacher guidance to assist teachers in engaging students. Examples include the following:

• The Teacher Edition provides Guided Student Discussion with guiding questions for teachers to create opportunities for students to engage in mathematical discourse. In Lesson 4.7, Step it Out, Sample Guided Discussion, students are asked “How can you tell if a product will be even? How can you represent the number 4 as the sum of two equation addends? So, if you multiply 7 by (2 + 2), what are the two smaller products? What statements can you write about whether the product of two odd numbers is even or odd? How can you prove why your statement makes sense using equal groups?”
• Critique, Correct, and Clarify is a strategy used to assist students in constructing viable arguments. In Lesson 2.2, On Your Own, Problem 7, students analyze a statement made by a fictitious student. Teachers are told to “Point out to students that in Problem 7, Katy’s statement about a gap when measuring the area of a figure may or may not be correct. Encourage students to describe why the statement is or is not correct and to review explanations with a partner. Students should refine their responses after their discussions with a partner.” In Lesson 9.6, On Your Own, Problem 6, students analyze two ways to estimate the difference of 524 - 365 and tell which estimate will be closer to the actual difference. Teachers are told to “Encourage students to describe why they think one estimate is closer to the actual difference and to review explanations with a partner. Students should refine their responses after their discussions with a partner.”
• The Teacher Edition includes Turn and Talk in margin notes to prompt student engagement. In Lesson 1.3, it states “Select students who used various strategies and tools and have them share how they solved the problem with the class. Encourage students to share with the class how they solved the problem. Have students discuss why they chose a specific strategy or tool.”
• Lesson 13.6, Connect Math ideas, Reasoning, and Language, it states “Ask students to share their strategies. Prompt discussion by asking ‘How are the approaches similar? How are they approaches different?”

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for explicitly attending to the specialized language of mathematics. The materials provide explicit instruction on communicating mathematical thinking with words, diagrams, and symbols. The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them. Examples are found throughout the materials.

• At the beginning of each module, Key Academic Vocabulary is highlighted for the teacher. These sections include both Prior Learning, Review Vocabulary and Current Development, and New Vocabulary.  Definitions are given for each vocabulary word.
• Within the lessons, new vocabulary is introduced in highlighted sections called Connect to Vocabulary. Lesson 13.1, “A whole is all of the parts that make up one shape or group. If all of the parts of a whole are the same size, then the whole is divided into equal parts.” Lesson 10.2 “To regroup is to exchange amounts of equal value to rename a number. Examples: 17 ones is 1 ten and 7 ones. 13 tens is 1 hundred and 3 tens.”
• In the lesson planning pages, Sharpen Skills for some lessons include Vocabulary Review activities. Lesson 10.1, “Objective: Students complete graphic organizers for the terms sum and expanded form.” “Materials: Word Descriptions graphic organizer,” “Have students work in small groups to complete a Word Descriptions for the term sum. Have students discuss the definition and state examples and non-examples of a sum. Then have students complete a Word Descriptions for the term expanded form."
• Guide Student Discussion provides prompts related to understanding vocabulary. Module 1, “Listen for student who correctly use review vocabulary as part of their discourse. Students should be familiar with the terms sum, addend, and equal groups.  Ask students what they mean if they use those terms.” “How could you use an array to represent each total?”
• Student pages include Connect to Vocabulary boxes that define content vocabulary. Lesson 4.1, “The Identity Property of Multiplication states that the product of any number and 1 is that number.”
• Vocabulary is highlighted and italicized within each lesson in the materials.
• There is a vocabulary review at the end of each module. Students do fill-in-the-blank with definitions or examples, create graphic organizers to help make sense of terms, or the teacher is prompted to make an Anchor Chart where students define terms with words and pictures, trying to make connections among concepts.

## Usability

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

### Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations that there is a clear distinction between problems and exercises in the materials.

Each module presents lessons with a consistent structure. During the instructional sections, which include Build Conceptual Understanding and Connect Concepts and Skills, students have opportunities to learn new content through examples and problems for guided instruction, step-by step procedures, and problem solving.

