## Alignment: Overall Summary

The materials reviewed for Core Curriculum by MidSchoolMath Grade math 6 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials meet expectations for rigor and practice-content connections.

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

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## Gateway 3:

### Usability

0
17
24
27
27
24-27
Meets Expectations
18-23
Partially Meets Expectations
0-17
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for focus and coherence. For focus, the materials assess grade-level content, and partially give all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, each grade’s materials are coherent and consistent with the CCSSM.

### Criterion 1a - 1b

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

6/6
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Criterion Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

### Indicator 1a

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

2/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8, Grade 6 meet expectations for assessing grade-level content.

The materials are organized by the Domains and Clusters delineated by CCSS. Each Cluster has a Milestone Assessment, and all assessments include multiple choice and/or multiple select. The assessments are aligned to grade-level standards, and examples include:

• In Milestone Assessment 6.NS.C, Question 11, “Which number sentence is true? a) $$-16 > -13$$ ; b) 3 $$< -3$$ ; c) $$-(-7) > 9$$ ; d) $$-18 < -14$$.”

• In Milestone Assessment 6.EE.A, Question 16, “$$b + b + b + b$$ and $$4b$$ are equivalent expressions because:  a) they both have b as a variable; b) they both have four terms; $$c$$) they both produce the same value no matter what number $$b$$ represents ; d) they both equal 4 when $$b = 1$$.”

• In Milestone Assessment 6.SP.B, Question 3, “Histograms, dot plots and box plots can all be used to display data. Which statement is true? a) Histograms show the distribution and the actual values of the data set; b) Dot plots show the distribution and the actual values of the data set; c) Box plots show the distribution and the actual values of the data set; d) Not enough information.”

• In Milestone Assessment 6.RP.A, Question 1, “Which statement correctly describes the image of clouds and suns? Select all the apply. a) For every three clouds, there are two suns; b) For every six clouds, there are nine suns; c) For every three suns, there are two clouds; d) For every two clouds, there are one sun.”

### Indicator 1b

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

2/4
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Indicator Rating Details

The instructional materials for Core Curriculum by MidSchoolMath 5-8, Grade 6 partially meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The instructional materials do not always attend to the full intent of the grade-level standards. Each lesson addresses one grade level standard with no standards absent from the materials. Lessons are three to four days long, and all students complete the same work. However, there are limited opportunities within each lesson to practice the content of the standards. Opportunities for practice include: Math Simulator, one to four questions; Practice Printable typically has six to ten questions; Clicker Quizzes include six questions; and the teacher can assign a specific domain in Test Trainer Pro. Since all standards are given the same attention, students have limited opportunities to engage in extensive work with grade-level problems to meet the full intent of all grade-level standards. Examples where the full intent is not attended to include:

• In 6.EE.C.9, Sister Act, students have very limited opportunity to analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the equation. In the Practice printable, one problem requires students to generate and solve a two-step equation, which is Grade 7 content. There is one problem for students to complete a table, then graph the coordinate points. There is one problem for students to write an equation from a table.

• In 6.SP.B.4 & 5, Shoot for the Moon, students do not describe the nature of the attribute under investigation, including how it was measured and its units of measurement (6.SP.5b). Students do not explain the units of measurement in the data they describe.

The Test Trainer Pro and Simulation Trainer are designed to provide additional, grade-level work, but all of the items for these two features are not available for review.

• In Test Trainer Pro, primarily used as a daily warm-up, there is no way for teachers to assign specific content other than a domain of standards.

• In Simulation Trainer, the content matches the lesson, but students can provide any number as an answer, then watch the steps worked out (no words) in a solution video. They’re presented with the same question again and can put in the correct answer, then watch the same solution again. If they get it correct the first time, they also watch the solution video. The next questions are not novel, but the same situation with new numbers. If students miss one, it resets them to the beginning, no matter where they were in the assignment. It is possible that some students would never complete a Simulation Trainer.

### Criterion 1c - 1g

Each grade’s materials are coherent and consistent with the Standards.

8/8
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Criterion Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for coherence. The majority of the materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

### Indicator 1c

When implemented as designed, the majority of the materials address the major clusters of each grade.

2/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8, Grade 6 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 125 out of 183, which is approximately 68%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 26 out of 37 lessons, which is approximately 70%.

• The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is 26 out of 36, which is approximately 72%.

A day level analysis is most representative of the instructional materials because this represents the class time that is devoted to major work of the grade including reviews, domain intensives, and assessments. As a result, approximately 68% of the instructional materials focus on major work of the grade.

### Indicator 1d

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

2/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8, Grade 6 meet expectations for supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of connections between supporting content and major work of the grade include:

• 6.NS.B.2, Which Way connects to 6.RP.3b as students divide multi-digit numbers to find unit rates. In the Practice Printable, Question 4, “Carlos and Doug went on a road trip. They recorded how far they traveled each day in a travel journal. If they drove for a total of 30 hours, what was their average speed?” The journal provides the data: Day 1, 450 miles; Day 2, 300 miles; Day 3, 350 miles, Day 4, 400 miles. Additionally, the Immersion & Data and Computation portions of the lesson require students to use ratio reasoning to determine which route is fastest.

• 6.G.A.2, River Rescue connects to 6.NS.A as students divide fractions by fractions to solve volume problems. In the Practice Printable, Question 6, “A right rectangular prism has a volume of $$20\frac{1}{4}$$ cubic units. The width is $$1\frac{1}{2}$$ cubic units, and the height is $$4\frac{1}{2}$$ cubic units. What is the length?”

• 6.NS.B.4, The Castle Guard connects to 6.EE.3 as students use the Greatest Common Factor to produce equivalent expressions. In the Practice Printable, Question 3, “For each sum or difference, factor out the GCF, and rewrite the sum or difference.”

### Indicator 1e

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

2/2
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Indicator Rating Details

The instructional materials for Core Curriculum by MidSchoolMath 5-8, Grade 6 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Examples include:

• 6.RP.A.3a, Clone Wars “connects 6.RP.A to 6.EE.C as students can use ratio reasoning as a means to analyze the graph of the relationship between independent and dependent variables.” In the Practice Printable, Question 2 shows two types of fish and the space required based on the number of fish. Question 3 states, “Using the tables and graph from Question 2 , write a few sentences comparing the ratios of the amount of space needed for each fish. How is this shown in the graph?”

• 6.SP.A.3, Periodontal Pockets connects 6.SP.A and 6.NS.B as students compute with multi-digit numbers to “calculate and analyze the mean and the mean absolute deviation of a data set.” In Practice Printable, Question 2 states, “Tyrell is looking for a new place to keep his sailboat. He loves to sail and is looking for a location that will provide great sailing conditions year round. Tyrell’s ideal wind speed for optimal sailing conditions is around 10 knots. Below is some data he has gathered to help him make his final decision. (provided: a table with two different rivers and the average wind speed for each month) a) What is the mean wind speed of each location? b) What is the median wind speed of each location? c) Calculate the MAD for each set of data.”

6.EE.B.6, Land in Lama “connects 6.EE.B to 6.EE.A as students solve real-world situations by writing, reading, and evaluating expressions where letters represent numbers.” In Practice Printable, Question 2 states, “David went into a floral shop to buy his mother some flowers. Depending on the season, carnations cost $$c$$ dollars; roses cost $$r$$ dollars; and tulips cost $$t$$ dollars. Vases are $12. Write an expression to represent David’s cost for 4 carnations, 5 roses, 3 tulips, and a vase.” ### Indicator 1f Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 2/2 + - Indicator Rating Details The instructional materials for Core Curriculum by MidSchoolMath 5-8, Grade 6 meet expectations for clearly identifying content from future grades and relating it to grade-level work and explicitly relating grade-level concepts to prior knowledge from earlier grades. Examples of clearly identifying content from future grades and relating it to grade-level work include: • 6.RP.A.1, For Every Day states “This activity connects 6.RP to 7.RP.A and 8.EE.B, as unit rate is the basis for work involving constant of proportionality and slope of linear equations.” • The game “Ko’s Journey” addresses several standards across grade levels. The Grade 6 standards include 6.RP.A.3a-c; 6.NS.B.3; 6.NS.C.6 and 8; and 6.G.A.2, though some of these have only one question. The game also addresses the Grade 4 concept of using a protractor and Grade 5 concepts including fractions, coordinate plane, and converting measurement units. The game introduces the Grade 8 concept of slope, though students are given formulas and directed through each equation. Examples of explicitly relating grade-level concepts to prior knowledge from earlier grades include: • 6.EE.B.7, The Sign of Zero states, “This activity connects 6.EE to 5.NF as students write and solve real-world problems involving multiplication of fractions and mixed numbers.” • 6.G.A.4, Build a Better Box states, “This activity connects 6.G.A to 5.G.B in that students will draw nets and apply area formulas using their knowledge of classifying two-dimensional figures.” ### Indicator 1g In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification. Narrative Evidence Only + - Indicator Rating Details The instructional materials for Core Curriculum by MidSchoolMath 5-8, Grade 6, in order to foster coherence between grades, can be completed within a regular school year with little to no modification. As designed, the instructional materials, with assessments, can be completed in 146-183 days. • There are five domains which contain a total of 37 lessons. Lessons are designed to take three to four days each, leading to a total of 111-148 lesson days. • There are five days for Major Cluster Intensives. • There are 30 assessment days including 10 days for review,10 spiral review days in the Distributed Practice Modules, and 10 milestone assessments. The Scope and Sequence Chart in the Teacher Edition provides pacing information. A lesson is designed for 60 minutes. ### Gateway Two ## Rigor & the Mathematical Practices #### Meets Expectations + - Gateway Two Details The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for rigor and balance and practice-content connections. The materials reflect the balances in the Standards and help students develop conceptual understanding, procedural skill and fluency, and application. The materials make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). ### Criterion 2a - 2d Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. 8/8 + - Criterion Rating Details The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications of mathematics, and do not always treat the three aspects of rigor together or separately. ### Indicator 2a 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 Core Curriculum by MidSchoolMath 5-8, Grade 6 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. Examples of problems and questions that develop conceptual understanding across the grade level include: • In 6.EE.A.3, Provision Problem states, “How many equivalent expressions can we create from this expression? $$24n-16n+12$$.” Suggested answers include: “Combine like terms. $$8n +12$$; Factor out GCF. $$4(6n-4n+3)$$; Factor out GCF & combine like terms $$4(2n + 3)$$; Factor out common factor (not GCF) $$2(12n-8n+6)$$; Factor out common factor (not GCF) & combine terms 2(4n + 6)”. • In 6.G.A.3, Fuel Factor, the teacher is prompted to ask students questions to further their thinking such as, “What is the direction for the course? What do you notice about the coordinates of the endpoints of horizontal line segments? What do you notice about the coordinates of the endpoints of vertical line segments? Imagine the coordinates on a grid. How might you find the length of a line segment connecting them? Since there is no grid, how might you find the length of the line segment anyway?” • In 6.NS.A.1, Mr. Mung’s Ice Cream, the teacher is prompted to complete this example using a bar diagram. “$$3\frac{1}{2}$$ is divided by $$1\frac{3}{4}$$. What is the quotient? We could draw a visual fraction model. We start by drawing a representation of $$3\frac{1}{2}$$. Then we separate the diagram into fourths because of the denominator of the divisor. We then ask ourselves how many groups of $$1\frac{3}{4}$$ are in $$3\frac{1}{2}$$? Then separate the diagram into groups of $$1\frac{3}{4}$$. We can see two groups of $$1\frac{3}{4}$$, so the quotient is 2.” Examples where students independently demonstrate conceptual understanding throughout the grade include: • In 6.EE.C.9, Sister Act, Practice Printable, Question 1 states, “A worker earns$17 per hour.  a.Write an equation to show the relationship between the hours she works (h) and the amount she is paid (p).  b. What is the independent variable? What is the dependent variable?”

