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

Title ISBN Edition Publisher Year
RCM06 National SW Volume 1 978-1-7280-1298-8 Curriculum Associates 2021
RCM06 National SW Volume 2 978-1-7280-1299-5 Curriculum Associates 2021
RCM06 CC TG Volume 1 978-1-7280-1304-6 Curriculum Associates 2021
RCM06 CC TG Volume 2 978-1-7280-1305-3 Curriculum Associates 2021
RCM08 National SW Volume 1 978-1-7280-1302-2 Curriculum Associates 2021
RCM08 National SW Volume 2 978-1-7280-1303-9 Curriculum Associates 2021
RCM08 CC TG Volume 1 978-1-7280-1308-4 Curriculum Associates 2021
RCM08 CC TG Volume 2 978-1-7280-1309-1 Curriculum Associates 2021
RCM07 National SW Volume 1 978-1-7280-1300-8 Curriculum Associates 2021
RCM07 National SW Volume 2 978-1-7280-1301-5 Curriculum Associates 2021
RCM07 CC TG Volume 1 978-1-7280-1306-0 Curriculum Associates 2021
RCM07 CC TG Volume 2 978-1-7280-1307-7 Curriculum Associates 2021
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### Overall Summary

The materials reviewed for i-Ready Classroom Mathematics Grade 7 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.

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

### Focus & Coherence

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

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

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

Within the i-Ready Classroom Mathematics materials, the Unit Assessments are found in the Teacher Toolbox and include two forms for Unit Assessment, Form A and Form B. Both Forms contain similar problems for each unit. The Unit Assessments can be found at the end of each unit in the materials.

Examples of assessment items in i-Ready Classroom Mathematics include:

• Unit 2, Unit Assessment, Form A, Problem 8, assesses 7.NS.1c as students use their understanding of subtraction of rational numbers as adding the additive inverse. “Why does -2.4 - (-7) have the same result as -2.4 + 7? Explain your reasoning.”

• Unit 3, Unit Assessment, Form B, Problem 3, assesses 7.NS.3 as students solve real-world problems involving the four operations with rational numbers. “A baker adds baking powder onto a food scale by teaspoons. The scale has marks every $$\frac{1}{10}$$g. Each teaspoon of baking powder weighs 3.81g. Between which two marks on the scale will the weight be after the seventh teaspoon is added to the scale? Show your work.”

• Unit 4, Unit Assessment, Form A, Problem 8, assesses 7.EE.4 as students use variables to represent quantities in a real-world problem. “Jameson Middle School gives bottles of water to teachers and students who are going on a field trip. The school orders 500 bottles of water. They plan to give 35 bottles of water to teachers. They ordered at least 2 bottles of water for each student. How many students could be going on the field trip? Show your work.”

• Unit 5, Unit Assessment, Form B, Problem 4, assesses 7.RP.3 as students solve problems using box plots. “The box plots show the amount of rainfall, in inches, in two different towns during storms. Express the difference in the median amount of rainfall as a multiple of the IQR for each data set. Show your work.”

• Unit 6, Unit Assessment, Form A, Problem 14, assesses 7.G.6 as students solve problems involving volume of rectangular prisms. “Dawn has a plastic container filled with slime. The container is a rectangular prism with a base that measures 4 in. by 6 in. and a height of 3 in. She wants to put the slime in a new container that is a rectangular prism with a base that measures 10 in. by 3 in. and a height of 5 in. What is the height of the empty space in the new container after the slime is added? Show your work.”

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. In the materials, there are ample opportunities for students to work with grade level problems. This includes:

• Lessons contain multiple opportunities for students to work with grade-level problems in the “Try It”, “Discuss It”, “Connect It”, “Apply It”, and “Practice” sections of the lessons.

• Differentiation of grade-level concepts for small groups are found in the “Reteach”, “Reinforce”, and “Extend” sections of each lesson.

• Fluency and Skills Practice problems are included in the Math Toolkit in addition to the lessons.