The materials distinguish between problems and exercises within each lesson. Lessons include Spark Your Learning or Step it Out, Turn and Talk, Build Understanding, Check Understanding, and On Your Own sections. Spark Your Learning Problems activate prior knowledge and introduce new mathematics to students. Build Understanding includes problems that help students build conceptual understanding of the mathematics topic being taught. Step It Out sections help students develop procedural skill and fluency.

Check Understanding and On Your Own sections include exercises that ask students to use the newly learned mathematics in each lesson. Additional Practice and Homework is available in separate student journal, providing more exercises for students to solve.

For example:

• In Lesson 15.4, Spark Your Learning poses a problems where students need to compare fractions with different numerators and denominators. In Build Understanding, students learn a strategy to use to compare fractions when they are both missing one piece. In Step It Out, students are reminded of previously learned comparison strategies, including the new missing piece strategy. Check Understanding and On Your Own sections provide exercises for students to use all three comparing strategies.
• In Lesson 5.4 Spark Your Learning students experiment with the following problem: “Darvin needs $200 to buy a new pottery wheel. So far, he has sold 7 bowls for$30 each. Does Darvin have enough to buy the new wheel?” Then, in the Build Understanding, students experiment with the patterns of multiples of ten so that in the On Your Own section they are able to multiply 4 x 30.

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations that the design of assignments is intentional.

Overall, lessons are sequenced and scaffolded so students develop understanding of mathematical concepts and skills. The lesson structure provides students with the opportunity to activate prior learning, build procedural skills, and engage with multiple activities that utilize concrete and abstract representations and increase in complexity.

Exercises are given in intentional sequences. In general, lessons are designed to begin with activating prior knowledge and build toward conceptual development and procedural skill. In the Spark Your Learning section of Lessons students use manipulatives and/or visual models to experiment with mathematics thus developing a concrete or representational understanding. This is followed by a Turn and Talk with a partner allowing students to process the connections they have found. Throughout the lessons, students are provided scaffolding with new content in the Build Understanding and Step It Out sections, where the abstract concept is broken down into smaller steps with additional turn and talk opportunities and  are provided with independent exercises to build understanding and mastery. The Check Understanding section provides a mid-lesson check-in and can be used to indicate the need to differentiate learning for students. Students practice the abstract concept in the On Your Own.

For example in Lesson 16.2, Spark Your Learning, students use manipulatives and visual models to solve the following problem: “Thea is a landscaper. According to her design, $$1\frac{2}{3}$$ of the garden should contain red roses. She planted red roses in 4/6 of her new garden, not $$1\frac{2}{3}$$. Has Thea made a mistake?” Students explore similar problems on a concrete and representational level throughout the Build Understanding section. They use rectangles as models of the area of a barn for jumping horses identify equivalent fractions. In On Your Own students find equivalent fractions using a number line.

Concepts are developed throughout the modules such as 3.OA.1.3 which is introduced in Module 1, continued in Module 3 and extended to multiples of 10 in Module 5 and then division in Modules 6, 7 and 8.

### Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for having a variety in what students are asked to produce.

There is variety in how students are asked to present mathematics. In Spark Your Learning, Build Understanding, and Step It Out sections, students are often asked to use visuals to show their thinking. Turn and Talk questions frequently ask students to construct arguments and give explanations. There are opportunities for students to produce answers and solutions in the On Your Own sections, while also providing opportunities for students to provide written explanations. Throughout the materials, students are asked to represent mathematics using equations.

Homework assignments ask for a variety of responses from fluency to higher-level thinking. For example, the Lesson 7.1 Homework assignment has 7 problems. The initial problem asks students to write an equation to model a real-world situation. In the next two problems students  complete a visual model of an equation. In problems 4-6 students find the unknown in an equation and then use a table in the last question to solve a word problem.

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.At the beginning of lessons they indicate what materials/manipulatives will be needed. In the lessons on the student pages, there is a picture of the manipulative that they will use. For example, in Lesson 1.2, students use two color counters, connecting cubes or a number line to represent the following problem. “LIng is at a fair with her friends Jimmy and Pablo. At a game booth, they each get 4 balls. How many balls do Ling and her friends get?” The manipulatives provide opportunities for students to develop a conceptual model of problems that they will then represent in pictorial form in their student workbook.

Examples of manipulatives for Grade 3 include: base ten blocks, connecting cubes, fraction circles, fraction strips, geo board, money, number line, pattern blocks, ruler, square dot paper, and two color counters.

Lesson 4.5, color tiles are as needed in the Almost There small-group option for differentiated instruction. Students use the tiles to make arrays, write an equation to represent the array, and rearrange the tiles to show the changing order of the factors.

The materials rely heavily on pictures of manipulatives. When physical manipulatives are called for in the Lesson Materials in the Teacher Edition, it is not always clear how they are to be used. There is sometimes direction for how they can be used in the differentiation section.

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
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Indicator Rating Details

The visual design of HMH Into Math Grade 3 is not distracting or chaotic.  The materials, both print and digital, follow a consistent format, which promotes familiarity with the materials and makes finding specific sections more efficient. The page layout in the materials is user-friendly. Tasks within a lesson are numbered to match the module and lesson numbers. There is much information provided, and pages are not overcrowded or hard to read. Graphics promote understanding of the mathematics being learned. Student practice problem pages include enough space for students to write their answers and provide explanations. The digital format is easy to navigate, but students have to scroll without being able to view much of the information at one time. The teacher edition provides information for teachers to be able to access digital resources. There is room for students to record answers and show their thinking.

Features of the materials are consistently presented, and the use of colored fonts supports identification of lesson components. For example, Turn and Talk opportunities are highlighted in yellow and Check for Understanding is always in red. Visual images mirror the situation in the problem or can be used by students as they solve the problem. For example, in Module 17, Lesson 2, On Your Own, includes an image of a scale with a cube puzzle and a yo-yo. Students are asked to write greater than or less than for “The mass of the cube puzzle is ____ the mass of the yo-yo.”

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
7/8
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that partially contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for providing quality questions to help guide students’ mathematical development.

Throughout the Teacher Edition questions are posted to help support teachers with questions to guide students’ mathematical development. Sections titled, Activate Prior Knowledge, Spark Your Learning, Build Understanding, Learn Together, and Turn & Talk, consistently provide questions to drive student discussion. For example:

• Lesson 7.2, Spark Your Learning, Persevere, provides the following questions for teachers: “What is the question asking you to do? How can you use the number of equal groups and the number in each group to write a multiplication question and a division question? ” In the same lesson the Step It Out Turn & Talk states, “What is the greatest number of multiplication and division facts that can be written for a set of numbers? What is the least? Provide examples.”
• Lesson 15.4, Spark Your Learning task, includes two questions: “How do you know what the whole is in the problem?” and “How can you use concrete or visual models to find who picked the greater amount of cherries?”
• Lesson 7.4, Step it Out, includes three questions:  “How can you find the number of lanes at Gutter Alley?” “What are you counting in each problem as you equal groups of 10?” and “Why can you choose to count up or count back to divide?”

### Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for containing ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials.

Throughout the teacher edition there are ample and useful annotations and suggestions on how to present the content in the student edition to all levels of math learners in the classroom. Specifically, the teacher edition includes sections titled, Lesson Focus and Coherence, Plan for Differentiated Instruction, Spark Your Learning, Motivate, Persevere,” and Leveled Questions” designed to assist the teacher in the mathematical standards and concepts that are present in the lesson. For example:

• Lesson 2.3, Plan for Differentiated Instruction, includes three columns titled, On Track, Almost There, and Ready for More. The guidance for teachers is designed to be used in small group instruction.
• Lesson 6.6, Activate Prior Knowledge, includes the following guidance for teachers: “Based on the students’ responses to the Problem of the Day, choose one of the following: Project interactive Reteach, Grade 3, Lesson 1.6 or Complete the Prerequisite Skills Activity.”

### Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
1/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 partially meet the expectations for containing adult-level explanations so that teachers can improve their own knowledge of the subject. The materials include adult-level explanations of the grade-level content, but the materials do not include adult-level explanations of advanced mathematics concepts so that teachers can improve their own knowledge of the subject.

This materials includes explanations and examples of the course level mathematics specifically for teachers that can improve their own knowledge of the subject. In the teacher edition modules there are small sections of examples and support for the adult in the math classroom as it relates to grade level math standards. For example:

• The Mathematical Progressions table in each module and lesson highlights Prior Learning, Current Development and Future Connections. In Lesson 4.2 this table identifies Prior Learning as a 1st grade standard that supports the Current Development - 3rd grade on level standard, and Future Connections to Grade 4 standards.
• Professional Learning describes “Visualizing the Math” present in each lesson. In Lesson 4.2, this is a summary on how visual models help with the distributive property and how they can assist students in forming mental images.
• The “Planning and Pacing” book includes a correlation chart for the math practices that defines each math practice in full.

### Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

Each module in the Teacher Edition includes Mathematical Progressions which lists prior learning, current development, and future connections. Similarly, the beginning of each lesson in the Teacher Edition includes Mathematical Progressions that show connections to prior and future grades’ standards, as well as other lessons within the program.

In the Planning and Pacing Guide, Progressions and Algebra Readiness notes “Algebra as a course of study today is integrated around four progressions of elementary and middle school content leading to the Algebra course: Number and Operations, Operations and Algebraic Thinking, Statistics and Probability, and Functions” and includes a table that shows how the domains in Grades K-5, 6-7, and Grade 8 / Algebra fit into these progressions.

### Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 provide a list of lessons in the teacher's edition, cross-­referencing the standards addressed, and a pacing guide.

Each course in this series includes a Planning and Pacing Guide that includes the standards and pacing (number of days) for each lesson. There is another standards chart in the Planning and Pacing Guide that lists each standard and correlation to Student Edition Lessons. In the Teacher Edition, the standards contained in each lesson are identified with written descriptions as well as listed under Current Development in the Mathematical Progressions chart.

### Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 include strategies for parents to support their students progress. The Family Resources tab include several resources for parents:

• “School Home letters inform families about the skills, strategies, and topics students are encountering at school.” Each module includes a letter, found online in 4 languages, providing vocabulary, a home activity, and discussion prompts. This letter is available in English, Spanish, Haitian-Creole, and Portuguese.
• Math on the Spot videos are available for specific lessons within a module online in Family Resources. For example, Module 1 includes a Math on the Spot video for Lessons 2 and 3.

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
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Indicator Rating Details

The instructional materials for Into Math Grade 3 explain instructional approaches used and how they are research-based.

The Planning and Pacing Guide contains Teacher Support Pages that include a section on Supporting Best Practices. “Into Math classrooms maximize student growth by providing teachers with content  designed around research-based, effective teaching practices such as those described in Principles to Actions (NCTM 2014).” These include:

• Establish mathematics goals to focus learning.
• Implement tasks that promote reasoning and problem solving.
• Use and connect mathematical representations.
• Facilitate meaningful mathematical discourse.
• Pose purposeful questions.
• Build procedural fluency from conceptual understanding.
• Support productive struggle in learning mathematics.
• Elicit and use evidence of student thinking.

The Planning and Pacing Guide describes four design principles from the Stanford Center for Assessment, Learning, and Equity (SCALE) that “promote the use and development of language as an integral part of instruction”. These principles are: Support sense-making; Optimize output; Cultivate conversation; and Maximize linguistic and cognitive meta-awareness. To address this, the instructional materials include language routines that “help teachers promote the design principles during instruction.” Each module contains a Language Development page in the Teacher Edition that states where the language routines should be used. On the lesson pages of the Teacher Edition, there are Support-Sense Making boxes that describe how the language routine can be used. Also, there are notes in the margin of the teacher’s edition providing connections from the strategy to the principle.

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
8/10
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 partially meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, and assessments that clearly denote which standards are being emphasized.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

• At the beginning of the year, students’ prior knowledge is gathered through a Prerequisite Skills Inventory. “This short-answer test assesses core precursor skills that are most associated with on-grade success.” (Assessment Guide)
• Each module begins with Are You Ready, a diagnostic assessment of prior learning related to the current grade-level standards. Intervention materials are provided to assist students not able to demonstrate the necessary skills. Commentary for each standard explains how the prior learning is relevant to the current module’s content.
• Prior learning is identified in the Mathematical Progressions section at the beginning of each module and lesson of the Teacher Edition.

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• The module overview in the Teacher Edition contains “Common Errors” as students engage in an introductory task and provides questioning strategies intended to build student understanding.
• The Spark Your Learning planning page for each lesson in the Teacher Edition includes a Common Error section related to the content of the lesson that identifies where students may make a mistake or exhibit misunderstanding. There is a rationale that explains the likely misunderstanding and suggests instructional adjustments or steps to help address the misconceptions.
• There are also “Watch For” boxes and question prompts that highlight areas of potential student misconceptions.

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
1/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 partially meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

• Each lesson ends with a few Spiral Review questions for ongoing practice in the More Practice/Homework section.
• Online interactive lessons and homework practice provide students with immediate notification that answers are correct or incorrect, but do not provide feedback for changing incorrect answers.
• The online lessons are the same as in the print textbook.
• Each Module Review has a scoring guide/checklist, so students know which questions they answer correctly. The scoring guide/checklist does not provide feedback for changing incorrect answers. The online Module Review does provide “Hints” to help with selection of answers.
• Digital assessments are auto-scored and generate recommendations that can provide feedback to teachers, but not directly to students.

The materials provide support for ongoing review and practice. Within each lesson there is an Activate Prior Knowledge/Problem of the Day. This is a review problem from prior units/lessons. Directly correlated with each question, there is teacher support on next steps based on the students’ responses.

### Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations that assessments clearly denote which standards are being emphasized.

The Lesson Focus and Coherence page indicates the CCSSM that will be addressed within the Lesson. Throughout the lesson there are then formative assessments in the Check for Understanding, On Your Own and More Practice/Homework.  Each module has an End of Module Test, the standards associated with each problem on this test can be found on the Individual Record Form within the Assessment Guide Book.

Each Unit has a summative Performance Task that includes the content focus in the teacher pages of the Assessment Guide.

### Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 partially meet the expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

• Each lesson has a diagnostic assessment, Are You Ready, correlated to standards and a suggested intervention for struggling students. The materials state that when using Online Ed, teachers can assign the Are You Ready digitally “to power actionable reports including, proficiency by standards, and item analysis.”
• “Check Understanding is a quick formative assessment in every lesson. Teachers use data to determine which students need additional small-group support and which students can continue on to independent practice or math center challenges.” (Planning and Pacing Guide) Check Understanding presents a limited number of questions, usually 1-3, which includes a digital option that can be assigned “to determine success with the learning objective, items to review, grouping and differentiation resources.”
• The Individual Record Forms in the Assessment Guide suggest Reteach Lessons that teachers can use for follow-up based on the module assessments, but there are no other suggestions for follow-up with students or guidance to teachers.
• The Individual Record Forms for the Prerequisite Skills Inventory, Beginning-of-Year, Middle-of-Year Test, and End-of-Year Tests do not suggest Reteach Lessons or provide other guidance that teachers can use for follow-up with students.
• The Performance Task Rubrics for the Unit Performance Tasks do suggest Reteach Lessons but do not provide any other guidance that teachers can use for follow-up with students.

### Indicator 3q

Materials encourage students to monitor their own progress.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 include Scales to Track Learning Goals at the end of each lesson. The Teacher Edition introduction states, “The scale below can help you and your students understand their progress on a learning goal. ”

Each lesson contains “I Can” scales with four levels of  “I Can” statements written in increased difficulty. While there is a note saying “The scale below can help you and your students understand their progress on a learning goal”  there is no explicit indication of how to use these scales.

At the end of On Your Own section is a Learning Mindset prompt where students write a response to reflect on the lesson. For example from Lesson 10.3 the Learning Mindset asks “What strategy did I use to subtract 3-digit numbers? Explain.”

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
11/12
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials partially embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• At the beginning of each module, Teaching for Depth provides information on strategies to use when teaching the concept, including Represent and Explain, which focuses on ways for students to describe and picture a concept, or Make Connections, which helps students understand a new idea by connecting it to previous knowledge.
• At the beginning of each module, Mathematical Progression makes connections to both prior and future skills and standards to scaffold instruction.
• At the beginning of each module, Diagnostic Assessment, Are You Ready?, allows teachers to “diagnose prerequisite mastery, identify intervention needs, and modify or set up leveled groups.”
• Each lesson provides Warm-up Options to activate prior knowledge such as Problem of the Day, Quick Check for Homework, and Make Connections.
• Throughout the lessons, there are notes, strategies, sample guided discussion questions, and possible misconceptions that provide teachers structure in making content accessible to all learners.
• Student practice starts with up to four Check Understanding exercises to complete with guidance before moving to independent work in On Your Own or More Practice/Homework.

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• There are Reteach and Challenge activities for each lesson.
• Each module includes Plan for Differentiated Instruction that provides teachers with teacher-guided, Small-Group Options and self-directed Math Center Options based on student need: On Track, Almost There (RtI), and Ready for More.
• Each lesson provides Leveled Questions in the teacher’s edition identified as DOK 1, 2, and 3 with an explanation of the knowledge those questions uncover about student understanding.
• There are four Language Routines to Develop Understanding used throughout the materials: 1) “Three Reads: Students read a problem three times with a specific focus each time.” 2) “Stronger and Clearer Each Time: Students write their reasoning to a problem, share, explain their reasoning, listen to and respond to feedback, and then write again to refine their reasoning.” 3) “Compare and Connect: Students listen to a partner’s solution strategy and then identify, compare, and contrast this mathematical strategy. And 4) “Critique, Correct, and Clarify: Students correct work that is not their own with a flawed explanation, argument, or solution method and share with a partner to reflect and then refine the sample work.”

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
1/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 partially meets the expectations for embedding tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

The Planning and Pacing Guide, Teacher Support, Access and Equity, and Spark Your Learning Tasks are “designed as ‘low-floor/high ceiling’ tasks that all students can access but that can also be extended to provide challenge.” Teachers are provided guidance on how to assist various levels of learners, depending on how they respond to the problem. For example, Lesson 3.3, Spark Your Learning has this prompt: “Your community wants to use wind turbines to bring electricity to homes.  Each wind turbine has 3 blades. Choose a number of wind turbines for your community from 5 to 9. How many blades are there? Show two different ways to find the number of blades.” This problem provides multiple entry points and solution strategies for students. However, Spark Your Learning is not present in every lesson.

Support for Turn and Talk in the teacher’s edition provides suggestions to help students using a variety of strategies. Teachers are often prompted to “Select students who used various strategies and have them share how they solved the problem with the class.”

### Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

In addition to the strategies for meeting the needs of a range of learners described in Indicator 3s, there is further support in place for English Language Learners (ELLs) and other special populations:

There is Language Development to support English Learners in each module which includes linguistic notes that provide strategies intended to help students struggling with key academic vocabulary such as: “Speak with students about words that can have multiple meanings….”, and “Visual cues help students…”  Language Development also includes information about the Language Routines embedded in the instructional materials: Three Reads; Stronger and Clearer Each Time; Compare and Contrast; Critique, Correct, and Clarify. These are identified by a pink box throughout lessons with speech bubble that identifies the Language Routine to be used.  In addition, there are supports for special populations including:

• Language Objectives are included in every lesson.
• There are Reteach, and RtI worksheets that can be assigned online or printed.
• There are Turn and Talk prompts designed to support students, for example, “go back and reread the problem and break it into pieces. For example: What do you know? What do you need to find?”
• A multilingual glossary is available online.

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

In addition to the strategies for meeting the needs of a range of learners described in Indicator 3s, there is further support in place for advanced students:

• There are optional lessons provided online that teachers may choose to utilize with advanced students.
• Each lesson has a corresponding Challenge page, provided in print or online, addressing the same concepts and standards where students further extend their understanding and often use more complex values in their calculations.
• On the module opener page, Extend the Task in the margin of the Teacher Edition provides ideas for extending the task.

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 3 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

The materials provide various demographic and personal characteristics. The instructional materials reviewed for this series meet the expectation for providing a balanced portrayal of various demographic and personal characteristics. Pictures of adults and children in the text show a variety of demographics and personal characteristics

There are a variety of names used in word problems throughout the text. The lessons contain a variety of tasks and situations in the story problems that interest students of various demographic and personal characteristics. There is a balanced approach to the use of gender identification.

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 provide opportunities for teachers to use a variety of grouping strategies.

In the Planning and Pacing Guide there is a section titled, Grouping and Recommendations. This section states, “One of the most valuable and time-saving tools for teachers is the Recommend Groups tool online. It synthesizes data from assessments and places students into leveled groups, which teacher can modify as needed. Recommended lesson-level resources for each group surfaced in the tool and can quickly be assigned to each group.”

• Each lesson provides teachers with a differentiated plan that includes small-group options.
• The materials provide students with self-directed activities at math centers.
• Throughout the materials, there are ample opportunities for students to Turn and Talk with a partner.
• Using the Check for Understanding, the teacher is directed to pull students into small groups and use the Teacher Tabletop Flipchart.

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 encourage teachers to draw upon home language and culture to facilitate learning.

• The student glossary is in both English and Spanish.
• Each module includes School-Home Letters in multiple languages: Spanish, English, Portuguese, and Haitian Creole.

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 3: integrate some technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; are intended to be easily customized for individual learners; and do not include technology that provides opportunities for teachers and/or students to collaborate with each other.

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 integrate some technology including digital lessons and virtual tools. Students can complete tasks and activities from the Student Edition through an interactive format.

• Students can draw pictures, create shapes, and type to show their thinking on the interactive lessons using a virtual sketchpad. Students complete tasks such as shading in bar diagrams, drag and drop the correct values into a table, or graph an equation.
• iTools virtual manipulatives are available online.
• On the Spot videos of specific lesson problems are in the online student resources and provide the opportunity for students to review their work with their families by watching the video. These focus on content rather than MPs.

### Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 are web-based and compatible with multiple internet browsers.

• The materials are platform-neutral and compatible with Chrome, ChromeOS, Safari, and Mozilla Firefox.

Materials are compatible with iPads, laptops, Chromebooks, and other devices that connect to the internet with an applicable browser.

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology through a website called Online ED, which parallels the print textbook.

• Lesson problems from the Student Edition, assessments, and unit performance tasks are provided to be completed and scored using technology, providing students with feedback on whether the answers are correct or incorrect.
• Online Ed is designed to make recommendations for differentiation after auto-scoring of Check Understanding problems within each lesson.
• There are growth monitoring assessments that are “designed to be administered in 40 minutes, 3 times per year. The system utilizes a secure bank of assessments to adapt to each student’s ability and maps progress on the Quantile Framework.” (Pacing Guide)
• Assessments can be created using a question bank that repeats the questions presented throughout the interactive lessons. However, teachers can modify questions and add new questions.
• The online system has dynamic reporting by assignment or standards. If teachers are using the online system, they can view student progress for interim growth, module readiness, and lesson practice and homework.

### Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 are intended to include opportunities for teachers to personalize learning for all students.

• Teachers can assign lesson problems and assessments, as well as view assessment analytics.
• Teachers can group students according to individual needs. The online component has Recommended Groups that “synthesizes data from assessments and places students into leveled groups.” (Pacing Guide) Recommended lesson resources can be assigned to each group.
• Teachers can create assessments using a bank of items.

The instructional materials reviewed for Into Math Grade 3 provide minimal opportunity to be adapted for local use.

• Pieces of a lesson can be assigned directly to students or groups of students.
• There is a question bank for teachers to create assessments. The bank repeats the questions that are already included in each lesson, and these questions can be modified.

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 3 do not incorporate technology that provides opportunities for multiple students to collaborate with the teacher or one another.

abc123

Report Published Date: 01/28/2020

Report Edition: 2020

Title ISBN Edition Publisher Year
Into Math Comprehensive Student Resource Print/Digital Package 6 Year 9780358155560 Houghton Mifflin Harcourt 2020
Into Math Comprehensive Teacher Resource Package Print/Digital Package 6 Year Digital 9780358156161 Houghton Mifflin Harcourt 2020

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

## Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

## Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

• Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
• Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

## Key Terms Used throughout Review Rubric and Reports

• Indicator Specific item that reviewers look for in materials.
• Criterion Combination of all of the individual indicators for a single focus area.
• Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
• Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
• Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

## Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.

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