## Alignment: Overall Summary

The instructional materials reviewed for HMH Into Math Grade 7 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 partially 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
35
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 7 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.
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Criterion Rating Details

​The instructional materials reviewed for HMH Into Math Grade 7 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.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 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 Interim Growth assessments.

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

• Module 1, Form B, Question 7 states: “Brody’s town is building a pool based on a scale drawing that is 20 cm by 10 cm and uses the scale 1cm:250 cm. What is the area of the pool, in square meters?” (7.G.1)
• Module 2, Form B, Question 6 states:  "The Shoe Stop is having a sale on sneakers. The original price for a pair of high-top sneakers was $135.00. The sale price for the sneakers is$94.50. What is the percent decrease in the price of the sneakers? A 30% B 40.5% C 42.9% D. 70%" (7.RP.3)
• Module 6, Form A, Question 11 states: “The drama club sold 209 evening show tickets for $18.50 each and some matinee show tickets. They want to make$5,700 for the two shows. If matinee tickets cost $11.75 each, how many matinee tickets do they need to sell to reach their target amount?” (7.EE.3) • Module 11, Form B, Question 8 states: "A hexagonal pyramid is sliced to make cross sections. Select the correct button in the table to show the shape of each cross section. A horizontal slice parallel to the base. A slice perpendicular to the base but both through the vertex. A slice perpendicular to the base through the vertex." (7.G.3) ### 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 + - Criterion Rating Details The instructional materials reviewed for HMH Into Math Grade 7 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 + - Indicator Rating Details The instructional materials reviewed for HMH Into Math Grade 7 meet expectations for spending a majority of instructional time on major work of grade. • The number of modules devoted to major work of the grade is 11 out of 15, which is approximately 73%. • The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 39 out of 59, which is approximately 66%. • The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 94 out of 136 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 66% 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 + - Criterion Rating Details The instructional materials reviewed for HMH Into Math Grade 7 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 + - Indicator Rating Details The instructional materials reviewed for HMH Into Math Grade 7 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: • In Lesson 1.6, students find the scale using complex fractions based on a given diagram (7.G.1, 7.RP.1), write the appropriate y = mx equation (7.RP.2c), and solve related problems using the equation. • In Lesson 7.5, students write and solve equations (7.EE.4) based on different angle relationships (7.G.5). For example, “Angle A and Angle B are adjacent. The sum of their measures is 92 degrees.” “Angle A measures (2x+5) degrees. Angle B is three times the size of angle A. Write an equation to determine the value of x. Then solve your equation and find the measures of both angles.” • In Lessons 10.1-10.4, students use formulas to find the circumference of a circle (7.G.4) and areas of various figures (7.G.6) in multiple real-world situations (7.EE.3). • Lesson 10.1 connects 7.G.4 to 7.RP.2 with “Describe what you notice about the ratio C/d in your table. Does the relationship between the circumference and diameter of a circle appear to be proportional? Explain.” • In Lessons 11.2-11.4, students use formulas and solve equations to find surface areas and volumes of various figures (7.G.6) in multiple real-world situations (7.EE.3). • In Lesson 12.2, students use a random sample and proportional reasoning (7.RP.2) to make inferences about a population (7.SP.1). For example, Step It Out Question 3 states: “A worker randomly selects one of every 7 sets from the 3,500 sets of headphones produced. The results are shown. Write the ratio of defective headphones to the total headphones in the sample. Then write the ratio as a decimal and solve an equation to find the number of headphones in the population that can be predicted to be defective.” • In Lessons 14.1-14.4, students use probabilities (7.SP.3), ratios, and proportional relationships to solve problems in real-world situations (7.RP.3). For example, in Lesson 14.4, Step It Out Question 2, students use proportional reasoning to predict the number of students in the whole school that prefer math. • In Lesson 15.4, students calculate simple and compound probabilities (7.SP.8) using rational numbers in various forms (7.NS.3). ### 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 + - Indicator Rating Details The instructional materials for HMH Into Math Grade 7 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 160 days: 106 days for lessons and 54 days for assessments. • The Planning and Pacing Guide and the Planning pages at the beginning of each module in the Teacher Edition provide the same pacing information. • Grade 7 has six units with 15 modules which contain a total of 59 lessons. • The pacing guide designates 41 lessons as 2-day lessons and 18 as 1-day lessons, leading to a total of 100 lesson days; a “day” is defined as one period in a traditional structure. • Each unit includes a Unit Opener which would take less than one day. There are six Openers for Grade 7 (6 days). • This is a total of 106 lesson days. Assessments included: • The Planning and Pacing Guide indicates a Beginning, Middle, and End of Year Interim Growth test that would require one day each (3 days). • Each module starts with a review assessment titled “Are You Ready?” There are 15 modules (15 days). • Each unit includes a Performance Task which indicates an expected time frame ranging from 25-45 minutes. There are six Performance Tasks for Grade 7 (6 days). • Each module has both a review and an assessment. There are 15 modules (30 days). • Based on this, 54 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 + - Indicator Rating Details The instructional