• Interactive tutorials for the majority of the lessons include a 17 minute interactive skill tutorial as an option for the teacher to assign to students.

Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

• Unit 1, Lesson 2, Session 3, Apply It, Problem 2, students compute unit rates involving ratios of fractions (7.RP.1). “Amare runs \frac{1}{10} mile in \frac{2}{3} minute. What is his speed in miles per minute? Show your work.”

• Unit 2, Lesson 8, Session 2, Apply It, Problem 7, students apply properties of operations as students add and subtract rational numbers (7.NS.1). “A dragonfish is swimming at -900m relative to sea level. It rises 250 m. What is the dragonfish’s new depth relative to sea level? Show your work.”

• Unit 3, Lesson 14, Interactive Tutorials provides extra problems in Equivalent Linear Expressions when students apply the distributive property to expand and factor linear expressions with rational coefficients. Students use the distributive property to write an equivalent expression (7.NS.3 and 7.EE.3). “$$3-(-4x+2)=3(-4x)+3(2)=-12x+6$$.”

• Unit 4, Lesson 16, Session 2, Practice, Problem 2, students analyze an expression in the context of situations and rewrite an expression in a different form to reflect a situation (7.EE.2). “Nathan is making blueberry and pineapple kebabs. Each kebab needs the same number of blueberries, b, and the same number of pineapple pieces, p.

• Nathan wants to check if he has enough of each type of fruit to make 12 kebabs. How can the expression 12b+12p help him do that?

• Nathan’s friend Linda offers to help him make some of the kebabs. Nathan wants to set aside enough fruit for her to make 3 of the kebabs. How can you rewrite 12b + 12p so that it shows the fruit for Nathan’s kebabs and the fruit for Linda’s kebabs separately?”

• Unit 5, Lesson 21, Session 2, Fluency and Skills Practice, students solve problems involving percent change (7.RP.3). “Find the percent change and tell whether it is a percent increase or a percent decrease. Problem 1, Original amount: 20  End amount: 15.”

• Unit 7, Lesson 30, Session 2, Connect It, Problem 4, students describe probability of an event occurring. (7.SP.5) “What word describes the probability of rolling an integer on a standard number cube? How can you describe the same probability with a number? Explain why you can describe the probability both ways.”

#### Criterion 1.2: Coherence

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for coherence. 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' | indicatorName}}

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. Materials were analyzed from three different perspectives; units, lessons, and days. Each analysis includes assessments and supporting work connected to major work of the grade.

• The approximate number of units devoted to major work of the grade is 4.5 out of 7 units, which is approximately 64%.

• The number of lessons, including end of unit assessments, devoted to major work of the grade is 31 out of 47 lessons, which is approximately 66%.

• The number of days, including end of unit assessments, devoted to major work of the grade is 98.5 out of 152, which is approximately 65%.

A day-level analysis is the most representative of the materials because the number of sessions within each topic and lesson can vary. When reviewing the number of instructional days for i-Ready Classroom Mathematics Grade 7, approximately 65% of the days focus on major work of the grade.

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

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

The instructional materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Throughout the materials, supporting standards/clusters are connected to the major standards/ clusters of the grade. The following are examples of the connections between supporting work and major work in the materials:

• Unit 1, Lesson 2, Session 3, Apply It, Problem 8, connects supporting work of 7.G.1 is connected to major work in 7.RP.1 as students compute unit rates associated with ratios of fractions to solve problems involving scale drawings. “Tyler looks at a map on his phone. He zooms in until the map scale for centimeters to kilometers is 0.3:15. How many centimeters does the map use to show 1 kilometer? a. $$\frac{2}{3}$$ b. $$\frac{3}{5}$$ c. 0.06 d. 1.5”

• Unit 4, Lesson 16, Session 3, Apply It, Problem 3 connects supporting work of 7.G.6 with the major work of 7.EE.2 when students rewrite expressions in order to find the area of the flag. "The spirit club is sewing school flags for the pep rally. The club members want to find the amount of striped fabric they need for one flag. Avery says they can use the expression $$5(4) + 7(4)$$. Pedro says they can use the expression $$(12⋅8)÷2$$. Explain why both students are correct.”

• Unit 5, Lesson 23, Session 2, Apply It, Problem 7 connects the supporting work of 7.SP.2 with the major work of 7.RP.3. Students must use proportional relationships to solve a multistep ratio problem to draw an inference about data. “A random sample of Grade 8 students at a school are asked whether they plan to take computer science in high school. Of those asked, 15 students plan to take computer science, 5 do not, and 7 are unsure. There are 326 Grade 8 students in the school. Based on the sample, about how many Grade 8 students in the school plan to take computer science in high school?”

• Unit 6, Lesson 28, Session 2, Apply It, Problem 7 connects supporting work of 7.G.5 to major work in 7.EE.4 as students construct equations to solve problems about angle measures, “∠A and ∠B are vertical angles. m∠A=(4x+6)$$\degree$$ and m∠B = (7x-66)$$\degree$$. What are m∠A and m∠B? Show your work.”

• Unit 7, Lesson 31, Session 1, Connect It, Problem 2c, connects supporting work of 7.SP.6 to major work of 7.EE.3 and 7.NS.2 as students determine the probability of an event and express it in fraction, decimal, and percent forms. “Each time Chantal selects a card from a bag, she performs one trial of an experiment. Chantal uses a box of marbles to conduct a different experiment. She selects a marble, records its color, and puts it back in the box. She does this several times. In all, she selects 5 red marbles, 3 blue marbles, and 2 yellow marbles. Chantel can use experimental probability to describe the likelihood of getting a particular result in an experiment. c. A probability can be expressed as a fraction, decimal, or percent. What is the experimental probability of selecting a red marble, expressed as a fraction? A decimal? A percent?”

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 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 of problems and activities that serve to connect two or more major clusters or domains in a grade are:

• Unit 2, Lesson 7, Session 2, Develop, Problem 1, connects major work of 7.NS.A to major work of 7.EE.B as students apply and extend understanding of adding and subtracting rational numbers and solve multi- step real work problems with positive and negative integers. “On the first play, Angel’s football team gains 5 yards from their starting position . On the second play, the team loses 7 yards. To find where the team is relative to its starting position, add 5 and -7. a. You can use integer chips to model $$5 + (-7)$$. Circle all the zero pairs. b. What is the value of the remaining chips? c. $$5 +(-7)$$. d. After the second play, where is Angel’s team relative to its starting position?

• Unit 3, Lesson 14, Session 2, Practice, Problem 4, connects the major work of 7.NS.A with the major work of 7.EE.B when students find the value of a given expression involving fractions. “Consider the expression $$-6\frac{3}{5}-(-7\frac{4}{15})+2\frac{1}{5}$$ . a. Estimate the value of the expression. b. Find the exact value of the expression. c. Use your estimate to explain if your answer to problem 4b is reasonable.”

• Unit 4, Lesson 18, Session 2, Apply It, Problem 8, connects major work of the grade of 7.EE.B to 7.NS.A as students solve algebraic equations involving rational numbers. “Solve $$-21=-\frac{1}{4}x+6$$. Show your work.”

• Unit 5, Lesson 20, Session 3, Connect It, Problem 4, connects the major work of 7.RP.A with the major work of 7.EE.A as students analyze an expression of a proportional relationship and identify equivalent expressions by using properties of operations. “Hiroaki uses the expression $$a+0.05a$$ to represent an amount increasing by 5%. Allen uses the expression $$1.05a$$ . Explain why both Hiroaki and Allen’s expressions are correct.”

Examples of problems and activities that serve to connect two or more supporting clusters or domains in a grade are:

• Unit 5, Lesson 24, Session 3, Apply It, Problem 8, connects the supporting work of 7.SP.A with the supporting work of 7.SP.B. Students draw a comparative inference from random samplings of two populations. “River county has 15,000 likely voters. A survey of 100 randomly selected voters in River County finds that 60 plan to vote to re-elect the current governor. Lake County has 12,000 likely voters. A survey of 125 randomly selected voters in Lake County finds that 90 plan to vote to re-elect the current governor. In which county can the current governor expect to get more votes?”

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

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.

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations that, 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. Each Unit contains the Teacher’s Guide which includes a Unit Flow and Progression video, a Lesson Progression, a Math Background, and a Lesson Overview that contains prior and future grade-level connections to the lessons in the unit. Examples include:

• Unit 2, Lesson 7, Overview, Learning Progression, prior grade learning is connected to understanding addition with negative integers. “In Grade 6, students learned that a negative number and its opposite are the same distance in opposite directions from 0 on a number line. They compared the values of negative numbers and placed them on horizontal and vertical number line diagrams. They also used positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.”

• Unit 3, Overview, Lesson Progression, Lesson 14, Use the Four Operations with Negative Numbers, builds on Grade 6, Lesson 7, Add, Subtract, and Multiply Multi-Digit Decimals, 6.NS.3. This lesson prepares students for Grade 8, Lesson 23, Find Square Roots and Cube Roots to Solve Problems, 8.EE.2.

• Unit 4, Beginning of Unit, Math Background, Future Learning, describes the future work connected to the unit. “Students will move on to deepen their understanding of expressions and equations as they work with multi-step equations, systems of equations, and functions. Students will write and solve linear equations with variables on both sides of the equal sign; explore one-variable equations with zero or infinitely many solutions; write and solve systems of two-variable linear equations; use functions to model linear relationships.” (8.F.4, F.IF.9)

• Unit 5, Lesson 20, Overview, Learning Progression, describes the connected work of later grades. “In later grades, students will use their knowledge of percentages to solve problems in math, science, social science, and real-world situations.” (S.MD.B)

• Unit 6, Math Background, Geometry, Prior Knowledge “Students should: be able to find the area of polygons by composing and decomposing them into triangles, be able to use a net to find the surface area of a right prism or pyramid, be able to find the volume of right rectangular prisms, be able to draw an angle with a given measure, and be able to write and solve equations in one variable” and “be able to convert measurement units by multiplying and dividing.” (6.G.A and 6.EE.B) Future Learning states, “Students will draw images of translations, reflections, rotations, and dilations, explore relationships involving angles of triangles and angles formed by parallel lines and transversals, find the volume of cylinders, cones, and sphere, apply what they learned about the conditions that determine a unique triangle to explore triangle congruence, construct triangles and other figures using a compass and a straightedge, and use plane sections to justify volume formulas.” (8.G.A, G.CO.A, G.CO.B, and G.MD.A)

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

In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.

The materials reviewed for i-Ready Classroom Mathematics Grade 7 foster coherence between grades because materials can be completed within a regular school year with little to no modification. In Grade 7, the 126 days of lessons, 13 days of assessments, 14 days of Math in Action lessons, and 5 days of supplementary activities are included in the total days represented in the materials for a total of 158 days.

• Materials include 7 Units divided into 33 Lessons which are divided into 126 sessions for a total of 126 days of instruction.

• Lesson 0 which includes an additional 5 days of work to create routines, develop structure, and set up the year of lessons.

• There are 7 additional days allotted for the end of unit assessments and 6 additional days for diagnostic assessments throughout the school year. This includes a total of 13 days for assessments.

• There are 7 Math in Action lessons divided into two sessions each for a total of 14 days.

According to i-Ready Classroom Mathematics Implementation, sessions are designed to be 45-60 minutes in length. Pacing information from the publisher regarding viability for one school year can be found in the Pacing Guide for the Year which is located in the Teacher Toolbox under the Program Implementation tab. The Pacing Guidance for the Year summarizes the amount of time for units, lessons, sessions, and assessments to be scheduled throughout the year.

### Rigor & the Mathematical Practices

The materials reviewed for i-Ready Classroom Mathematics Grade 7 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).

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor and Balance

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.

The materials reviewed for i-Ready Classroom Mathematics Grade 7 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' | indicatorName}}

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. The lessons include problems and questions that develop conceptual understanding throughout the grade-level. Examples include:

• Unit 2, Lesson 7, Session 1, “Model It”, Problem 1, students solve addition and subtraction problems with rational numbers, with teacher support (7.NS.A). “Neva plays a video game. On her first turn, she gets 3 points. On her second turn, she loses 3 points.The expression 3 + (-3) represents her score after the two turns. You can use integer chips to find the sum of 3 and -3. a. The sum of any number and its opposite is 0. Another term for opposites is additive inverses. Since the sum of 1 and -1 is 0, 1 and -1 form a zero pair. Circle the zero pairs in the model. b. How many points does Neva have after her second turn? c. What is 3 + (-3)?”

• In Unit 4, Lesson 17, Session 2, “Model It”: Equations, Problem 3, students develop conceptual understanding of writing equations, comparing models, and reasoning about equations (7.EE.4). “a. Complete the equation to model 3 times the sum of k and 8 is 36. b. You can think of k+8 as the unknown quantity. How could you find the value of k+8? What is the value of k+8? c. How could you use the value of k+8 to find the value of k? d. How can you check that the value of k is correct?”

• Unit 7, Lesson 30, Session 2, “Model It”, Problem 1, students develop the conceptual understanding of describing probabilities involving numbers (7.SP.5). Students first describe events in words. “A bag contains 6 red marbles, 6 green marbles, and 12 blue marbles. Paloma reaches into the bag and selects a marble without looking.” Students are asked to name impossible, unlikely, equally likely as not, likely and certain events based on this scenario. Problem 2 connects this same scenario to a number line and fractions. “Draw a line from each event to show the probability of that event.” Students then associate each event with its place and proximity to 0,$$\frac{1}{2}$$ and 1 on the number line.

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade through the use of visual models, real world connections, mathematical discussion prompts, concept extensions, and hands-on activities. Examples include:

• Unit 2, Lesson 9, Session 1, “Model It”, Problem 5, students extend previous understandings of addition and subtraction to develop conceptual understanding of adding and subtracting rational numbers (7.NS.1). After completing Problems 3 and 4 involving representations of expressions using number chips, students are asked to compare the two problems to explain how subtracting a negative number is the same as adding a positive number. “Compare the models in problem 3 and 4. How do they show that -5-(-2) is the same as -5+2?

• Unit 3, Lesson 11, Session 3, “Apply It”, Problem 5 is an opportunity for students to independently engage in writing while developing conceptual understanding of multiplication of positive and negative integers (7.NS.2). “Think about multiplying two integers. When will the product be less than 0? When will the product be greater than 0?”

• Unit 6, Lesson 29, Session 3, Practice, Problem 1, students reason about geometric shapes with given conditions  as they create different triangles using the angle measurements or side lengths (7.G.2). “Consider the triangles at the right. a. Are the triangles the same? Explain your reasoning. b. How could you form a different triangle with a 30$$\degree$$ angle, a 40$$\degree$$ angle, and a 5-unit side length?” The text includes an image with two congruent triangles in different orientations with a 30$$\degree$$ angle, a 40$$\degree$$ angle, and a 5-unit side length between the two angles.”

##### Indicator {{'2b' | indicatorName}}

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Within each lesson, there is a Session that provides additional practice for students to have in class or as homework. Additionally, many lessons include a Fluency & Skills Practice section. Examples include:

• Unit 1, Lesson 6, Session 2, Apply It, Problem 9, students examine the relationship between circumference and area of a circle (7.G.4). Students solve, “The diameter of a gong is 20 inches. Find the approximate circumference of the gong, using 3.14 for \pi . Then find the exact circumference of the gong. Show your work.”

• Unit 3, Lesson 12, Session 2, Apply It, Problem 7, students extend their understanding of multiplication and division of fractions to rational numbers as they solve, “A peregrine falcon dives for prey. Its elevation changes by an average of -11.5 meters every second. The dive lasts for 3.2 seconds. What is the change in the falcon’s elevation? What does this mean in the context of the problem? Show your work.” (7.NS.3)

• Unit 4, Lesson 18, Session 4, Apply It, Problem 9, students rewrite an expression in different forms to shed light on the problem and how the quantities in it are related. (7.EE.2) “Damita says the equations 0.8x=0.8=1.6 and \frac{4}{5}(x-1)=1\frac{3}{5} are the same. How can she show this, without solving the equations?”

Materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Within each lesson, students engage with practice problems independently at different sections of the lesson. Examples include:

• Unit 2, Fluency and Skills Practice, Problem 2 and 6, students subtract positive and negative fractions and decimals (7.NS.1).  Problem 2 “-8.2-4.2” and Problem 6, “$$7\frac{3}{4}-4\frac{1}{4}$$”

• Unit 4, Lesson 15, Sessions 4, Apply It, Problem 6, students explore equivalent expressions by expanding expressions (7.EE.1).  “Which expressions are equivalent to \frac{1}{5}x(5y+60)? Select all that apply. a. \frac{1}{5}(2xy+20x+3xy+40x)  b. xy+60x  c. y+12x  d. 25xy+300x  e. 13xy f. x(y+12).”

• Unit 5, Lesson 20, Session 1, Practice, Problem 3, students demonstrate procedural skill and fluency through solving multi-step percent problems. (7.RP.3) “Last year, a rapper performed 40 times. This year, the rapper performs 125% of that number of times. a. How many times does the rapper perform this year? b. Check your answers to problem 3a. Show your work.”

##### Indicator {{'2c' | indicatorName}}

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for being designed so teachers and students spend sufficient time working with engaging applications of the mathematics.

Engaging routine and non-routine applications include single and multi-step problems. Examples include:

• Unit 2, Lesson 10, Session 3, Try It, routine problem, students add and subtract negative and positive numbers (7.NS.1) to solve real-world problems. “Mel releases a lantern for the Lantern Festival. She stands in a field that is 0.5m below sea level. The lantern rises 913.9m. Then the candle in the lantern goes out. The lantern comes down 925.2m to land on the surface of a lake. What is the elevation of the lake relative to sea level?”

• Unit 5, Lesson 20, Session 2, Try It, routine problem, students use proportional relationships to solve multistep ratio and percent problems (7.RP.3). “Dario borrows $12,000 to buy a car. He borrows the money at a yearly, or annual, simple interest rate of 4.2%. How much more interest will Dario owe if he borrows the money for 5 years instead of 1 year?” • Unit 7, Lesson 31, Session 3, Try It, non-routine problem, students approximate the probability of a chance event by using data from a previous trial, and predict the approximate relative frequency given the probability (7.SP.6). “Luis sets his music app to play a certain playlist on shuffle. His app tracks the genre of each song played. Luis plays the same playlist on shuffle again and this time plays 130 songs. Based on the previous results, predict the number of country songs that will play.” There is a picture included that shows the results of the previous trial (Hip-Hop 5, Pop 9, Rock 12, and Country 14). Materials provide opportunities for students to independently demonstrate routine and non-routine applications of the mathematics throughout the grade level. Examples include: • Unit 1, Lesson 5, Session 3, Refine, Problem 3, routine problem, students identify the constant of proportionality and reason about the quantities in the problem to write an equation and solve a real- world problem (7.RP.2 and 7.RP.3). “Deyvi goes to a carnival with$20.00. He spends $2.00 to get in and the rest on ride tickets. Each ticket is$1.50. How many tickets does Deyvi buy? a. 9 tickets, b. 12 tickets, c. 13 tickets, d. 14 tickets.”

• Unit 3, Math in Action, Session 2, non-routine problem, students solve a multi-step real-life problem posed with rational numbers in any form including whole numbers, fractions, and decimals (7.EE.3). “Captain Alita’s next flight will travel from Los Angeles to Chicago. Her plane will carry cargo in addition to passengers and their baggage. Look at the information about Captain Alita’s flight and the cargo that needs to be shipped from Los Angeles to Chicago. Decide which cargo should go on Flight 910. Take all volume and weight restrictions into account, and try to carry as much cargo as possible.” The book includes the following information for students to use: Maximum payload (weight of passengers + bags + cargo): 44,700 lb, Weight of passengers + carry-on bags: 28,196 lb, Weight of checked baggage: 3,7,57 lb, Total volume of cargo holds: 1,041 $$ft^3$$ and volume of checked baggage: 747 $$ft^3$$. “The airline restrictions are that flights should carry no more than 80% of their maximum payload and checked baggage travels in the cargo holds, but carry-on bags do not.”  There is also a chart included with the type of cargo, number of containers, volume of each container ($$ft^3$$), and weight of each container (lb) for each type of cargo. The values include fractions and decimals.

• Unit 5, Lesson 21, Session 3, Apply It, Problem 6, non-routine problem, students apply information in different contexts to find percent error (7.RP.3). “The proper air pressure for Caitlin’s bicycle tire is 30 pounds per square inch (psi). The percent error in Caitlin’s current tire pressure is 15%. What are the possible current tire pressures for Caitlin’s tires? Show your work.” Problem 7, students find the percent error, “Jaime estimates it will take 8.5 hours to read a book. It actually takes Jaime 10 hours to read the book. What is the percent error in Jaime’s estimate? Show your work.”

##### Indicator {{'2d' | indicatorName}}

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.

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations in that 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. The Understand lessons focus on developing conceptual understanding. The Strategy lessons focus on helping students practice and apply a variety of solution strategies to make richer connections and deepen understanding. The units conclude with a Math in Action lesson, providing students with routine and non-routine application opportunities.

All three aspects of rigor are present independently throughout each grade level. Examples include:

• Unit 2, Lesson 8, Session 2, Problem 5, Fluency Skills & Practice contains multiple problems for students to add integers (7.NS.1). “Find each sum -13 + 7.”

• Unit 2, Lesson 9, Session 1, Model It, Problem 5, students develop conceptual understanding of adding and subtracting rational numbers (7.NS.1). After completing Problems 3 and 4 involving representations of expressions using number chips, students compare the two problems to explain how subtracting a negative number is the same as adding a positive number. “Compare the models in problem 3 and 4. How do they show that -5-(-2) is the same as -5+2?”

• Unit 4, Lesson 19, Session 2, Apply It, Problem 7, students engage in application as they construct simple equations and inequalities to solve problems by reasoning about the quantities, (7.EE.4). “The sum of 43.5 and a number, n, is no greater than 50. What are all possible values of n? Show your work.” In the teacher notes, it suggests to encourage students to use a table, number line or other visual model to support their thinking and in particular for teachers, “Students should recognize that the phrase no greater than is represented by a less than or equal to symbol. A sum that is not greater than 50 could either equal 50 or be any value less than 50.”

Multiple aspects of rigor are engaged simultaneously to develop students' mathematical understanding of a single unit of study throughout the grade level. Examples include:

• Unit 3, Lesson 13, Lesson Quiz, Problem 5, students attend to procedural skill and fluency and application as they apply properties of operations to calculate with numbers in any form and convert between forms as appropriate (7.EE.3). “A cooler contains 4L of water. The cooler has marks on it at every 02. L. Water bottles are filled with water from the cooler, and each bottle holds approximately \frac{4}{9}L. After 4 water bottles are filled, between which two marks is the water level in the cooler? Show your work.”

• