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Report for 6th Grade

Overall Summary

The instructional materials reviewed for Reveal Math Grade 6 meet expectations for alignment to the CCSSM. ​The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor. The materials meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

6th Grade
Alignment
Meets Expectations
Usability
Meets Expectations

Focus & Coherence

The instructional materials reviewed for Reveal Math Grade 6 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.

Gateway 1
Meets Expectations

Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

​The instructional materials reviewed for Reveal Math Grade 6 meet expectations for not assessing topics before the grade level in which the topic should be introduced. Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

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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.

The instructional materials reviewed for Reveal Math Grade 6 meet expectations that they assess grade-level content.

The materials provide three versions of each Module assessment which include a variety of Item types as well as a Performance Task for each Module. In addition, there are quarterly benchmark tests to show growth over the year.

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

• Benchmark 2 Assessment, Item 2: “Which expression is not equivalent to the other three? $$0.3^2 + 8; 2^3 + 0.09; 2^3 + 0.03^2; 3^2 ÷10^2 + 2^3$$(6.EE.2c)
• End of Course Test, Item 2: “Students at a middle school were surveyed about their favorite cafeteria food. The table shows the results of the survey. Drag the tiles to order the favorite meals from least percent of students (at the bottom) to greatest percent of students (at the top).” Students order: 32 %, 1/5, 0.23, and 1/4. (6.RP.3c)
• Module 4 Test Form A, Item 3: “One winter night, the temperature outside was 3°F. Overnight, the temperature dropped to –17°F. How many degrees did the temperature drop overnight? Describe the steps you would follow to find the answer using a number line.” (6.NS.6)
• Module 1 Performance Task: “Mr. Jackson coaches the junior varsity track team. He has entered his athletes in a triathlon. He needs information to help him motivate and prepare his athletes for this challenging event. The triathlon consists of 1 mile of swimming, 25 miles of biking, and 6 miles of running. Mr. Jackson estimates that the average time spent on each phase of the race will be 30 minutes for swimming, 75 minutes for biking, and 60 minutes for running. He sets up a training schedule that includes two sports each day.” There are five parts to the Performance Task: students write ratios to represent the relationship between the two sports on a given day, set up a ratio table, graph the ordered pairs from the table on a coordinate plane, describe how the ratios of times compare for each pair of sports, represent average speed of each sport as a unit rate, and use the information in the tables to answer questions. (6.NS.4; 6.RP.A)
• Module 10 Test Form A, Item 1: “Which of the following are statistical questions? Select all that apply. A) How many 5 km marathons are in Kentucky in October? B) How many pairs of running shoes do you own? C) How many miles is a 5 km marathon? D) How many feet are in a mile? E) How fast can you run? F) How many marathons have you run?” (6.SP.1)

Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. The materials are digital and download as a word document, making it easy to modify or omit Items. These items include:

• Benchmark Test 2, Item 14: “All entrees cost $10 at the Roadside Diner. Each side dish is an additional$2. The equation y = 2x + 10 describes the total cost, y, for the number of side dishes, x. Graph the equation of the line.” (8.F.3)
• End of Course Test, Item 3: “An electronics store reduces the price of a printer by 25%. The sale price is marked at $46.50. A) What percent of the original price is the sale price? B) What was the original price of the printer?” (7.RP.3) • Module 2 Test Form A, Item 13: “The regular price of a baseball hat is$14.45. If Carlos buys the baseball hat on sale for 20% off the regular price, how much change will he receive after paying with $20?” (7.RP.3) • Module 2 Test Form A, Item 19: “A grocery store purchases bags of chips for$2 and marks the price up by 152%. The store is having a sale where everything is on sale for 10% off. Choose the most reasonable estimate for the final price of a bag of chips. A) $0.30 B)$2.70 C) $3.30 D)$4.54” (7.RP.3)

Rigor & Mathematical Practices

The instructional materials reviewed for Reveal Math Grade 6 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).

Gateway 2
Meets Expectations

Criterion 2.1: Rigor

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.

The instructional materials reviewed for Reveal Math Grade 6 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.

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

The instructional materials reviewed for Reveal Math Grade 6 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The structure of the lessons provide several opportunities that address conceptual understanding, and the materials include problems and questions that develop conceptual understanding throughout the grade-level.

• In the Teacher’s Edition, both Modules and Lessons begin with The Three Pillars of Rigor where conceptual understanding for the topic is briefly outlined. For example, Lesson 2-2 states, “In this lesson, students continue to develop understanding of percents. They begin to understand that percents greater than 100% represent numbers greater than 1 and percents less than 1% represent numbers that are significantly less than the whole.”
• In Explore & Develop, Explore is “intended to build conceptual understanding through Interactive Presentations that introduce the concept and can be completed by pairs on devices or as a whole class through digital classroom projection.” For example, in Lesson 5-4, “Students will examine what happens to the value of an algebraic expression as the values of each of the variables change. Throughout this activity, students will use Web Sketchpad to explore the changing values of variables by using a slider. Students will use their observations to make conjectures about how the values of the variables impact the value of the algebraic expression.” (6.EE.6)
• Some Interactive Presentations (slide format) introduce vocabulary and methods to complete concepts. These Presentations include Teaching Notes with suggestions for student activities. For example, Lesson 1-2, Learn Slide 2, “Present students with the ratio table showing the relationship between the number of cups of Greek yogurt and the number of cups of flour in the pizza dough recipe. You may wish to have a student reveal how ratio tables show both an additive structure and multiplicative structure. Encourage students to attend to the differences in structures.” (6.RP.1) Related student pages contain examples involving bar models, ratio tables, and double number lines for students to build understanding. Teachers can use presentations during instruction, and students access presentations independently as needed.

Examples of the materials providing opportunities for students to independently demonstrate conceptual understanding include:

• In Lesson 1-1 Learn, “The students at Madison Middle School are going on a field trip. The principal requires one teacher chaperone for every eight students attending the field trip. Drag a possible combination of students (S) and teachers (T) to see if the bus will move. Then hit GO! to see if the bus will move. The bus will only move if the relationship is maintained of one teacher for every eight students. One of the buses has 16 students on it. How many teachers need to be on the bus to serve as the chaperone? Drag the appropriate number of teachers (T) onto the bus. Then hit GO! to see if the bus will move.” (6.RP.1)
• In Lesson 4-1 Explore, “Students will work in pairs to progress through the activity. Students will first use a thermometer to explore positive integers. They will then explore a thermometer with both positive and negative values. Finally, students will engage in the drag and drop activity that involves placing the negative numbers on the thermometer and explore how they relate to their everyday lives.” (6.NS.5)
• In Module 5, Test Form A, Question 19B, “Explain how using the Distributive Property can help you use mental math to multiply numbers.” (6.EE.3)
• In Lesson 8-2 Explore, students use Web Sketchpad to explore how the area of a parallelogram is related to the area of triangles. “What do you notice about the base and height of the triangle and the base and height of the parallelogram? Make a conjecture about how to use what you know about the area of the parallelogram to find the area of triangle DEF? Explain your reasoning.” (6.G.1)
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Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials reviewed for Reveal Math Grade 6 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The structure of the lessons includes several opportunities to develop these skills. The instructional materials develop procedural skill and fluency throughout the grade-level.

• In the Teacher’s Edition, both Modules and Lessons begin with The Three Pillars of Rigor where procedural skill and fluency for the topic is briefly outlined. For example, Module 5, “In this module, students use their understanding to build fluency with using powers and exponents, order of operations, and mathematical properties, as well as evaluating multi-step algebraic expressions and generating and simplifying equivalent algebraic expressions.”
• In Explore & Develop, Develop gives students multiple examples to practice “different strategies and tools to build procedural fluency.” For example, Lesson 6-2, Example 2, students are shown how to solve one-step addition problems with whole numbers using algebra tiles, a bar diagram, and the Subtraction Property of Equality; then in Example 3, students are encouraged to “adhere to the Subtraction Property of Equality” when the problem involves fractions: “Solve 3 3/4 + m = 7 1/2. Check your solution.” (6.EE.7)
• Some Interactive Presentations (slide format) demonstrate procedures to solve problems. For example, in Lesson 3-4, students are shown the “equation method” to divide fractions, “Find the reciprocal of the divisor and multiply.” (6.NS.1)
• Some Checks address procedural skills and fluency. For example, Lesson 8-3, Example 1 Check: Given bases of 6.1 and 10 units and a height of 9.7 units, “Decompose the trapezoid to find its area.” The intent is to use the area formulas for a rectangle and a triangle. (6.G.1)

The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade-level.

• Lesson 3-1. Example 2, Divide Multi-Digit numbers. Find 5,272 ÷ 64. Move through the steps to solve by annexing the zero.” The steps are all demonstrated and written out. (Divide from left to right, Multiply 8 x 64, then subtract. Multiply 2 x 64, then subtract. There is a remainder. Annex a zero) (6.NS.2)
• Lesson 3-2, Learn - Multiply Decimals, “When multiplying a decimal by a decimal, multiply as with whole numbers. To place the decimal point in the product, find the sum of the number of decimal places in each factor. The product has the same number of decimal places. If there are not enough decimal places in the product, annex zeros to the left of the first non-zero digit.” (6.NS.3)
• In Lesson 9-1, Practice Questions 1-6, “2) Roy made a jewelry box in the shape of a rectangular prism with the dimensions shown. What is the volume of the jewelry box?; 4) The rectangular prism shown has a volume of 115 cubic yards. What is the length of the prism?” (6.G.2)
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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

The instructional materials for Reveal Math Grade 6 meet expectations for being designed so that teachers and students spend 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 knowledge of the grade-level.

• In the Teacher’s Edition, Modules and Lessons begin with The Three Pillars of Rigor where application for the topic is briefly outlined. For example, in Module 7, “In this module, students draw on their knowledge of tables, equations, and the coordinate plane … to apply their understanding of relationships between two variables to solve real-world problems.”
• Each Module includes a Performance Task that addresses application. For example, in Module 6, Performance Task, “The students in the chorus will be performing at an amusement park. After the performance, the students will get to go on the rides. The students sell scones at breakfast during the school year to help raise money for the trip. Part A. Parents volunteer to make the scones. They are given a recipe. The recipe calls for 6 1/2 cups of flour. Duyl has already added 2 3/4 cups of flour. How much more flour will he need to add? Use a bar diagram to model this situation. Then write and solve an addition equation to find the answer. How can you check your answer? Explain.”
• Some Checks address application. For example, in Lesson 9-3, Apply, Check, “The dimensions of two climbing walls that are in the middle of an obstacle course are shown. How much greater is the surface area of Wall B than Wall A?” (6.G.4)
• Some Exit Tickets address application. For example, in Lesson 5-5, Exit Ticket, “Samantha and her sister have 250 roses and 175 peonies. If they want to use all of the flowers, how many identical centerpieces can they make, if they want to have as many as possible? Write a mathematical argument that can be used to defend your solution.” (6.NS.4)

The instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts.

• In Lesson 1-5, Apply, Inventory, “The manager of an office supply store decides to hold a Buy 2, Get 1 Free sale on all reams of paper. A ream of paper holds 500 sheets of paper. The sale is held for one week and a total of 154 reams were sold (not including the ones given away for free). If each ream of paper cost the store 4.50, how much money did the store lose by giving away the free reams of paper?” (6.RP.3) • In Lesson 1-8, Apply, “Keshia can ride her bike 15 miles in 90 minutes. She wants to ride in a bike-a-thon that consists of two trail options, a 56-mile trail or a 36-mile trail. At her current rate, how many more minutes will it take her to ride 56 miles than 36 miles? If she wants to ride for about 4 hours, which trail should she choose?” (6.RP.3) • In Lesson 3-5, Example 1, “Faye is making party favors. She is dividing 3/4 pounds of cashews into 12 packages. How many pounds of cashews are in each package?” (6.NS.1) • In Lesson 6-2, Practice Question 12, “Create. Write and solve a real-world problem that can be solved with a one-step addition equation.” (6.EE.6,7) • In Lesson 8-1, Practice Question 10, “Create. Draw and label a parallelogram with a base that is 2 times its height and has an area that is less than 100 square yards.” (6.G.1) Indicator {{'2d' | indicatorName}} 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. The instructional materials for Reveal Math Grade 6 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Many of the lessons incorporate two aspects of rigor, with an emphasis on application, and practice problems for students address all three aspects of rigor. All three aspects of rigor are present independently throughout the materials, and examples include: • In Lesson 4-1, Explore and Develop, Learn, students place positive and negative numbers on a number line to represent a quantity in a familiar situation, emphasizing conceptual understanding. “Select the button to see where negative and positive integers are on the number line. Watch animations to see how integers are used in real life.” Example, “A football team has a 10 yard loss on a play. Write an integer to represent the situation.” (6.NS.5,6) • In Lesson 3-4, Practice, students divide fractions by fractions, emphasizing procedural skill. “Divide. Write in simplest form. 1) 5/6 ÷ 5/12; 4) Chelsea has 7/8 pound of butter to make icing. Each batch of icing needs 1/4 pound of butter. Write and solve an equation that models the situation. Then interpret the quotient.” (6.NS.1) • In Lesson 8-4, Explore and Develop, Apply, Home Improvement, students use area formulas to solve real-world and mathematical problems. “Takeru is planning to paint the walls of his bedroom which is in the shape of a rectangular prism. The bedroom has one window and two doors. The dimensions of the window and doors are shown in the table. If one gallon of paint covers about 150 square feet, how many gallons of paint are needed to cover the walls of a room that is 20 feet long, 15 feet wide, and 8 feet high?” (6.G.1) Examples of the materials integrating at least two aspects of rigor include: • In Lesson 2-4, Explore and Develop, Examples 1 and 2, students develop understanding of finding the percent of a number using the rate per 100 and mental math, equivalent ratios, bar diagrams, and double number lines. In Example 3, students develop procedural skill by using ratio tables and equivalent ratios to find the percent of a number when the percent is greater than 100. The goal for the lesson is students “Come up with their own strategy to solve an application problem involving attendance: Book Fair - Students were asked which night they planned on attending the book fair. The results of the survey are shown in the table. Twenty percent of the students who planned to attend on Wednesday attended on Thursday instead. Twenty-five percent of the students who planned to attend on Thursday attended on Wednesday instead. Which day, Wednesday or Thursday, had a greater actual attendance? By how many students?” (6.RP.A) • In Lesson 10-1, students develop understanding of the difference between a statistical and non-statistical question, and students practice the steps to answer a statistical question by collecting data and organizing the data in a table or graphical display for analysis/summary. Throughout the lesson, students have multiple opportunities to demonstrate understanding and practice the skills. For example, “Practice Question 5: Suppose you want to determine the number of siblings each of your classmates have. You survey them using the question How many siblings do you have? The responses were 1, 4, 2, 3, 0, 1, 0, 5, 1, 2, 2, 3, 0, 1, 2, 0, 1, 1, 6, 2 siblings. Organize the data by completing the table and analyze the results.; Practice Question 8: “Multiselect. Which of the following are statistical questions? Select all that apply.” (6.SP.1) Criterion 2.2: Math Practices Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice The instructional materials reviewed for Reveal Math Grade 6 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' | indicatorName}} The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. The instructional materials reviewed for Reveal Math Grade 6 meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade-level. All 8 MPs are clearly identified throughout the materials, including: • The materials contain a Correlation to the Mathematical Practices PDF which includes explanations and descriptions of the MPs and examples of MPs located in specific lessons. • Within the digital module opener and lesson, the Standards tab contains a list of the MPs found in that specific module/lesson. The same list is part of the Teacher Edition PDF. Throughout each lesson, the program indicates each opportunity for students to engage in the practices, with an MP symbol and a description of how to connect the MP to the content within the lesson. • In Reflect and Practice, questions intended to engage students in the MPs are specifically noted with an MP symbol. The Teacher Edition states which of the MPs each practice question is intended to align with. • Performance Task rubrics list which MPs students are intended to engage in during the task. • Each component of the digital materials (Learn, Explore, Examples, Apply) contains an About this Resource narrative explaining how related MPs should specifically be addressed within the activity. The same information is found in the Teacher Edition PDF in the margin labeled MP Teaching the Mathematical Practices. • Each lesson includes Launch - Today’s Standards: How can I use these Practices?. The Teacher’s Notes recommend that teachers, “Tell students that they will be addressing these content and practice standards in this lesson. You may wish to have a student volunteer read aloud How Can I meet this standard? and How can I use these practices? and connect these to the standards.” Examples of the MPs being used to enrich the mathematical content include: • MP1: In Lesson 1-2, Explore and Develop, Apply - Packaging, students persevere with this non-routine application problem that requires multiple steps. “A toy store sells assorted marbles, sold in small or large bags. The table shows the number of each color of marble in the small bag. The manager of the store wants to maintain the same ratio of each color of marble in the large bag as in the small bag. Each marble costs 20 cents. If the large bag contains 20 green marbles, how much does the large bag cost?” • MP7: In Lesson 7-1, Practice Question 9, students use the structure of an expression to find the value of a variable given a rule and a value (in this case, the output) for the other variable (the input). “Identify Structure. Complete the table by finding the input values: Students are given the rule 2x-2.5 and the outputs 7.5, 10.5, 13.5.” • MP8: In Lesson 4-2, Explore and Develop, Example 3, students use regularity in repeated reasoning to make a conjecture about the number of negative signs in an expression. For example, “-[-(-3)].” Students start by identifying the original integer, then they “Talk About It: Compare the opposite of the opposite of a number to the original number.” There are instances where the labeling of MPs is inconsistent, and examples of this include: • In Lesson 2-2, the materials identify MPs 1, 2, 3, and 5, and during the lesson, students utilize MPs 2, 5, and 7. • In Lesson 1-7, the print materials identify MPs 1, 2, 3, and 6, and the digital materials also identify MP4. Indicator {{'2f' | indicatorName}} Materials carefully attend to the full meaning of each practice standard The instructional materials reviewed for Reveal Math Grade 6 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of MP5. In the Teacher’s Edition, teachers are occasionally prompted to encourage students to compare tools, but students do not choose the tools. Examples include: • In Lesson 1-8, Today’s Standards, “I can use a double number line to represent and solve rate problems.” In Lesson 2-1, Today’s Standards, “I can use a 10x10 grid and a bar diagram to model percents.” In Module 2, Performance Task: Fractions, Decimals, and Percents, Part B, "What is the least number of drops of red, blue, and yellow pigment that Ava can add to a gallon of white paint so that the custom color consists of 25% red, 35% blue, and 40% yellow pigment? Use a bar diagram to solve.” • In Lesson 1-6, "[A]s students discuss the Talk About It! in slide 2, encourage them to use reasoning about the number of sections a bar diagram would need to have in order to convert 126 inches to yards. 'Why might it not always be advantageous to use a bar diagram to convert measurement units? Would you choose to use a bar diagram to convert 126 inches to yards? Why or why not?'” Examples of the materials attending to the full meaning of MPs include: • MP1: In Lesson 3-3, Explore and Develop, Apply - Cooking, “The table shows the ingredients needed to make one batch of salad dressing. A chef has 3 tablespoons (T) of garlic. She made the greatest number of whole batches possible. How much garlic remained? (*The recipe shows 2/3 T Garlic.) Talk About It! How could you solve this problem another way?” • MP2: In Lesson 9-1, Explore and Develop, Apply - Comparisons, “A movie theater sells three different-sized boxes of popcorn. If the boxes are rectangular prisms, which size of popcorn is the better buy? (*3 sizes with dimensions given.) Talk About It! Suppose the dimensions of each box doubled. Would the answer remain the same? Explain your reasoning.” • MP4: Students create situations such as in Lesson 2-1, Practice Question 14, “Create. Write a real-world problem that involves a percent less than 50%. Then model the percent.” or in Lesson 7-1, Practice Problem 10, “Model with Mathematics. Write about a real-world situation that can be represented with a two-step equation. Write the equation and explain the meaning of the variables.” Also, in Apply problems, teachers are prompted, “Instead of instructing students on a particular strategy, encourage them to use their own strategies to solve the problem and to evaluate their progress along the way. They may or may not find that they need to change direction or try out several strategies.” • MP7: In Lesson 3-2, Practice Question 15, “Explain how you know that the sum of 26.541 and 14.2 will be greater than 40.” In Lesson 5-3, Explore and Develop, Learn, “Talk About It! In the expression $$2x^2y + 4xy^2$$, explain why $$2x^2y$$ and $$4xy^2$$ are not like terms.” Teacher notes add, “Encourage students to analyze the structure of each term and note that in the first term, x is squared, and in the second term, y is squared. Since each term has a different exponent of both x and y, they are not like terms.” • MP8: In Lesson 3-1, Explore and Develop, Example 2, “Find 5,272 64. Talk about it! How do you know when you are done dividing?” This is an example of students noticing that when dividing they are repeating the same calculations over and over again and concluding that they have a repeating decimal. Also in Lesson 5-5, Teacher notes, “Teaching the Mathematical Practices. 8 - Look for and Express Regularity in Repeated Reasoning. In Exercise 18, students will use repeated reasoning to find the LCM of 160 and 480 by thinking first about the LCM of 16 and 48.” Indicator {{'2g' | indicatorName}} Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by: Indicator {{'2g.i' | indicatorName}} Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. The instructional materials reviewed for Reveal Math Grade 6 meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Examples of the materials prompting students to both construct viable arguments and analyze the arguments of others include: • Talk About It! in lesson examples are often opportunities for students to create viable arguments. For example, in Lesson 1-2, “Why might a ratio be more advantageous to use than a bar diagram when finding the quantity of each ingredient needed to make 5 pizzas?” • In Lesson 1-4, Exercise 6, students construct an argument to defend their chosen display and why they think it is more advantageous than other displays. In Exercise 8, students diagnose and explain why Avery’s solution is incorrect and correct the solution. • In Lesson 1-7, Exit ticket, “Mr. Blackwood is buying boxes of snack-size bags of crackers to pack in his family’s school lunches. The first box costs9.80 and contains 20 bags. The second box contains 30 bags and costs $13.50. Write about it! Which box is the better buy? Write a mathematical argument that can be used to defend your solution.” • In Lesson 2-5, Practice Question 18, “Justify Conclusions. A store is having a 40% off sale. If you have$38, will you have enough money to buy an item that regularly sells for \$65.99? Write an argument to justify your conclusion.”
• Write About It! within lesson examples are often opportunities for students to engage with MP3. In Apply of many lessons, students are prompted to “Write About It! Write an argument that can be used to defend your solution.”
• In Lesson 4-2, Practice Question 19, “Justify Conclusion. A student states that -x is always equal to a negative integer. Is the student correct? Justify your reasoning.”
• In Lesson 4-3, Practice Question 12, “Justify Conclusions. A student said -5 is less than -4 and |-5| is less than |-4|. Is the student correct? Justify your reasoning."
• In Lesson 5-4, Practice Question 17, “Find the Error. Evaluating the expression 4b + c for b = 2 and c = 3. Find the student’s mistake and correct it.”
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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.

The instructional materials reviewed for Reveal Math Grade 6 meet the expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are multiple locations in the materials where teachers are provided with prompts to elicit student thinking.

• In Resources, there is a Correlation to the Mathematical Practices, Grade 6, which defines the Standards for Mathematical Practice. For example, MP3 is defined, there are examples where MP3 “Students are required to justify their reasoning and to find the errors in another’s reasoning or work. Look for the Apply problems and the exercises labeled as Make a Conjecture, Find the Error, Use a Counterexample, Make an Argument, or Justify Conclusions. Many Talk About It! question prompts ask students to justify conclusions and/or critique another student’s reasoning. In the Teacher Edition, look for the Teaching the Mathematical Practices tips labeled as this mathematical practice.”
• There are Questions for Mathematical Discourse in the Develop and Explore of each lesson. For example, in Lesson 6-1, the teacher notes suggest, “Guide students through the example using these questions for mathematical discourse, Why is 3 not a solution?; Once you know that 3 is not a solution, how do you know to check numbers greater than 3, as opposed to less than 3?; Once you know that 4 is a solution, do you need to check whether 5 is a solution? Explain.”
• Talk About It! is designed to elicit student justification. For example, in Lesson 5-5, Learn, “Talk About It! When is making a list of the factors difficult to do?” The teacher’s notes provide guidance, “Encourage students to think about the process they use to find the factors of very large numbers in order to make a plausible argument and justify their reasoning.”
• The materials also prompt teachers to have students share their responses to Write About It!. Teacher guidance throughout the materials states, “As students respond to the Write About It! prompt, have them make sure their argument uses correct mathematical reasoning. If you choose to have them share their responses with others, encourage the listeners to ask clarifying questions to verify that the reasoning is correct.” The Write About It! prompts typically read, “Write an argument that can be used to defend your solution.”
• The Teacher Edition includes Teaching the Mathematical Practices tips which involve developing arguments. In Lesson 10-4, Teaching the Mathematical Practices, Exercise 7: “Students determine the validity of the statement. Encourage students to use the structure and characteristics of a box plot to determine the statement is false.; Exercise 9, “Encourage students to explain why the student’s thinking is correct.”
• Teacher’s Notes often give prompts and suggestions for facilitating arguments. For example, in Lesson 2-2, Practice Question 11, Collaborative Practice states, “Find the Error. A student said that to represent 0.2% with a 10x10 grid, you should shade 2 squares in the grid. Find the student’s error and correct it.” The teacher notes include, “Have students work together to prepare a brief explanation that illustrates the flawed reasoning. For example, the student in the Exercise thinks that 0.2% is equivalent to 2%. Have each pair or group of students present their explanation to the class.”
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Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Reveal Math Grade 6 meet the expectations for explicitly attending to the specialized language of mathematics.

The materials use precise and accurate mathematical terminology and definitions, and the materials support students in using them. Teacher’s guides, student books, and supplemental materials explicitly attend to the specialized language of mathematics.

• In Resources, there is a Correlation to the Mathematical Practices, Grade 6, which defines the Standards for Mathematical Practice. For example, MP6 is defined, there are examples where MP6 can be found, and states, “Students are routinely required to communicate precisely to partners, the teacher, or the entire class by using precise definitions and mathematical vocabulary. Look for the exercises labeled as Be Precise. Many Talk About It! prompts ask students to clearly and precisely explain their reasoning. In the Teacher Edition, look for the Teaching the Mathematical Practices tips are labeled as this mathematical practice.”
• In each Module introduction, What Vocabulary Will You Learn? prompts teachers to lead students through a specific routine to learn the vocabulary of the unit.
• Many Lessons have a “Language Objective.” For example, in Lesson 9-2, “Students will describe how nets can help find the surface area of rectangular prisms, correctly using a noun (rectangle) and the adjective form of the noun (rectangular).”
• In each lesson, Math Background briefly describes key concepts/vocabulary or directs teachers to an online component to learn background. Definitions are not included, but are accessible in the glossary. Glossary definitions are precise and accurate, and there are definitions for math content and math models. In addition, the glossary references the lesson where the vocabulary is introduced.
• The lesson Launch includes a vocabulary section that introduces new vocabulary for the lesson. During Develop and Explore, the new vocabulary is always bolded and defined. For example, in Lesson 5-5, Learn: “A common factor is a number that is a factor of two or more numbers.”
• In Lesson 4-5, What Vocabulary Will You Learn?, students use the prefix quad- to begin to understand “quadrant”. Teachers ask students to consider other words they know with quad- as a prefix.
• When students see vocabulary in successive lessons, What Vocabulary Will You Use? assists teachers in facilitating discussions that help students apply the vocabulary they have previously learned.
• In Lesson 5-1, Teaching Notes for Interactive Slideshows, “Students will learn the definitions of exponent, power, and base. Play the animation for the class. Students will learn how to write a power using a base and an exponent and how to label each part of the expression, including expressions with multiple bases and exponents."
• In Lesson 2-6, Practice Question 11, “Be Precise. Of the number of sixth grade students at a middle school, 120 prefer online magazines over print magazines. Of the number of seventh grade students, 140 prefer online magazines. A student said that this means a greater percent of seventh grade students prefer online magazines than sixth grade students? Is the student correct? Use precise mathematical language to explain your reasoning.”
• Each Module includes a Vocabulary Test. “This summative assessment asset is designed for students to demonstrate their knowledge, understanding, and proficiency of the vocabulary covered in this module.”

Usability

Gateway 3
Meets Expectations

Criterion 3.1: Use & Design

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

The instructional materials reviewed for Reveal Math Grade 6 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.

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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.

The instructional materials for Reveal Math Grade 6 meet the expectations that there is a clear distinction between problems and exercises in the materials.

In the instructional sections of each lesson, students complete examples and problems to learn new concepts through strategies such as guided instruction, step-by-step procedures, interactive slideshows, and problem solving.

Each lesson ends with independent practice, which include exercises that allow students to independently apply what they have learned. Some of the practice problems parallel the examples presented in the lesson, while others are labeled as Higher-Order Thinking Problems or Test Prep.

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

The instructional materials for Reveal Math Grade 6 meet the expectations that the design of assignments is intentional and not haphazard.

Modules include a Launch, which provides students an overview of the topics found in the module. A Vertical Alignment tab provides teachers information on Vertical Alignment between and within grade levels. Lessons are presented in a logical order that builds coherence throughout the grade.

Each Lesson follows a consistent format that develops learning through building conceptual understanding, providing opportunity for practice of procedural skills, and providing application in real-world situations. Exercises intentionally encourage a progression of understanding and skills, and the format includes three main sections, each including multiple parts:

• Launch: Warm Up (addresses prerequisite skills); Launch the Lesson (includes class discussions and short videos; Today’s Standards; and What Vocabulary Will You Learn?.
• Explore and Develop: Explore (provides Inquiry questions for the students to explore); Learn (guided instruction); Examples (scaffolded problems for students to work through); Apply (guided application problems); and Check (one problem follows each example to assess student understanding).
• Reflect and Practice: Exit Ticket; Practice Problems; Spiral Review Lesson; and Assessments (when applicable).
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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.

The instructional materials for Reveal Math Grade 6 meet the expectations for prompting students to show their mathematical thinking in a variety of  ways. Examples include:

• In Lesson 1-7, students record responses using their notebooks, paper, or other note-taking device.
• In Lesson 4-4, students verbally defend or critique the work of others in written form to show understanding when ordering rational numbers in various forms.
• In Module 6, students build models for a problem using bar diagrams and equations.
• In Lesson 7-3, students use a diagram and a coordinate plane to represent a linear equation.
• In Lesson 5-3, students use manipulatives (algebra tiles), in student pairs, to write algebraic expressions.
• In Lesson 9-3, students construct written responses to explain their thinking when finding surface area of triangular prisms.
• In Module 7, Performance Task, students evaluate data in a table and graph, generate equations, complete tables, and explain their reasoning related to the situation.
• In all lessons, students use a digital platform to conduct and present their work.
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Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials for Reveal Math Grade 6 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of virtual manipulatives, although the materials rarely include physical manipulatives.

• Manipulatives and other mathematical representations are consistently aligned to the mathematical content in the standards.
• Virtual manipulatives, such as number lines, double number lines, bar diagrams, pie charts, algebra tiles, x-y tables, coordinate planes, and flashcards, are used for developing conceptual understanding.
• There are embedded links to programs such as Web Sketchpad and eTools.
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The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The instructional materials for Reveal Math Grade 6 are not distracting or chaotic and support students in engaging thoughtfully with the subject.

The page layout in the materials is consistent, user-friendly, clearly labeled, and not overcrowded or hard to read. The graphics within both the Student book and Online Interactive material are colorful, engaging, and represent items that are relevant. Each section of the Lesson is found in separate documents, making it easy to navigate, though only a limited amount of information can be viewed on each page. Student practice problem pages are available in digital, download, and print form and include enough space for students to write their answers and provide explanations.

Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

The instructional materials reviewed for Reveal Math Grade 6 partially 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. It does not include explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

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

The instructional materials for Reveal Math Grade 6 meet the expectations for providing teachers with quality questions for students. These questions support teachers in planning and providing effective learning experiences.

• Questions are consistently provided throughout each lesson to help guide students’ mathematical development. The questions develop vocabulary of the  lesson, encourage mathematical discourse, develop conceptual understanding, promote justifications of thinking, and include differentiated questions to ask while students engage in the Interactive Presentation. Examples include: “If the triangles are similar, what do you know about the lengths of the sides?”and “What does it mean if your answer is not a whole number?”
• The Teacher Edition provides question prompts that are additional to what is in the student materials.
• Explore sections include Inquiry Questions such as, “Why is writing an equation a useful way to represent and solve a real world problem?”
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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.

The instructional materials for Reveal Math Grade 6 meet the expectations for containing annotations and suggestions on presenting the content and using embedded technology for student learning.

The Teacher’s Edition contains annotations and suggestions in the margin notes at every phase of instruction, including students’ independent practice. In addition, teachers are provided with ample planning information at the Module and Lesson levels.

Annotations and suggestions at the Module level include:

• Module Goal
• Focus (standards addressed)
• Be Sure to Cover (prerequisites required)
• Coherence (vertical alignment)
• Rigor (how rigor is specifically addressed in the module)
• Suggested Pacing
• Analyze the Probe (what the probe measures, targeted misconceptions, when to assign the probe, actions that should be taken after the probe)
• Essential Questions (suggestions for students’ graphic organizers)
• What Will You Learn? (students self ratings before and after)
• Dinah Zike Foldables (instructions for foldables)
• Launch the Module (notes on what the Launch video addresses)
• Pause and Reflect
• What Vocabulary Will You Learn?
• Are You Ready? (prerequisite information)
• Mindset Matters (notes on risk taking, regular reflection, “Not Yet” Doesn’t Mean “Never”, etc.)

Annotations and suggestions at the Lesson level include:

• Content standards and Mathematical Practices
• Essential Question
• Lesson Activities
• Differentiate (including Resources and Language Development Support)
• Vertical Alignment (containing Previous, Now, and Next learning)
• Rigor
• Mathematical Background
• What if my students don’t have devices?

Cues to reference online resources include:

• Additional teaching notes
• Videos on how to teach the Mathematical Practices
• Assistance with the Talk About It! questions to promote discourse
• Performance reports of the checks
• Extra examples
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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.

The instructional materials for Reveal Math Grade 6 partially meet the expectations for containing adult-level explanations so teachers can improve their own knowledge of the subject.

There are a limited number of “The Why Behind the Math” videos for teachers “that dive into math concepts. Dr. Nevels explores the "what" and “why” behind the math, addresses misconceptions, and gives strategies you can use to help students understand math more deeply.” These provide insight for teachers and could also be used with students. Videos may be added as there are “coming soon” flags.

In each lesson, Mathematical Background addresses the mathematical content of the lesson, but the descriptions are primarily procedures and definitions rather than designed to improve teacher knowledge, for example:

• In Lesson 3-5, “To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. To perform division with mixed numbers, first write them as fractions. A mixed number can be written as a fraction by writing the whole number portion as a fraction and then finding the sum of the two fractions.”
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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.

The instructional materials for Reveal Math Grade 6 do not meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

• Vertical alignment is provided, but does not explain the role of the grade-level mathematics in the context of the overall mathematics curriculum for grades K-12. Previous, Now, and Next include connections within the grade level or to the grade levels immediately before and after the current grade.
• The publisher intends to address this with a resource that is “Coming Soon in 2019”: Content Progressions Resources - "This library contains resources that show the progression of math concepts for elementary through high school math.” Cathy Seeley will discuss what to expect in each course and point out critical areas students will learn. She will “give insight into the progression of math concepts from previous grades to the current grade and beyond.”
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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).

The instructional materials for Reveal Math Grade 6 provide a list of lessons, cross referencing standards, and a pacing guide. Recommended Pacing is provided and includes instructional times for each lesson and module. Major work standards are identified, and a correlations document, found in the front matter of the Teacher’s Edition and in the online resources, shows which standards are addressed in each lesson. Within each online module, there is a tab for pacing and standards addressed.

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

The instructional materials for Reveal Math Grade 6 include strategies for parents to support their student’s progress. In each Module, the Launch includes a family letter written in English. Family letters can be added to the student pages, included in the Launch presentation, emailed, or sent home with students. The letter explains what students have previously learned, what they will learn in the current module, vocabulary that will be used, and how parents can provide support including suggested activities for home that might be helpful to support students in the content of the module. There is also an invitation to contact the teacher if more information is needed. The parent letter can be read aloud in the docReader.

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

The instructional materials for Reveal Math Grade 6 contain explanations of the instructional approaches of the program and identification of the research-based strategies.

In the Teacher Edition, the Guiding Principles of Reveal are based on current mathematics education research: Rigor, Productive struggle, Formative assessment, Rich tasks, Mathematical discourse, and Collaborative learning.

The expert advisors are listed with a short note from each about instruction that aligns with current research. These include sense-making in mathematics, students discussing their thinking and the thinking of others, supporting students with technology as they construct mathematical understanding, sparking student curiosity, promoting productive struggle, creating enjoyable mathematical experiences for students, and using formative assessment to elicit student misconceptions and addressing them through instruction.

In the online resources, teachers are provided with a short video by Cathy Seeley that discusses the teacher’s role using the Reveal program and how the program aligns with current research in mathematics education.

Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

The instructional materials reviewed for Reveal Math Grade 6 partially meet the 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 and strategies for teachers to identify and address common student errors and misconceptions. The assessments do not clearly denote which standards are being emphasized.

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

The instructional materials for Reveal Math Grade 6 meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels. There are multiple opportunities to gather information about prior knowledge and prepare for the content addressed in the Module.

In the beginning of the school year, Diagnostic and Placement Tests can be assigned to determine whether a student has mastered prerequisite concepts for the current course.

At the beginning of each Module, Be Sure to Cover lists prerequisite skills required for the module. The Module Pretest can be used to diagnose student readiness for the module, and Are You Ready? has a few exercises over necessary prerequisite concepts. The Teacher Edition contains an extensive list of prerequisite concepts.

At the beginning of each Lesson, Warm-Up exercises address prerequisite skills for the lesson.

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

The instructional materials for Reveal Math Grade 6 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• Formative Assessment Math Probes by Cheryl Tobey provide an analysis of targeted misconceptions. “This formative assessment asset helps the teacher to target common misconceptions students may have about the mathematics covered in this module. The Teacher’s Guide provides a key as well as a description of common misconceptions, and how they might be addressed.” There is one per Module which can be completed more than once to ensure that misconceptions have been addressed.
• Each lesson notes anticipated misconceptions, and teachers are provided ideas to help students address them.
• Within Independent Practice, there are Common Misconception pointers related to specific problems such as, “Students may mistakenly order integers based on absolute value rather than numerical value or vice versa.” and “Some students may not identify like terms correctly when one of the coefficients is 1 or -1 since the number 1 is not written explicitly.”
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Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials for Reveal Math Grade 6 meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

• After each example in a lesson, there is a Check to assess understanding of that component of the lesson. These are done online so teachers can access performance reports. If students do not “pass”, teachers can assign relevant practice.
• Exit Tickets are provided in every lesson.
• Put It All Together, mid-module, formative assessments provide opportunities to assess student understanding of multiple lessons.
• Classroom discourse has students discuss their thinking and provides another formative assessment opportunity for teachers to identify what students have learned and respond with appropriate prompts and clarifications.
• Test Practice pages are provided at the end of each module to help students review module content and prepare for online assessments. Many of the exercises mirror the questions students will see on the online assessments.
• Each lesson contains additional digital practice allowing students to complete several problems, getting immediate feedback about what is correct.
• Some lessons include a digital Spiral Review containing content from multiple lessons. The resource notes specify the exact concepts on the Spiral Review.
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Materials offer ongoing formative and summative assessments:
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Assessments clearly denote which standards are being emphasized.

The instructional materials for Reveal Math Grade 6 do not meet the expectations for assessments clearly denoting which standards are being emphasized.

• Summative assessments are available online; however, standards are not linked to the online assessments or specific items. Standards for the overall Module are identified; assessments align to the Module lessons.
• Performance Tasks Rubrics provide a list of standards correlations for the assessment as a whole but not for individual questions. Performance Tasks are optional (not built into the suggested pacing guide), so they may not be utilized.
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Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The instructional materials for Reveal Math Grade 6 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.

• In the Checks, completed after each Example in the lessons, teachers can reference the performance results and are guided to assign differentiated practice as needed for remediation.
• A chart is provided for teachers on the End of Module Review pages. Related standards and lessons for each question are referenced and can be used to determine areas of strength/weakness.
• Summative assessments are available and scored online. No answer keys or suggestions for follow-up are available.
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Materials encourage students to monitor their own progress.

The instructional materials for Reveal Math Grade 6 provide opportunities for students to monitor their progress.

• At the beginning of each Module, students are provided with a Before and After chart that lists each topic of the lesson. Students place a check in three separate columns: don’t know, have heard of it, or know it!. At the end of the Module, students revisit this chart in Rate Yourself to determine how their understanding has grown.
• At the end of each Module, students provide a written response to prompts such as explaining one thing they have learned and one question they still have about the module content.
• Reflect on the Module has students answer the Essential Question of the Module, often by completing a graphic organizer.
• Within each lesson, Pause and Reflect provides prompts for students to consider their learning such as, “Did you ask questions about today’s lesson? Why or why not?” “Where in the lesson did you feel the most confident? Why?” “Are you ready to move on to the Example? If yes, what have you learned that you think will help you? If no, what questions do you still have? How can you get those questions answered?”

Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

The instructional materials reviewed for Reveal Math Grade 6 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 include extension activities for advanced students, but do not present advanced students with opportunities for problem solving and investigation of mathematics at a deeper level. 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.

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Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials for Reveal Math Grade 6 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• Each module introductory page includes Be Sure to Cover which identifies prerequisite skills students need for the module content.
• Each module and lesson includes tabs for pacing and vertical alignment. Vertical Alignment makes connections to both prior and future knowledge and skills to assist with sequencing instruction.
• The Warm Up at the beginning of each lesson “helps the teacher determine whether students are proficient in the prerequisite skills needed for this lesson.”
• Each Module includes a Pretest that can be used to “diagnose students' understanding of the prerequisite skills required for this module.”
• Teachers Notes are embedded alongside the lessons and student tasks that provide prompts that scaffold instruction.
• Discussion questions are embedded in the Examples and Apply tasks.
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Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials for Reveal Math Grade 6 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• The opening page to each lesson contains Differentiate that lists learning resources available for use. These are identified and color-coded in the Teacher Edition as Approaching Level (AL), On Level (OL), and Beyond Level (BL). They include collaboration strategies, Remediation and Extension Tasks, and Arrive Math which is an intervention program integrated into Reveal Math.
• Questions for Mathematical Discourse in the Teacher Edition margin are also identified and color-coded as AL, OL, or BL.
• After each problem during the instruction portion of the lesson, there is a computer-based Check to gauge student understanding. The Teacher’s Guide provides direction on using the data to assign practice problems and other exercises.
• Each lesson has Additional Examples that help students reinforce their understanding of the concept. It includes an extra problem for the teacher to use, as well as questions to help elicit meaningful responses.
• Supporting All Learners, an online resource, includes a Language Development Handbook which provides graphic organizers, note taking using sentence frames, and vocabulary worksheets.
• Digital Differentiate activities include auto-scored Lesson Practice problems, Collaboration Strategy activities related to the math concepts/vocabulary, prerequisite skill Review activities, and a Personal Tutor.
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Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials for Reveal Math Grade 6 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

• Talk About It! and Write About It! prompts often encourage students to describe their approaches to problems and to think about other possible approaches.
• Each lesson presents an Inquiry question for students to explore, often with a digital resource such as Web Sketchpad.
• Apply tasks include a variety of entry-points and a variety of solution strategies.
• Common prompts for Apply problems involve different approaches to the tasks or strategies that students could use.
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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).

The instructional materials for Reveal Math Grade 6 meet the expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations.

In the Teacher’s Edition, ELL icons introduce various supports specifically related to students’ native languages such as a Spanish Interactive Student Edition, Digital Spanish Personal Tutors, or a Multilingual eGlossary. Additional supports for ELLs and other special populations include:

• Math-Language Building Activities
• Language Scaffolds
• Think About It! and Talk About It! prompts that assist in deepening understanding
• Audio options
• Graphic organizers
• Web Sketchpad, Desmos, eTools
• A Language Development handbook found online in Program Resources.
• Language Objectives for almost every lesson
• What Vocabulary Will You Learn? at the beginning of each lesson. The Teacher Edition provides a prompt for ELL students: “As you proceed through the chapter, introduce each vocabulary term using the following routine. Ask the students to say each term aloud after you say it. Define...Example…Ask...”
• Each module has a Foldable Study Organizer containing key concepts/vocabulary which students create.

The Arrive Math Booster is a Tier 2 intervention program which provides digital mini-lessons for students who need a different presentation of the content addressed in the lesson.