materials for Into Math Grade 7 meet expectations for being consistent with the progressions in the Standards. In general, the materials identify content from prior and future grade-levels and relate grade-level concepts explicitly to prior knowledge from earlier grades. In addition, the instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. • In the Teacher Edition, the introduction for each module includes Mathematical Progressions, which lists standards under the areas of Prior Learning, Current Development, and Future Connections and clarifies student learning statements in these categories. For example, Module 5, Multiply and Divide Rational Numbers states, “Prior Learning: Students fluently added, subtracted, multiplied, and divided multi-digit decimals using the standard algorithm for each operation.” (6.NS.3); “Current Development: Students develop and use the rules for multiplying signed numbers.” (7.NS.2); “Future Connections: Students will apply the properties of integer exponents to generate equivalent numerical expressions.” (8.EE.8) • The beginning of each module has Teaching for Success, which sometimes includes Make Connections. Make Connections references prior learning. For example Module 8 states, “In this module, students will build on their prior knowledge of inequalities to solve both one and two-step inequalities. Students will also solve real-world mathematical problems using numerical and algebraic expressions and equations.“ • In Activate Prior Knowledge at the beginning of each lesson, content is explicitly related to prior knowledge to help students scaffold new concepts. • Some lessons provide direct scaffolding for students reminding them of prior learning. For example, in Lesson 1.1, Build Understanding, Question 1d, students complete a table comparing Small Jars of Salsa and Ounces of Salsa and are instructed, “You previously learned that a unit rate is a rate in which the second quantity in the comparison is one unit…” (6.RP.2). In Lesson 4.1, Build Understanding, Question 1b states, “Recall that the absolute value of a number is the number’s distance from 0 on a number line.” • Each module includes a diagnostic assessment, Are You Ready?, that explicitly identifies prior knowledge needed for the current module. For example, Module 2, Are You Ready? states, “Complete these problems to review prior concepts and skills you will need for this module.” Students multiply decimals by whole numbers (5.NBT.7) and find a percent of a whole (6.RP.3c). In this module, students use these skills to find percent change, find markups, discounts, taxes, gratuities, commissions, fees, and simple interest (7.RP.3).” • In the Module Opener, "Assess Prerequisite Concepts" identifies content as prerequisite knowledge including the grade and module where the prerequisite concept is addressed. Examples of the materials providing all students extensive work with grade-level problems include: • In the Planning and Pacing Guide, there is a Correlations chart that outlines the mathematics in the materials. According to this chart, all grade-level standards are represented across the 15 modules. Within each lesson, Check Understanding, On Your Own, and More Practice/Homework sections include grade-level practice for all students. Margin notes in the Teacher Edition also relate each On Your Own practice problem to grade-level content. Examples include: • In Lesson 2.1, More Practice, Question 9 states, “In Cary’s basketball career, he’s made 80% of his free throws, plus or minus 5%. If he attempts 200 free throws this season, what is the range of successful free throws he can expect to make? Show your calculation." (7.RP.3, 7.EE.3) • In Lesson 7.4, On Your Own, Question 5 states, "Dirk sold 7 more than 2 times as many gym memberships this month than last month. This month he sold 43 memberships. A. Use arithmetic to find the number of memberships Dirk sold last month. B. Use algebra to find the number of memberships Dirk sold last month. C. Compare the sequence of math operations in Part A and Part B." (7.EE.4a) When work is differentiated, the materials continue to develop grade-level concepts. An example of this is Lesson 2.2, which explores markups and discounts. The corresponding Reteach page provides guided notes for students to follow in order to access the concept and the Challenge page lists the cost of pants, socks, and a shirt before they are marked up by a store. Students calculate the percent increase given, new sales prices, the new price after a coupon is used, and finally investigate if the store will break even if they offer a percent discount equal to the percent markup of an item. ### 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. 2/2 + - Indicator Rating Details The instructional materials reviewed for HMH Into Math Grade 7 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: • In Lesson 2.2, both Learning and Language objectives are “Calculate markups, markdowns, retail prices, and discount prices, and represent them using equations of the form y = kx” and “Use the terms markup, markdown, and retail price to explain the solutions to real-world problems,” shaped by 7.RP.A. • In Lesson 9.4, the learning objective is “Draw, construct, and analyze two-dimensional figures, including circles,” shaped by 7.G.A. • In Lesson 12.2, the learning objective is “Use a random sample to make inferences about a population,” shaped by 7.SP.A. 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: • In Lesson 2.1, students perform operations with rational numbers (7.NS.A) to solve multi-step problems involving percent of change (7.RP.A). • In Lesson 2.3, students write and solve an equation (7.EE.B) to calculate the cost of dinner including a tip (7.RP.A). • In Lesson 4.4, students solve multi-step real-world problems by writing equations (7.EE.B) and performing appropriate calculations while applying the properties of operations (7.NS.A). • In Lesson 6.3, students find the unit rate (7.RP.A) in kilometers per hour working with rational numbers (7.NS.A) for a “walking tour that is 10 1/10 kilometers long.” • In Lesson 7.2, students write an expression that shows the perimeter of a yard with side lengths that contain variables and rational number coefficients and create an equivalent expression by combining like terms (7.EE.A), which requires them to add rational numbers (7.NS.A). ### Gateway Two ## Rigor & Mathematical Practices #### Meets Expectations + - Gateway Two Details The instructional materials reviewed for HMH Into Math Grade 7 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 + - Criterion Rating Details The instructional materials reviewed for HMH Into Math Grade 7 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 + - Indicator Rating Details The instructional materials for HMH Into Math Grade 7 meet expectations for developing 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. Build Understanding and Step it Out introduce mathematical concepts, and students independently demonstrate their understanding of the concepts in Check Understanding and On Your Own problems at the end of each lesson. • In Lessons 3.1 and 3.2, students develop conceptual understanding of integer addition and subtraction by representing the operations on number lines. For example, in Build Understanding, Part A states, “Latrell spins a wheel to find out how many points he adds to his score. The wheel stops on ‘-5 points.’ Use the number line to add -5 points to Latrell’s score. Then complete the equation.” (7.NS.1) • In Module 5, students build understanding of multiplying and dividing rational numbers. For example, students represent multiplication of positive and negative numbers with repeated addition on a number line. In Lesson 5.2, students investigate signs of products as the number of negative factors change. (7.NS.2) • In Lesson 7.1, Build Understanding, Question 2, students rewrite the discount expression p + p + 0.60p and explain why the expressions are equivalent. (7.EE.2) ### 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 + - Indicator Rating Details The instructional materials for HMH Into Math Grade 7 meet expectations for attending to those standards that set an expectation of procedural skills. The materials include problems and questions that develop procedural skills and provide opportunities for students to independently demonstrate procedural skills throughout the grade. The materials develop procedural skills in On Your Own, and students demonstrate procedural skills in More Practice/Homework. • Throughout Modules 3 and 4, students evaluate addition and subtraction problems with various rational numbers. For example, in Lesson 3.3, On Your Own, Questions 10-13, students "Find rational numbers to complete each equation. Use the number line to help. ___ + ___ = –8.75; ___ + ___ = –1 3/4; ___ + ___ = –9.25; ___ + ___ = 0.” In Lesson 4.1, More Practice/Homework, Question 10, students solve 100 + (-26) and Question 12, students solve "75 + (–30)." (7.NS.1) • Throughout Modules 5 and 6, students evaluate multiplication and division problems with various rational numbers. For example, in Lesson 5.2, More Practice/Homework, Question 7 states, “Find each quotient: -27/5”. In Lesson 6.1, More Practice/Homework, Question 3, states, "5 - 44 x (0.75) - 18 / ⅔ x 0.8+ (-⅘)." (7.NS.2) • In Lesson 7.2, students write linear expressions and apply properties of operations to generate equivalent expressions. For example, “students factor expressions using the GCF: 3x-30, students simplify expressions using properties of operations: (t–5) + (–2t+3), students also expand expressions using the Distributive Property and then simplify the expressions: (4x-7.2)+(-5.3x-8).” (7.EE.1) • In Lesson 7.4, students solve two-step equations involving rational numbers and equations written in the forms px + q = r and p(x+q) = r. For example, On Your Own, Questions 8-15 and 19-27, students solve equations in this form: “-9d-1=17, 2+1/6a=-4, 2x-5=15.” (7.EE.4a) ### 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 + - Indicator Rating Details The instructional materials for HMH Into Math Grade 7 meet expectations for teachers and students spending sufficient time working with engaging applications of the 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 concepts of the grade-level, and students independently demonstrate the use of mathematics flexibly in a variety of contexts. During Independent Practice and On Your Own, students often engage with problems that include real-world contexts and present opportunities for application. More Practice and Homework contains additional application problems. • In Module 2, students solve multi-step ratio and percent problems. For example, in Lesson 2.1, Check Understanding, Question 1 states, “Peggy earned$20 for each lawn she mowed last summer. This summer, she raised her price to $23 per lawn. What is the percent of Peggy’s change?” and in Lesson 2.2, On Your Own, Question 8 states, “Shelly’s boutique had a labor day sale featuring 25% off any item. Tammy wanted to buy a blouse that originally sold for$21.99. To the nearest cent, how much will it cost her before tax to buy the blouse during the sale?” (7.RP.3)
• In Modules 4 and 5, students solve real-world problems involving the four operations with rational numbers. For example, in Lesson 4.4, Check Understanding, Question 1 states, “Soojin is adding some lengths of wood she used for a project. The lengths of wood are 1 2/3, 3 3/4, and 2 1/4 feet. How much wood did she use in all?”, and in Lesson 5.4, On Your Own, Question 4 states “A butterfly is flying 8 3/4 feet above the ground. It descends at a steady rate to a spot 6 1/4 feet above the ground in 1 2/3 minutes. What is the butterfly’s change in elevation per minute?” (7.NS.3)
• In Lesson 6.3, Check Understanding, Question 1 states, “A block of clay contains 20 4-ounce portions of clay. A ceramics teacher wants to use the block to make as many spheres of clay as possible, each weighing ⅖ pound. How many spheres can she make?” and in Lesson 6.2, students use estimation to check reasonableness, such as “The dimensions of a room with one window and one door at a community center are shown. Ivan wants to have the four walls painted. The painter says the area is 542.2 square feet. Estimate the total area that needs to be painted. Was the painter’s answer reasonable. Explain.” (7.EE.3)
• In Lesson 8.3, students write and solve two-step inequalities given a real-world scenario, such as “Ariana started a saving account with $240. She deposits$30 into her account each month. she wants to know how many months it will take for her account to have a balance greater than $500. Write and solve an inequality that represents this situation. How many months will it take for her account to have a balance greater than$500? Explain.” (7.EE.4b)

### 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.
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 meet expectations for the three aspects of rigor not always being treated together and not always being treated separately. In general, two, or all three, of the aspects are interwoven throughout each module. The Module planning pages include a diagram showing the first few lessons addressing understanding and connecting concepts and skills and the last lessons addressing applications and practice.

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

• In Lesson 12.1, the materials address conceptual understanding of statistics by having students determine where to locate a fast-food restaurant. Students discuss the terms population, sample, representative, and bias and identify them in different contexts. Students participate in class discussion and Turn and Talk, making generalizations and inferences, before working independently. In Build Understanding, students answer, "Of the representative samples of the population, which is most representative of the population? Explain."
• In Module 8, students develop procedural skill by writing, solving, and graphing the solutions to one- and two-step inequalities. The inequalities incorporate rational numbers in various forms (i.e., integers, fractions, and decimals). For example, “...solve the inequality. Graph the solution. - 1/10 a - 2/5 > 3/10.”
• In Lesson 15.4, students conduct simulations and find experimental probabilities: “Allie is a softball player. She has a batting average of 0.600. This means Allie gets a hit 60% of the time. Design a simulation using slips of paper and a box to predict the probability of Allie getting a hit in at least 2 of her next 5 at bats. Perform the simulation and use your results to predict the probability of Allie getting a hit in at least 2 of her next 5 at bats.”

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

• In Lesson 5.3, students develop conceptual understanding of converting fractions to decimals using multiple representations including a double number line with one side as decimals and one side as fractions and long division. Students develop procedural skill by converting fractions to decimals in numerous problems, such as “Hayley is buying herbs. She wants to buy ⅚ ounce of basil. The scale she is using to weigh the basil displays the weight as a decimal. How will she know when the display on the scale is correct to the tenths’ place? Explain your reasoning.”
• In Lesson 10.1, students develop conceptual understanding of the formula for circumference by examining the relationship between circumference (C), diameter (d), and pi. Students complete a table finding the ratio, C/d, for various circular objects, and they rewrite =Cd to reveal the formula for the circumference of a circle. Throughout the remainder of the lesson, students use the formula to solve real-world problems, for example, “Toni rides the Ferris wheel shown for 15 revolutions. A. How far does Toni travel in one revolution? How far does Toni travel for the entire ride?”

### Criterion 2e - 2g.iii

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

The instructional materials reviewed for HMH Into Math Grade 7 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.
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade-level.

All eight MPs are clearly identified throughout the materials, including:

• MPs are identified in both the Planning and Pacing Guide and the Teacher Edition.
• The Planning and Pacing Guide explains each MP and provides a correlation to specific lessons.
• MP1 is correlated with “every lesson,” but it is not identified in the Focus and Coherence pages of the Teacher Edition for each lesson with other identified MPs.
• The Teacher Edition labels an MP for the Build Understanding and Step It Out tasks.
• The Module Review includes a question labeled "Use Tools" in the student edition where students choose a tool and explain their choice.

Examples of the MPs being used to enrich the mathematical content include:

• Lesson 3.1 identifies MP2 and MP5 as the focus MPs for the lesson. The materials identify MPs 2 and 5 with each of the Build Conceptual Understanding tasks.
• Some lessons include an explanation about the connection to the MP in Professional Learning. For example, in Lesson 4.4, the explanation for MP2 states, “This lesson calls for students to decontextualize problems and represent them abstractly using expressions, including sums and differences of rational numbers and integers. The students then contextualize using quantitative reasoning to attend to the meaning of the quantities, not just how to compute with them.”

### Indicator 2f

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

The instructional materials reviewed HMH Into Math Grade 7 partially meet expectations for carefully attending to the full meaning of each practice standard (MP).

The materials do not attend to the full meaning of MP4 and MP5. For MP4, mathematical models are provided for students, and they use tools as directed by the materials, examples include:

• MP4: In Lesson 14.2, Question 4 states, “Wei has two different routes he takes to a park. He labels the routes A and B. He takes route B about 33% of the time. Describe a simulation Wei could perform using a number cube to estimate the number of times he will take route B to the park if he goes to the park 60 times.” Modeling with mathematics is prescribed because students are to use a number cube.
• MP5: Throughout Module 3, students use given number lines to build understanding of adding or subtracting rational numbers, and no other tools are used or mentioned. In Lesson 9.1, students construct an irregular decagon on grid paper, with given side lengths, and directions to guide their placement. The tools to use are given.
• In the Spark Your Learning problems and most module reviews, there are general notes for teachers to ask the students. For example, “If students need support, guide them by asking, Which tool could you use to solve the problem? Why is this tool more strategic?” or “State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.”

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

• MP1: In Lesson 5.1, Spark Your Learning states, “Arnot wins a $50 gift card for a virtual reality arcade. If he does not use the card for a whole year, the balance on the card will be reduced by$5 each month that it continues to go unused. What will be the change in the value of the card if Arnot doesn’t use it for 18 months?” Space for students to work and possible methods of arriving at a solution are provided.
• MP2: In Lesson 5.4, Question 3 states, “Tanisha takes a dance class that is $12.50 per class. The charge appears as negative on her account balance until she makes her monthly payment. Suppose the balance on Tanisha’s account for a 2-week period is -$100. If Tanisha attended at least 1 dance class per week, how many classes could she have attended each week? Explain your reasoning.”
• MP6: In Lesson 6.3, Question 4 states, “What was the total value of Mr. Liling’s shares, rounded to the nearest cent, at the end of 2017?”
• MP7: In Lesson 5.1, Build Understanding, Part 3 states, “You can use what you know about multiplying signed numbers to figure out the rules for dividing signed numbers. In multiplication, if one factor is 0, the product will be 0. In division, the divisor cannot be 0. Division by 0 is undefined. A) Use the fact the division and multiplication are inverse operations to complete the number statements in the table. B) Use your results from step A to complete the table. C) Complete the rules for division of rational numbers.”
• MP8: In Lesson 5.3, Question 7 states, “Look for Repeated Reasoning. Convert each fraction in the table to a decimal. Describe a pattern in the results. Does this pattern continue? Why or why not?”

### Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

### 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 7 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

An often-used strategy in these materials is Turn and Talk with a partner about the related task. Often, Turn and Talks require students to construct viable arguments and analyze the arguments of others. In addition, students justify their reasoning in practice problems.

• In Lesson 3.2, Question 9 states, “Leah said that when you add two negative integers the result must be negative. Do you agree or disagree? Use a number line to help explain your answer.”
• In Lesson 3.3, Question 2 states, “Jasmin evaluated the expression 10-(-3) and says it is equal to 7. Is she right? If not, what was her mistake?”
• In Lesson 4.2, Spark Your Learning, Turn and Talk prompts, “Write an addition expression that could be used to solve the problem. Does order matter in this problem? Why or why not?”
• Lesson 9.4 states, “Travis draws a triangle with three 60° angles and three sides of length 5 inches. A. Can Margarita draw a triangle with the same angle measures as Travis's triangle but with different side lengths? Why or why not? B. Can she draw a triangle with the same side lengths as Travis’s triangle but with different angle measures? Explain.”
• In Lesson 10.2, Question 7 states, “A classmate states that if the radius of a circle is doubled, then the area is doubled. Do you agree or disagree, how much larger do you think the area will be?”
• In Lesson 13.1, students analyze data on wait times for two food trucks using dot plots and tables, and they answer “Based on the data, which food truck would have more predictable wait times? Explain.”
• In Lesson 13.2, On Your Own states, “After looking at the box plots, Tomas expresses surprise that most award-winning actresses are under the age of 40. Martha disagrees, pointing out that the right whisker is the longest part of the Best Actress box plot. Therefore, she argues, there are more winners between the age of 41 and 62 than in the other intervals. Determine which friend is correct, and explain why.”
• In Lesson 14.4, Question 14 states, “Construct Arguments. Jiany was concerned about a particularly busy intersection because it did not have a stop sign. She took a survey of 100 people who used that intersection. Seventy-five people she spoke to support putting in a stop sign. The town’s population is 4,480. Write a percent equation and also use proportional reasoning to estimate how many people in the town support the stop sign. Then make an argument as to why Jiang’s survey results may not be a good predictor of town opinion.”

### 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 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.

• The Teacher Edition provides Guided Student Discussion with questions to encourage students to explain their thinking. For example, Lesson 5.3 states, “When you divide two nonzero integers, how do you know if the quotient is positive or negative?” and Lesson 3.1 states, “When you start with a negative temperature and move down on the number line, is the temperature increasing or decreasing? Why?”
• Turn and Talks are provided multiple times per lesson. For example, in Lesson 10.3, Task 2, Turn and Talk states, “What do you notice about the width of a vertical cross section through the centers of the bases and the diameter of the horizontal cross section? Is this true for all cylinders? Explain.” Teachers are given a possible answer as well as additional guidance to assist students in constructing arguments, for example, “If some students are having trouble understanding that the width of a vertical cross section through the center of a cylinder is the same length as the diameter of a horizontal cross section from the same cylinder, ask other students who understand to explain their thinking.”
• The Teacher Edition includes Build Shared Understanding in margin notes to prompt student engagement. For example, in Lesson 4.1, “Select students who used various strategies and tools to share with the class how they solved the problem. Have students discuss why they chose a specific strategy or tool.”
• The Teacher Edition also provides Cultivate Conversation prompts in the lessons. For example, Lesson 4.2 states, “Stronger and Clearer. Ask students to describe in their own words what it means that addition and subtraction are inverse operations. Ask how inverse operations are like opposite numbers. Ask them to describe how the addition of a negative number is like subtraction and the subtraction of a negative number is like addition.”
• In lesson planning pages, sometimes Professional Learning provides a rationale for a lesson labeled “Using Mathematical Practices and Processes.” For example, Lesson 5.2, which is labeled MP3, states, “In this lesson, students derive the rules of multiplying three or more signed numbers by experimentation, reducing their observations to a general rule. They then share their strategies with other class members and respond to their classmates ' comments. They listen to their classmate’s strategies, decide whether they make sense, and ask questions or help clarify.”

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 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, including:

• Key Academic Vocabulary is listed at the beginning of the module in a table that includes any prior vocabulary relevant to the lesson and new vocabulary.
• Each lesson includes a Language Objective that emphasizes mathematical terminology. For example, Lesson 5.3 states, “Use mathematical terminology to explain how to express quotients in different forms.”
• In the module planning pages, there is a Linguistic Note on the Language Development page which provides teachers with possible misconceptions relating to academic language For example, Module 2 states, “Speak with students about words which can have multiple meanings. The word change can have multiple meanings in mathematics. When working with money, change can indicate an amount of money returned from a transaction or it can indicate coins. In this lesson, percent change, describes the percent of increase or decrease in an amount compared to its original amount.”
• In Sharpen Skills in the lesson planning pages, some lessons include Vocabulary Review activities. For example, in Lesson 3.2, students use a graphic organizer to make sense of the term absolute value by using examples and visual models.
• Guided Student Discussion often provides prompts related to understanding vocabulary, such as in Module 13, which states, “Listen for students who correctly use review vocabulary as part of their discourse. Students should be familiar with the terms mean, median, range, interquartile range, center of data, and spread of data. Ask students to explain what they mean if they use those terms.”
• Student pages include vocabulary boxes that define content vocabulary.
• Vocabulary is highlighted and bold within each lesson in the materials. Terms are highlighted in blue if it is meant to review and yellow if it is new vocabulary.
• There is a vocabulary review at the end of each module where students match new vocabulary terms with their meaning and/or examples provided, fill-in-the-blank with definitions or examples, or create a graphic organizer to help make sense of terms.
• The Teacher Edition sometimes suggests creating an Anchor Chart to “connect math ideas, reasoning, and language” where students define terms with words and pictures, trying to make connections among concepts. For example, Lesson 10.2 shows a sample anchor chart that includes vocabulary related to circumference, area, and cross sections.
• There is an Interactive Glossary at the end of the text where the definition and a visual (e.g., diagrams, symbols, etc.) are provided for each vocabulary word. In the student book, the instructions read, “As you learn about each new term, add notes, drawings, or sentences in the space next to the definition. Doing so will help you remember what each term means.”

## Usability

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 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.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 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.

Additional practice is provided in a separate student journal which allow students to independently show their understanding of the material. Exercises and problems are designed for students to demonstrate understanding and skills in application and non-application settings. Test Prep and Spiral Review also include exercises.

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 meet the expectations that the design of assignments is intentional and not haphazard.

Overall, lessons are intentionally sequenced and scaffolded so students develop understanding of mathematical concepts and skills. The structure of a lesson 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. Examples include:

• Spark Your Learning serves to motivate and set the stage for students to learn new material and persevere through a related mathematical task.
• Build Understanding and Step It Out provide opportunities for students to learn and practice new mathematics, as well as “connect important processes and procedures” according to the Planning and Pacing Guide.
• Check Understanding provides a formative assessment opportunity after instruction.
• On Your Own, More Practice/Homework, Test Prep, and Spiral Review in each lesson support students in developing independent mastery of the current lessons as well as reviewing material from previous lessons.
• Lessons are in a logical order that build coherence throughout the grade level.

### 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.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 meet the expectations for having a variety in what students are asked to produce, for example:

• Performance Tasks: Unit 3, Jessica’s Cell Phone Plan states “Jessica’s cell phone plan charges her a monthly fee plus a charge for each text message she sends. The cost of her cell phone is shown in the table.” This is followed by six questions relating to evaluating data and generating equations to compare options.
• STEM activities: Unit 4 states, “A rectangular electronic game board is 16.5 inches by 12 inches. It includes a grid with 8 rows of 8 squares, each 0.5 inch on a side. When you aim at any of the red squares, data are collected on the accuracy of the laser hits. What are the ratios of (a) the area of one square to the area of the board, and (b) the combined area of the squares to the area of the board? Explain.”
• Show written calculations and solutions
• Verbally defend or critique the work of others to show understanding
• Analyze double number lines and bar diagrams
• Build models for a problem by using diagrams and equations
• Use a diagram and a coordinate plane to represent a linear equation
• Compare multiple representations - table, graph, equation, situation - of data
• Use a digital platform to conduct and present their work
• Use manipulatives, especially in small groups, to represent mathematics
• Construct written responses to explain their thinking

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 present and, when appropriate, are connected to written methods.

• The series does not involve extensive use of manipulatives, however, when they are included, they are consistently aligned to the expectations and concepts in the standards.
• Most hands-on manipulatives are integrated in supplemental, small-group, differentiated instruction activities, and warm-up options.
• Examples of manipulatives include: Two-color counters, calculator, coins, number cubes, playing cards, string, square tiles, unit cubes, colored chips, algebra tiles, grid paper, index cards, anchor charts, ruler, compass, protractor, geometry software, bar diagrams, fraction strips, number lines, decimal grids, x-y tables, and pie charts.

### Indicator 3e

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

The instructional materials for HMH Into Math Grade 7 is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

The entire series, both print and digital, follows 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. Though there is a lot of information given, 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.

### 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 7 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.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 meet the expectations for providing quality questions to help guide students’ mathematical development.

There are Guided Student Discussion questions and sample student answers throughout the Teacher Edition including on the Module Opener page, Warm Up Options, Spark Your Learning, Build Understanding, Common Errors, and Step It Out pages that correspond to the tasks or exercises on the page. Each module review also contains suggested questions intended to have students summarize concepts and skills developed within the module.

Each lesson introduction poses an essential question intended to guide student learning. For example, in the Lesson 4.2, the Essential Question is “How can you calculate the difference of two integers?”

The Spark Your Learning planning page in the Teacher Edition includes examples of student work which show On Track, Almost There, and Common Errors. Each example has suggested questions for teachers to correct or advance student thinking. For example, in Lesson 7.1, On Track about Linear Expressions states, “How can we verify a written rule?”

### 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.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 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.

In the Module planning pages, there is a variety of information that can help teachers understand the materials in order to present the content. Each lesson identifies the relevant content standards and Mathematical Practices, an Essential Question, Learning Objective, Language Objective, materials needed, and Mathematical Progressions Across Grades that contain prior learning, current development, and future connections. Unpacking the Standards provides further explanations of the standards’ connections. This section gives an explanation of the content standard contained in the lesson and Professional Learning, which sometimes contains information about the practice standard contained in that lesson. Teaching for Depth provides teachers with information regarding the content and how this relates to student learning.There are additional suggestions about activating prior knowledge or identifying skills in Warm-up Options, activities to Sharpen Skills, Small-Group Options, and Math Centers for differentiation.

There are two prompts in each module related to Online Ed: “Assign the auto-scored Are You Ready for immediate access to data and grouping recommendations” and “Assign the auto-scored Module Test for immediate access to data.” Within lessons, there are multiple prompts. Warm-Up Options and Step It Out both have an icon “Printable & projectible” which states “More print and digital resources for differentiation are available in the Math Activities Center” and “Assign the auto-scored Check Understanding for immediate access to the data and recommendations for differentiation.”

### 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 7 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. Examples of the grade-level explanations include:

• At the beginning of each module, the teacher’s edition includes Teaching for Depth that provides a brief overview of the mathematics contained in the module. For example, Module 3 states, “Students are often taught to add two negative integers by finding the sum of the absolute values of the integers and taking the opposite of the result, as shown. -1 + (-3) = -(1 + 3) + -4 This rule can be written as -a + (-b) = -(a + b), where a and b are positive integers. Notice -a + (-b) is the additive inverse of a + b because their sum is 0. The Inverse Property of Addition is an important property related to additive inverses. It states that the sum of a number and its additive inverse is 0.”
• In addition, Teacher to Teacher From the Classroom gives tips or anecdotes about the module content. For example, Module 5 states, “When I reflect on my students’ struggles with multiplying and dividing rational numbers I discover that my students lack real understanding of the operations of multiplication and division altogether. I devote time to students revisiting ideas around multiplication and division and the relationship between the two. I need students to understand what multiplying does to numbers, and conversely what dividing does. We talk and think about rational number operations as an extension of what we already know about and how that operation works on whole numbers. Dedicating time to establish this solid foundation up front saves me tons of time down the road. When I need support figuring out how to do this, go to resources like Beyond Invert and Multiply by Julie McNamara. Deepening my own understanding of the mathematics and connections to prior grades deeply impacts my ability to support students in their own sense making about operations with rational numbers.”

### 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.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 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 Across the Grades 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 discusses the “four progressions of 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 3-5, 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).
Narrative Evidence Only
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 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, pacing is provided in the module planning pages, and 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.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 include strategies for parents to support their students progress. The Planning and Pacing Guide describes strategies to Connect with Families and Community:

• The student materials contain Math on the Spot problems that have videos connected to them. The materials state, “Math on the Spot video tutorials provide instruction of the math concepts covered and allow for family involvement in their child’s learning.” There are generally 1-3 problems per module.
• The materials state, “Family letters inform families about the skills, strategies, and topics students are encountering at school.” Each module includes a letter, found online in four languages, providing vocabulary, a home activity, and discussion prompts.

### Indicator 3l

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

The instructional materials for HMH Into Math Grade 7 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 was 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 embrace these 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 7 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.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 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, which states, “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.
2/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 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 6 partially meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. The materials do not provide feedback in online lessons, and in the Module Reviews.

• Each lesson ends with two or three 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.
• The online lessons are the same as in the print textbook and provide immediate notification of correct or incorrect answers, but do not provide feedback for changing incorrect answers.
• 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.
• Digital assessments are auto-scored and generate recommendations that can provide feedback to teachers but not directly to students.

### Indicator 3p

Materials offer ongoing formative and summative assessments:

### 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 7 meet the expectations that assessments clearly denote which standards are being emphasized.

The standards alignment for each item on the Prerequisite Skills Inventory, Beginning-of-Year, Middle-of-Year, End-of-Year, and Module Tests are listed in the Assessment Guide on Individual Record Forms. Each Performance Task includes the standards in the teacher pages of the Assessment Guide, although the individual questions do not indicate which standards are being assessed.

### 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.
1/2
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Indicator Rating Details

The instructional materials for HMH Into Math Grade 7 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 “for immediate access to data and grouping recommendations.”
• The Planning and Pacing Guide states, “Check Understanding is a quick formative assessment in every lesson used to determine which students need additional support and which students can continue on to independent practice or challenges.” Check Understanding presents a limited number of questions, usually one to three, which includes a digital option that can be “auto-scored online for immediate access to data and recommendations for differentiation.”
• 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 not suggest Reteach Lessons or provide other guidance that teachers can use for follow-up with students.

### Indicator 3q

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

The instructional materials for HMH Into Math Grade 7 include Scales to Track Learning Goals at the end of each lesson. The Teacher Edition introduction states, “The scales below can help you and your students understand their progress on a learning goal. Scales are also available in Module Resources.” The scale progresses from 1 to 4. For example from Grade 7, Lesson 1.1 states:

1. “I cannot identify unit rate yet.
2. I can identify unit rates in tables but I still need help with writing the correct quantities in the numerator and denominator.
3. I can identify unit rates in tables by myself with few mistakes.
4. I can identify and use unit rates to complete tables and compare quantities without mistakes and explain it to others.”

Each lesson includes “I’m in a Learning Mindset!” which gives students a prompt regarding the purpose of the lesson. For example, Perseverance states, “What strategies do I use to stay on task when working on my own?” and Strategic Help-Seeking states, “What is challenging about subtracting integers? Can I work through it on my own, or do I need help?”

### Criterion 3r - 3y

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

The instructional materials reviewed for HMH Into Math Grade 7 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 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 7 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 Across the Grades 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 My 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 7 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/Mixed Ability, 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 three “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.” and 3) “Compare and Connect: Students listen to a partner’s solution strategy and then identify, compare, and contrast this mathematical strategy.”

### Indicator 3t

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

The instructional materials for HMH Into Math Grade 7 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

• Each unit includes a STEM Task and a Unit Project which include multiple entry-points and a variety of solution strategies. Teachers are provided with possible answers as well as What to Watch For tips, which include “Watch for students who become discouraged by a task and quickly give up. Strategies that may help these students include: working with a supportive partner, dividing the task into smaller steps, and reminding themselves that working at a difficult task is valuable, even if the task is not completed. Taking on new challenges is how we learn” and “Watch for students who are reluctant to stretch themselves on a challenging task. Encourage these students to: identify similarities between the current task and tasks they have completed successfully in the past, identify one or more promising strategies or approaches, and try one of the strategies.”
• Each lesson begins with Spark Your Learning, which is an open-ended problem that allows students to choose their entry-point for applying mathematics and can be solved in a variety of ways. There are suggestions in the teacher’s edition to help students access the context of the problem. For example, in the side margin of the teacher’s edition, Motivate provides prompts. Grade 6, Lesson 9.1 states, “Introduce the problem. Point out that the problem does not state the amounts of money that Bella and Tia have, only that the two amounts are equal. Nevertheless, this information is enough to find a solution.” Grade 7, Lesson 1.1 states, “Introduce the problem. Ask them if they have ever used a recipe. Tell students to discuss and share with their team members in a small group.” Grade 8, Lesson 5.2 states, “Introduce the problem. Ask students if they have ever set daily goals in reading or running or some other activity. Invite students to discuss and share with their partner or team members in a small group.”
• 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 7 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. Examples include:

• For ELLs, there is Language Development 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,” “Listen for students who do not distinguish between minus...and the negative sign,” and “Visual cues help students…”
• Language Objectives are included in every lesson.
• There are Teacher Tabletop Flipchart Activities referenced in the teacher’s edition for RtI support.
• There are Reteach, RtI Tier 2, and RtI Tier 3 worksheets that can be assigned online or printed.
• There are Turn and Talk prompts designed to support students in other special populations, such as “go back and reread the problem and break it into pieces. For example: What do you know? What do you need to find?”

### 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 7 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. Examples include:

• 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’s 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 7 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics. Examples include:

• Lessons contain a variety of tasks that interest students of various demographic and personal characteristics.
• Names and wording are chosen with diversity in mind. The materials include various names throughout the problems (e.g., Jayson, Suyin, Malik, Tressa, Anton, Jasmine, Yu, Felice, Sonia, Roselyn, Tracy, Tran, Arie, Miguel, Maria) that are used in ways that do not stereotype characters by gender, race, or ethnicity.
• When multiple characters are involved in a scenario, they are often doing similar tasks or jobs in ways that do not express gender, race, or ethnic bias, and there is no pattern in one character using more/fewer sophisticated strategies.
• When people are shown, there is a balance of demographic and personal characteristics.

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 provide opportunities for teachers to use a variety of grouping strategies. Examples include:

• 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.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 encourage teachers to draw upon home language and culture to facilitate learning. Examples include:

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

### Criterion 3aa - 3z

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 7: 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 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.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 are web-based and compatible with multiple internet browsers. Examples include:

• 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. Online use was difficult on a Chromebook, there are scrolling and loading issues as well as difficulty seeing all pieces of the interactive editions.
• The materials are not compatible with an Android device (using Chrome browser). Although the website can be reached, it is not possible to zoom in or out, nor can one move the screen, so a student cannot access the entire screen.

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 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. Only one module per grade is currently available in the digital format, so some of the evidence is stated in the materials but has not actually been observed. Examples include:

• 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.
• Growth monitoring assessments 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 cannot modify questions nor 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.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 are intended to include opportunities for teachers to personalize learning for all students. Full functionality of online materials is not accessible at the time of this review. Examples include:

• 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 which “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 HMH Into Math Grade 7 provide minimal opportunity to be adapted for local use. Full functionality of online materials is not accessible at the time of this review. Examples include:

• 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 cannot 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.).
Narrative Evidence Only
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 do not incorporate technology that provides opportunities for multiple students to collaborate with the teacher or one another.

### 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.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials reviewed for HMH Into Math Grade 7 integrate some technology, including digital lessons and virtual tools. Students can complete tasks and activities from the Student Edition through an interactive format. Examples include:

• 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 the bar diagrams to represent 5/9 ÷ 2/9, drag and drop the correct values into a table, or graph an equation. (Note: The backspace button, generally used to make a correction, is interpreted as the “back” button, returning to the previous screen and losing all work.)
• Only one module per grade is currently available in the interactive lessons, so there is no way to know if the sketchpad is the only manipulative offered. No other virtual manipulatives were found.
• 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.
abc123

Report Published Date: 2020/05/21

Report Edition: 2020

Title ISBN Edition Publisher Year
HMH Into Math Comprehensive Student Resource Print/Digital Package 6 Year, Grade 7 9780358158967 Houghton Mifflin Harcourt 2020
HMH Into Math Comprehensive Teacher Resource Package Print/Digital Package 6 Year Digital, Grade 7 9780358160366 Houghton Mifflin Harcourt 2020

## Math K-8 Review Tool

The mathematics review criteria identifies the indicators for high-quality instructional materials. The review criteria 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 review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complements the review criteria 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.

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.