• In 6.RP.A.1, For Every Day, Practice Printable, Question 4 states, “To make a deep orange color, Regina mixed 8 drops of red paint and 2 drops of yellow paint. Describe the relationship between the red paint and yellow paint in at least 4 different ways.”

### Indicator 2b

Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

2/2
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Indicator Rating Details

The instructional materials for Core Curriculum by MidSchoolMath 5-8, Grade 6 meet expectations for attending to the standards that set an expectation of procedural skill and fluency.

The instructional materials develop procedural skill and fluency throughout the grade level in the Math Simulator, examples in Teacher Instruction, Cluster Intensives, domain specific Test Trainer Pro and the Clicker Quiz. Examples include:

• In 6.NS.B.2, Which Way, the Teacher Instruction directs teachers to say, “perform long division and make sure to line up columns.” Three different example problems are provided. Steps for the division algorithm are shown three days in a row during the lesson. Students also see the completed algorithm for at least 15 practice problems. 6.NS.2 is practiced in two other units and in the game Ko’s Journey.

• In 6.NS.B.3, Enter the Dragon, the Teacher Instruction has the teacher walk through the steps for the four operations, repeatedly asking, “What is the process to (add, subtract, multiply, divide) decimals?” The Math Simulator provides five sets of three problems for students to solve. After each set, the correct answer and process is worked out for the student. There are decimal calculations in eight other lessons.

• In 6.EE.A.1, I Dream of Djinni, the Teacher Instruction supports students in procedural skills related to exponents. The terms base and exponent are introduced, and the teacher walks through examples where the base and exponent are unknown. Then, the teacher walks through evaluating an expression that involves an exponent and requires using the order of operations.

• In 6.EE.A.2c, Real Stories of the AIF (Accident Investigation Force), the teacher provides instruction for using an expression for drag factor, a formula to convert between Farenheit and Celsius, and an expression with multiple variables. The teacher prompt states, “It’s important to substitute values carefully; many mathematicians put parentheses around each value to make sure they have substituted it correctly and in the right spot,” and later, “When substituting in for variables in formulas or expressions, it’s often helpful to put the values in parentheses to help keep them separated and to remain clear on the operations to be used on each value.”

Examples of students independently demonstrating procedural skills and fluencies include:

• In 6.NS.B.2, Which Way, the Clicker Quiz contains six questions that involve long division, including five word problems and one problem that requires interpreting a quotient in multiple ways (remainder, fraction, decimal). In the Practice Printable, there are four problems in Question 1, “Find each quotient” and four word problems that require long division. For example, Practice Printable Question 1a states, “$$40,584 ÷ 76$$”; Question 5 states, “The city of Vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards. If the width of the park is to be 84 yards, how much fencing does the city need to surround the park?”

• In 6.NS.B.3, Enter the Dragon, the Practice Printable contains four problems each for adding, subtracting, multiplying and dividing multi-digit decimal numbers. The Clicker Quiz contains six problems, one problem each for each of the four operations, and two word problems that require using multiple operations to solve. For example, Practice Printable, Question 2 states, “$$70.64 + 0.0059$$”;  Question 6 states “$$43.02-0.0078$$”; Question 10 states “$$48.5 ⋅ 1.604$$”; Question 14 states “$$0.5208 ÷ 6.2$$”.

• In 6.EE.A.1, I Dream of Djinni, one question in the Clicker Quiz shows an image of a man thinking $$7^6$$ and a woman thinking $$6^7$$ and states, “$$7×7×7×7×7×7$$ Ryan and Jane are thinking about writing this expression using an exponent. Who is correct?” In the Practice Printable, Question 4 states, “Fill in the missing information for each row.” A three column table with the headings “exponential form, expanded form and standard form,” is provided.

In 6.EE.A.2c, Real Stories of the AIF, Practice Printable, Question 1 states, “Complete the chart using the formula for area of a triangle, $$A=\frac{1}{2}bh$$”; students are given a table with 5 pairs of base and height values, and calculate the area. In Practice Printable, Question 2 states, “Evaluate each expression in the chart if $$a=2, b=4, c=6$$ and $$d=3$$”; the chart contains six expressions using the variables.

### Indicator 2c

Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

2/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8, Grade 6 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics. Engaging applications include single and multi-step problems, routine and non-routine problems, presented in a context in which mathematics is applied.

Examples of students engaging in routine application of skills and knowledge include:

• In 6.RP.A.3c, Stealing Home, an example states “Country music makes up 75% of Ashley’s music collection. If she has 33 albums that are by country artists, how many albums does she have in her entire music collection?

• In 6.NS.A.1, Mr. Mung’s Ice Cream, Practice Printable, Question 6 states, “Milo bags groceries at a local market. The plastic bags he uses are designed to hold 25 pounds. If a typical water bottle weighs $$1\frac{1}{4}$$ pounds, how many bottles could Milo put in a bag (assuming they all fit)?”

• In 6.EE.7, The Sign of Zero, Practice Printable, Question 2 states, “The map at the right shows points A, B, and C. Say the distance from point A to point C is three times the distance from point A to point B, and the distance from point A to point C is 105 miles. What is the distance from point A to point B?”

• In 6.RP.A.3a, Clone Wars, Practice Printable, Question 4 states, “Kennedy thinks the best orange juice is made using 3 cups of water and 5 cups of juice concentrate. How many cups of water and juice concentrate will she need to make 40 cups of juice? Create a table or diagram to show your reasoning.”

Examples of students engaging in non-routine application of skills and knowledge include:

• In 6.SP.B.4 & 5, Shoot for the Moon!, Practice Printable, students write a newspaper article based on data from a survey including “a headline, graphical display, the number of observations, at least one graphic, a description of how the survey was conducted, the measures of center including mean, median and mode. Report all measures of variability and striking deviations.”

• In 6.NS.C.7c, Day by Day, the Practice Printable includes: At Wonder Toys, new employees receive a 30-day evaluation that ranks bad days and good days on a scale of -10 to 10. “Miss Brooks has a new assistant at Wonder Toys named Mary Smithson. The time has come for Mary’s 30-day evaluation. Based on the number of bad days, Mary thinks she may lose her job. Miss Brooks explains that, along with the number of good and bad days, she has to look at the magnitude of the good and bad days to determine job performance. Use Mary Smithson’s evaluation to explain what Miss Brooks is talking about and to determine whether Mary has a good evaluation or a poor evaluation.”

• In 6.RP.A.2, Road Trip Ratios, Practice Printable, Question 7 states, “Pareesa bought two new aquariums, each holding exactly 200 gallons of water. One aquarium will hold only small fish and the other will hold large fish. She will buy 5 small fish for every 10 gallons of water in the aquarium. She will buy 8 large fish for every 40 gallons of water in the aquarium. How many total fish will Paressa have? What will be the ratio of large fish to small fish?”

### Indicator 2d

The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

2/2
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Indicator Rating Details

The instructional materials reviewed for Core Curriculum by MidSchoolMath 5-8, Grade 6 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

Examples of the three aspects of rigor being present independently throughout the materials include:

• In 6.NS.C.5, Weather Bear, students develop conceptual understanding of the meaning of positive and negative numbers. During Teacher Instruction, these examples are provided:  “Let’s look at a different example of walking forwards and backwards. What is the meaning of taking 5 steps forward? What is the meaning of taking 2 steps backward? What is the meaning of zero in this case?; Now, let’s look at gaining and losing yards in football. What is the meaning of a gain of 6 yards? What is the meaning of a loss of 4 yards? What is the meaning of zero in this case?”

• In 6.NS.C.6c, Special Intelligence, students develop procedural skill in plotting points. In the Practice Printable, Question 4, students “Plot each point on the coordinate plane, and label it with the corresponding letter.” Students are given nine points to plot, including some with $$\frac{1}{2}$$, to ensure they have multiple opportunities to plot points on the coordinate plane.

• In 6.EE.A.2c, Real Stories of the AIF, students evaluate expressions at specific values of their variables that arise from formulas used in real-world problems. In the Practice Printable, Question 3 states “The cost of a pass to the amusement park for 5 days or less is $$50+10n$$, where $$n$$ is the number of days you are visiting. The cost for a pass to the amusement park for more than 5 days is $$45+10(n-1)$$, where $$n$$ is the number of days you are visiting. a) If you plan on visiting for 5 days, what is the cost of the pass? b) What would be the cost for visiting for 6 days? c) Is it a better deal to visit for 5 or 6 days? Explain. d) What would be the cost to visit for one week?”

Examples of multiple aspects of rigor being engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study include:

• In 6.G.A.1, The Lilliput Regatta, students use their conceptual understanding of area to find the area of right triangles, other triangles, special quadrilaterals, and polygons in application problems by composing into rectangles or decomposing into triangles and other shapes. The teacher shows students how to decompose figures, find missing dimensions, and calculate the area of each region. Students also practice procedural skills while finding the areas of figures throughout the lesson. For example, Practice Printable, Question 2 states, “What is the area of figure ABCD, in square centimeters?” (figure ABCD is a kite).

• In 6.EE.B.6, Land in Lama, students use their understanding of variables to represent numbers as they develop skill in writing equations that represent real-world problems. In the Practice Printable, Question 2 states, “David went into a floral shop to buy his mother some flowers. Depending on the season, carnations cost c dollars; roses cost r dollars; and tulips cost t dollars. Vases are \$12. Write an expression to represent David’s cost for 4 carnations, 5 roses, 3 tulips, and a vase.”

### Criterion 2e - 2i

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

10/10
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Criterion Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Each Detailed Lesson Plan, Lesson Plan Overview, includes one to three MPs and describes how the lesson connects to the MPs. In addition, each Detailed Lesson Plan includes a specific tip from Jo Boaler that provides guidance about how to connect the MPs with the lesson. In the Teacher’s Guide, Protocols to Support Standards for Mathematical Practice includes, “To support the Standards for Mathematical Practice, MidSchoolMath has compiled a ‘Top 10’ bank to include protocols (or instructional moves) that teachers use to structure learning experiences to deepen the understanding of the SMP. Recommended protocols for each lesson are found in the Detailed Lesson Plans with teacher instructions to implement.” The protocols are directly related to the MPs they best support.

### Indicator 2e

Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

2/2
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Indicator Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 6 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Examples where MP1 (Make sense of problems and persevere in solving them) is connected to grade-level content include:

• In 6.EE.A.2c, Real Stories of the AIF, Lesson Plan Overview, “In Data & Computation, students face a challenge that they have not yet likely encountered, the '30df' formula that looks complex and includes a square root symbol. Students are encouraged to slow down (per Jo Boaler’s tip) and grapple with ‘I Wonder..., I Notice…’ supported by teacher prompts, to help them start to make sense of the things that may not yet be understood or known. Perseverance is also encouraged as teachers help students understand that mistakes and struggle create brain growth.”

• In 6.NS.C.8, The Mark of Zero, Detailed Lesson Plan, “During Immersion and Data & Computation, students receive information that initially seems vague. As they explore the statements provided to them in conjunction with the ‘map’ (coordinate plane), they begin to see more value in the statements, can infer more specific details, and consequently change course as needed. The ‘Think-Pair-Share’ protocol aids students in making sense of the problem, as they look for entry points to its solution.”

• In 6.RP.A.3b, Vacation Day, Lesson Plan Overview, Applying Standards for Mathematical Practice, “During Immersion, students use a ‘Think-Pair-Share’ protocol to determine what they need to know and begin a solution pathway. In Data & Computation, students recognize that equivalent ratios and the unit rate can give them important information about the guard’s wages. Students can use ratio tables, double number lines, and other strategies to solve the problem, and have the opportunity to share their strategies.”

Examples where MP2 (Reason abstractly and quantitatively) is connected to grade-level content include:

• In 6.NS.C.5, Weather Bear, Detailed Lesson Plan states, “During Immersion and Data & Computation, students will recognize that a positive number, a negative number, and zero have specific meanings within a context. Students will make sense of real-world quantities and their relationships when looking at altitudes. Students will also recognize that numbers, such as 7 and -7, are opposite values and are in opposite direction from zero on a number line.”

• In 6.RP.A.1, For Every Day, Lesson Plan Overview, Applying Standards for Mathematical Practice, “During Data & Computation, students compute the quantitative ratio of two quantities, contextualize it to make meaning of a ‘real-world’ situation, then express it using ratio language.”

• In 6.EE.B.7, The Sign Of Zero, Lesson Plan Overview, Applying Standards for Mathematical Practice, “During Immersion, students have the opportunity to make initial sense of what is being asked, by talking with a partner about what was presented in the video, specifically a diagram that is shown a second time. The ‘Think-Pair-Share’ protocol allows students to gain a perspective other than their own. During Data & Computation, students receive additional quantitative information whose meaning must be attended to when building symbolic equations of the mathematical relationship. After solving the equation, students must attend fully to its meaning in the situation, as it's not the final answer; an additional operation must be performed to get the intended value.”

### Indicator 2f

Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

2/2
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Indicator Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 6 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials include 10 protocols to support Mathematical Practices. Several of these protocols engage students in constructing arguments and analyzing the arguments of others. When they are included in a lesson, the materials provide directions or prompts for the teacher to support engaging students in MP3. Examples include:

• “Lawyer Up! (12-17 min): When a task has the classroom divided between two answers or ideas, divide students into groups of four with two attorneys on each side. Tell each attorney team to prepare a defense for their ‘case’ (≈ 4 min). Instruct students to present their argument. Each attorney is given one minute to present their view, alternating sides (≈ 4 min). Together, the attorneys must decide which case is more defendable (≈ 1 min). Tally results of each group to determine which case wins (≈ 1-2 min). Complete the protocol with a ‘popcorn-style’ case summary (≈ 2-3 min).”

• “Math Circles (15-28 min): Prior to class, create 5 to 7 engaging questions at grade level, place on different [sic] table-tops. For example, Why does a circle have 360 degrees and a triangle 180 degrees? Assign groups to take turns at each table to discuss concepts (≈ 3-4 min each table).”

• “Quick Write (8-10 min): After showing an Immersion video, provide students with a unique prompt, such as: ‘I believe that the store owner should…’, or ‘The person on Mars should make the decision to…’ and include the prompt, ‘because…’ with blank space above and below. Quick writes are excellent for new concepts (≈ 8-10 min).”

• “Sketch It! (11-13 min): Tell students to draw a picture that includes both the story and math components that create a visual representation of the math concept (≈ 5-7 min). Choose two students with varying approaches to present their work (≈ 1 min each) to the class (via MidSchoolMath software platform or other method) and prepare the entire class to discuss the advantages of each model (≈ 5 min).”

The materials include examples of prompting students to construct viable arguments and critique the arguments of others.

• In 6.EE.A.2c, Real Stories of the AIF, Practice Printable, Question 3c, “The cost of a pass to the amusement park for 5 days or less is $$50 + 10n$$, where $$n$$ is the number of days you are visiting. The cost for a pass to the amusement park for more than 5 days is $$45+10(n-1)$$, where $$n$$ is the number of days you are visiting. Is it a better deal to visit for 5 or 6 days? Explain.”

• In 6.SP.B.4 & 5, Shoot for the Moon!, Practice Printable, Introduction Problem, “What could the newspaper article look like? Be sure to include a headline, graphical display, the number of observations, a description of how the survey was conducted, the measures of center including mean, median and mode. Report all measures of variability and striking deviations. Choose the most appropriate measure of center and measure of variability and defend your choices; include a closing comment.” In the Simulator question, “Choose the most appropriate measure of center and measure of variability and defend your choices.”, and in Practice Printable, Questions 2c-d states, “What is the better measure of center for this data set? Why? Which is the better measure of variation of this data set? Why?”

• In 6.RP.A.3c, Stealing Home, Practice Printable, Question 3, “Tyrell took a history test. He answered 21 of the 25 questions correctly. In order to get an ‘A’ on the test he needs to get at least a 90%. Did Tyrell get an ‘A’ on his history test? Explain your reasoning.”

• In 6.SP.A.3, Periodontal Pockets, Practice Printable, Question 1, “All sixth graders at Madison Middle School were given a math and reading placement test at the beginning of the year. a) If you wanted to know on average if sixth grade students scored better on the math test or reading test, would you consider the measure of center of the data or the measure of variability of the data? Explain your reasoning. b) If you wanted to see how consistent (or similar to each other) the scores on the respective tests were, would you focus on the measure of center of the data or the measure of variability of the data? Explain your reasoning.”

• In 6.NS.C.7c, Day by Day, Practice Printable, Introduction Problem, “Use Mary Smithson’s evaluation to explain what Miss Brooks is talking about and to determine whether Mary has a good evaluation or a poor evaluation.”

The materials provide guidance for teachers on how to engage students with MP3. In several lessons, the Detailed Lesson Plan identifies MP3 and provides prompts that support teachers in engaging students with MP3. Examples include:

• In 6.NS.C.7d, Coffee Accounting, “In Data & Computation, students take the practice test by themselves, then work with another student to justify their conclusions in the ‘Study Hall’ protocol. Because the order of the wording impacts the meaning of the statements, students practice a logical progression of statements. Paired students explore the truth of their partner’s conjectures, and ask rich questions and critique the reasoning of other students. The following Teacher Prompts encourage students to explain their reasoning and examine their partner’s reasoning and logic. Did your study hall partners present a logical argument? Can you repeat what another student’s logic is? Did you notice any flaws in their logic? Can you draw a picture to explain your reasoning? Is there another way to explain your own logic?”

• In 6.NS.C.7c, Day by Day, Data & Computation “includes prompts that support students in developing their own arguments and critiquing those of others: 2. Use the ‘Quick Write’ protocol, where students are prompted to write down ideas about whether Rob is having good days or bad days, and prompted to make a conclusion with supporting evidence. It is important that students are not given too much information, or prompted with guiding questions at this stage. 3. Have students join with two other students. Each student has 2 minutes to present their ‘Quick Write.’ During which the other two students act as supervisors, and are there to provide feedback they feel would be helpful in strengthening the conclusion. Use the following  prompts with students to encourage the critique process: ‘I was confused when you ____.  ‘It might be more clear if you said ________. ‘Can you re-state that in a different way?’"

### Indicator 2g

Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

2/2
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Indicator Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 6 meet expectations for supporting the intentional development of MP4 and MP5 for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Examples of the intentional development of MP4 to meet its full intent in connection to grade-level content include:

• In 6.EE.A.2c, Real Stories of the AIF, Lesson Plan Overview, “MP4: Model with mathematics. On Day 1, during the Data & Computation phase, the students will decide how fast the driver was driving using the ‘$$30df$$’ formula. The students will use the formula to identify the rate of speed on a specific road surface.”

• In 6.EE.B.6, Land in Lama, the Detailed Lesson Plan states, “MP4: Model with mathematics. In Land in Lama, students are tasked with representing the cost of the land through an expression, which is, in essence, a modeling task. Further supporting the practice, during Immersion, the problem is relatively unstructured, requiring students to determine what they need to know, and analyzing how the problem might be solved while making assumptions about the relationships between unknown quantities. Visual representation the students develop supports clarity of thinking about their model and assumptions. Students refine their model as more information is given during Data & Computation. The full intent of the practice occurs as students create their own variables and include them as part of the expression.”

• In 6.G.A.2, River Rescue, the Detailed Lesson Plan states, “MP4: Model with mathematics. River Rescue opens with a unique protocol that leads students to begin modeling with mathematics right away in Immersion. Students imagine a flowing river and must try to think of a way to determine the amount of water that is flowing per second. They team in small groups, using their intuition to guide them in an early attempt to model the situation. They draw pictures and discuss ideas in an attempt to find an entry point into the upcoming task. In Data & Computation, students calculate the flow rate of the river (modeled as volume of a rectangular prism with fractional side lengths). In Resolution, students revise their thinking, comparing not only their answer, but their original conceptual ideas of how to calculate flow rate.”

Examples of the intentional development of MP5 to meet its full intent in connection to grade-level content include:

• In 6.RP.A.3c, Stealing Home, the Detailed Lesson Plan states, “MP5: Use appropriate tools strategically. During Data & Computation and Practice Printable, students discover that two parts of a percent problem are given (whole, part, or percent) and a third unknown part must be determined. Students can use different tools that help them see that 100% splits up into parts (double number lines, tape diagrams, ratio tables, etc.).” In the Practice Printable, Question 5 states, “Solve each problem below by using a table of equivalent ratios, a tape diagram, a double number line or an equation. a) 75 is 15% of what number? b) What is 60% of 210? c) 120 is 30% of what number? d) 160 is 20% of what number?”

• In 6.SP.B.4&5, Shoot for the Moon!, the Detailed Lesson Plan states, “MP5: Use appropriate tools strategically. In Data & Computation, students are asked "What could the newspaper article look like?" This general question requires students to consider the tools available to them and to make personal choices as to how to use them. These include mathematical tools (graphs, tables, mathematical graphics, etc.) and also physical tools ( rulers, graph paper, pencils, etc.). Technology tools (computers, tablets, calculators, spreadsheets, and graphical display software) may also be considered.”

### Indicator 2h

Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

2/2
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Indicator Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 6 meet expectations for supporting the intentional development of MP6: Attend to precision for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials use precise and accurate terminology and definitions when describing mathematics, and the materials provide instruction in how to communicate mathematical thinking using words, diagrams, and symbols. Examples include:

• Each Detailed Lesson Plan provides teachers with a list of vocabulary words and definitions that correspond to the language of the standard that is attached to the lesson; usually specific to content, but sometimes more general. For example, 6.NS.3 states “Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.” The vocabulary provided to the teacher in 6.NS.B.3, Enter the Dragon is, “Decimal number: A number that can show place value less than 1; represents values such as tenths, hundredths, thousandths, etc.”

• The vocabulary provided for the teacher is highlighted in red in the student materials on the Practice Printable.

• Each Detailed Lesson Plan prompts teachers to “Look for opportunities to clarify vocabulary” while students work on the Immersion problem which includes, “As students explain their reasoning to you and to classmates, look for opportunities to clarify their vocabulary. Allow students to ‘get their idea out’ using their own language but when possible, make clarifying statements using precise vocabulary to say the same thing. This allows students to hear the vocabulary in context, which is among the strongest methods for learning vocabulary.”

• Each Detailed Lesson Plan includes this reminder, “Vocabulary Protocols: In your math classroom, make a Word Wall to hang and refer to vocabulary words throughout the lesson. As a whole-class exercise, create a visual representation and definition once students have had time to use their new words throughout a lesson. In the Practice Printable, remind students that key vocabulary words are highlighted. Definitions are available at the upper right in their student account. In the Student Reflection, the rubric lists the key vocabulary words for the lesson. Students are required to use these vocabulary words to explain, in narrative form, the math experienced in this lesson. During ‘Gallery Walks,’ vocabulary can be a focus of the ‘I Wonder..., I Notice…’ protocol.”

• Each lesson includes student reflection. Students are provided with a list of vocabulary words from the lesson to help them include appropriate math vocabulary in the reflection. The rubric for the reflection includes, “I clearly described how the math is used in the story and used appropriate math vocabulary.”

• Vocabulary for students is provided in the Glossary in the student workbook. “This glossary contains terms and definitions used in MidSchoolMath Comprehensive Curriculum, including 5th to 8th grades.”

• The Teacher Instruction portion of each detailed lesson plan begins with, “Here are examples of statements you might make to the class:” which often, though not always, includes the vocabulary with a brief definition or used in context. For example, the vocabulary provided for 6.RP.A.3c, Stealing Home is “Part”, “Whole”, and “Percent.” The sample statements provided are, “Remember there are always two parts of the percent problem given from the part, whole, or percent; Remember that the percent of a quantity is per 100; In Stealing Home, we had to help find the number of runs Jackie Robinson would score during the 1948 season; We can convert the percent to a rate per 100, so 52% is $$\frac{52}{100}$$; A ratio table can be created using the percent as a rate of 100, and then other helpful equivalent ratios can be identified.”

### Indicator 2i

Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

2/2
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Indicator Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath 5-8 Grade 6 meet expectations for supporting the intentional development of MP7 and MP8 for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Examples of the intentional development of MP7 to meet its full intent in connection to grade-level content include:

• In 6.NS.B.4, The Castle Guard, the materials state, “MP7: Look for and make use of structure. On Day 1, during both the Immersion and Data & Computation phases, students will understand the differences on how to calculate the greatest common factor and least common multiple between two numbers.” Optional teacher prompts include, “What do we know about the number of days that each guard works? How can we use a number line as a tool to show when the guards work? Does the LCM or GCF need to be found when the guards work together again? How do we find the LCM? What are the multiples of 2? What are the multiples of 4? What are the multiples of 5? What is the LCM of 2, 4, and 5? When will the guards work together again?”

• In 6.RP.A.3d, Saffron Shuffle, Lesson Plan Overview, “MP7: Look for and make use of structure. During Data & Computation, students work together to notice that ratios can be used to convert a measurement from one unit to another. By using ratios written in fraction form as conversion factors, students recognize the structure of the fraction, where a common numerator and denominator make 1 (cancel each other out).Students use this structure repeatedly to keep track of units during conversion and to cancel them out as needed to end with the appropriate unit.”

• In 6.G.A.3, Fuel Factor, the Detailed Lesson Plan states, “MP7: Look for and make use of structure. During Immersion and Data & Computation, students will recognize that endpoints for horizontal line segments have the same y-coordinate, and the length of such segments can be found by subtracting the x-coordinates because the grid structure shows the lengths to be the distance between x-coordinates. Similarly, endpoints for vertical line segments have the same x-coordinate, and the length of such segments can be found by subtracting the y-coordinates because the grid structure shows the lengths to be the distance between y-coordinates. Students are able to make use of these structures for the practical purpose of determining the length of the race course.” The prompts provided for teachers include: “What is the direction for the course? What do you notice about the coordinates of the endpoints of horizontal line segments? What do you notice about the coordinates of the endpoints of vertical line segments? Imagine the coordinates on a grid. How might you find the length of a line segment connecting them? Since there is no grid, how might you find the length of the line segment anyway? What is the total distance of the course? For how many megaspans do the sisters think the ship will last?”

Examples of the intentional development of MP8 to meet its full intent in connection to grade-level content include:

• In 6.NS.C.6b, Treasure Trail, the Detailed Lesson Plan states, “MP8: Look for and make use of structure. During Data & Computation, students have opportunity to recognize the coordinate plane as a structure that aids them in seeing a repeated pattern for coordinates that are reflected. During Resolution, teacher prompts during the ‘Number Talk’ ask students to identify the constant pattern of how coordinates are affected by reflection and to explain how the grid lines in the coordinate plane aided them in realizing the general rule.”

• In 6.EE.A.1, I Dream of Djinni, the Detailed Lesson Plan states, “MP8: Look for and express regularity in repeated reasoning. On Day 1, during the Data & Computation phase, students will try to determine which prize (option 1 or 2) will have the greatest number value. The students will create a chart to write down the information they already know about options 1 & 2 and then move towards using repeated multiplication to trigger other tools or strategies that will produce the correct solution.”

• In 6.G.A.1, The Lilliput Regatta, Lesson Plan Overview, “MP8: Look for and express regularity in repeated reasoning. During Data & Computation and Practice Printable, as students repeatedly calculate the area for each geometrical shape, they are able to see that they can manipulate the shape to find faster and easier ways to determine the area. They can repeatedly cut and re-form the shape into parts, or can double its size and divide by two, or use other methods to determine the area. The regularity in the repeated reasoning is that the area is always the same, no matter how they manipulate the shape so long as its size is not changed.”

## Usability

#### Meets Expectations

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Gateway Three Details

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports, for Criterion 2, Assessment, and for Criterion 3, Student Supports.

### Criterion 3a - 3f

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

9/9
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Criterion Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the materials, contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject, include standards correlation information that explains the role of the standards in the context of the overall series, provide explanations of the instructional approaches of the program and identification of the research-based strategies, and provide a comprehensive list of supplies needed to support instructional activities.

### Indicator 3a

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

0/2

### Indicator 3b

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

0/2

### Indicator 3c

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

0/2

### Indicator 3d

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

Narrative Evidence Only

### Indicator 3e

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

0/2

### Indicator 3f

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

0/1

### Criterion 3i - 3l

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

10/10
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Criterion Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for Assessment. The materials: have assessment information included in the materials to indicate which standards are assessed, include an assessment system that provides multiple opportunities throughout the grade to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up, and provide assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices.

### Indicator 3i

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

0/2

### Indicator 3j

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

0/4

### Indicator 3k

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

0/4

### Indicator 3l

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

Narrative Evidence Only

### Criterion 3m - 3v

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

8/8
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Criterion Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics, extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity, strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics, and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

### Indicator 3m

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

0/2

### Indicator 3n

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

0/2

### Indicator 3o

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

Narrative Evidence Only

### Indicator 3p

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

Narrative Evidence Only

### Indicator 3q

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

0/2

### Indicator 3r

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

0/2

### Indicator 3s

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

Narrative Evidence Only

### Indicator 3t

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

Narrative Evidence Only

### Indicator 3u

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

Narrative Evidence Only

### Indicator 3v

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

0/2

### Criterion 3w - 3z

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

0/0
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Criterion Rating Details

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 include a visual design that is engaging and integrates digital technology, when applicable, with guidance for teachers. The materials: integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, have a visual design that supports students in engaging thoughtfully with the subject, and provide some teacher guidance for the use of embedded technology to support and enhance student learning.

### Indicator 3w

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

Narrative Evidence Only

### Indicator 3x

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

Narrative Evidence Only

### Indicator 3y

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

Narrative Evidence Only

### Indicator 3z

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

Narrative Evidence Only
abc123

Report Published Date: 2021/04/22

Report Edition: 2021

## Math K-8 Review Tool

The K-8 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 complement 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.