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Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials for Reveal Math Grade 6 partially meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. There are multiple attempts to address the needs of advanced learners, but they do not always provide students with opportunities to explore or experience enrichment in their learning.

Extensions are included but often do not present students with opportunities for problem solving and investigation of mathematics at a deeper level. Tasks are guided or modeled rather than students investigating on their own.

For example, Extension about the Golden Ratio in an interactive slideshow, Lesson 1-1:

• Slide 1 explains the Golden Ratio: “The Golden Ratio is a ratio approximately equal to 1.618. The Golden Ratio appears in geometry, art, and architecture. Many artists and architects used the Golden Ratio to achieve balance and beauty in paintings, sculptures, and buildings. To visualize the Golden Ratio, divide a line segment into two parts as shown. The longer part, a, divided by the smaller part, b, should be equal to the length of the whole segment, a + b, divided by the longer part, a. When this happens, the ratio of a to b is approximately equal to 1.618, the Golden Ratio.” A model is shown.
• On Slide 2, a line segment is drawn and students are to determine if it represents the Golden Ratio. Students are given steps to work through the problem.
• On Slide 3, students are given a third line segment and asked to independently determine if the line segment represents the Golden Ratio.

Other activities provide more opportunities for students to investigate and discover such as:

• Differentiate Activity: “To extend students understanding of graphing and comparing ratio relationships, have them research the Internet, newspapers, or magazines, for real-world uses, such as comparing the ratio of gallons of gas to miles driven for various types of vehicles. You may wish to have students present their findings to the class.”

Differentiated teacher prompts also address levels of learners, including Beyond Level (BL), which attempts to investigate concepts at a greater depth such as:

• Beyond Learning: “If the depth of the moat was half of the height of the sand castle, what negative number would represent the depth of the moat?”
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Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials for Reveal Math Grade 6 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

• Multinational names are used in the examples and practice. Cartoon characters presented in the textbook represent students of both genders and various ethnicities.
• The diversity of names throughout the problems 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 not expressing 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.
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Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials for Reveal Math Grade 6 provide opportunities for teachers to use a variety of grouping strategies. Throughout the lessons, the materials use an identifiable symbol for whole groups, small groups, and individual instruction. These icons are posted at the top of the teacher’s edition pages and within the materials. Pairs/Small Groups is a common structure to allow students to process and explain verbally.

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Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials for Reveal Math Grade 6 encourage teachers to draw upon home language and culture to facilitate learning.

• The student glossary is printed in both English and Spanish.
• Personal tutor videos are in both English and Spanish.
• Interactive Student Edition eBook, Spanish Sampler - currently available for only one Module at each grade.
• Each Module includes a Family Letter in English that describes the program and resources that are available to students.

Criterion 3.5: Technology

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

The instructional materials reviewed for Reveal Math Grade 6: integrate technology in ways that engage students in the mathematics; 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.

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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.

The instructional materials for Reveal Math Grade 6 are web-based and compatible with multiple internet browsers. The teacher resources and student books are platform neutral and can be accessed on mobile devices.

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Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

The instructional materials for Reveal Math Grade 6 include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

• Check and Apply problems within the lessons are designed to be completed and scored online.
• Each lesson has an optional Practice set of content questions designed to be completed and scored online, with instant feedback for responses as correct or incorrect.
• Some lessons have a Spiral Review designed to be completed and scored online, with instant feedback for responses as correct or incorrect.
• Each module has one or two Put It All Together reviews over multiple lessons which can be completed and scored online, with instant feedback for responses as correct or incorrect.
• Each module has a Formative Assessment Probe that can be completed via technology, but not auto-scored.
• All module and benchmark assessments are designed to be completed and scored online, with instant feedback for responses as correct or incorrect.
• Assessments can be created using various item banks organized by module, practice, or test questions. Questions contain tech-enhanced capabilities and can be edited and saved in the My Questions folder.
• The Reveal Math Reporting Dashboard provides data on completed assignments and assessments. An Item Analysis Report and a Standards report are available for a specific class or individual students.
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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.

The instructional materials for Reveal Math Grade 6 include opportunities for teachers to personalize learning for all students.

• Teachers have the option to assign approaching level, on-level, or beyond level practice problems and assessments.
• Teachers can select and assign individual practice items for student remediation based on the Check formative assessment data.
• Teachers can create and assign classes online.
• Arrive Math Booster Mini-lessons and LearnSmart are often referenced in the materials as options to provide more support; however, currently, there is nothing available to review.

The instructional materials for Reveal Math Grade 6 are not easily customized for local use.

• The materials provide differentiated intervention, but Modules and Lesson components are sequenced in a particular order for students to develop understanding and complete the independent practice.
• There is some flexibility in presentation because teachers can “pick and choose” how many examples to use based on the needs of their students or allow independence in working through the interactive slideshows rather than providing guidance.
• Teachers can create and upload files, attach links, and attach docs which can be assigned to students.
• Teachers can create assessments using a bank of items or using self-written questions and assign to students.
• There are additional Examples and Apply problems that could be assigned as needed.
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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.).

The instructional materials for Reveal Math Grade 6 do not provide opportunities for teachers to collaborate with other teachers or students to collaborate with other students via technology.

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

The instructional materials for Reveal Math Grade 6 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software.

• Each module begins with Launch, a video about the topics in the Module and how they are applied in real world.
• Personal Tutor videos are in Review and Assess for students to watch independently if they need examples explained.
• There are interactive tools and virtual manipulatives such as Web Sketchpad, eTools, Desmos, Virtual Manipulatives, flashcards, etc. Students are routinely directed to the tools, but they are not able to access these tools on their own.
• Interactive slideshows and assessments allow students to use features such as drag and drop, multi-select, swipe, type, and expand features.
• Interactive slideshows encourage students to watch videos and animations within the presentations, reviewing prerequisite concepts and seeing mathematical processes for current skills. Note-taking and problem-solving are included in presentations.

Report Overview

Summary of Alignment & Usability for Reveal Math | Math

Math 6-8

The instructional materials reviewed for Reveal Math Grades 6-8 meet expectations for alignment to the Common Core State Standards for Mathematics and meet expectations for usability. The instructional materials meet expectations for Gateway 1, focus and coherence, Gateway 2, rigor and balance and practice-content connections, and Gateway 3, instructional supports and usability indicators.

6th Grade
Alignment
Meets Expectations
Usability
Meets Expectations
7th Grade
Alignment
Meets Expectations
Usability
Meets Expectations
8th Grade
Alignment
Meets Expectations
Usability
Meets Expectations

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Overall Summary

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Usability
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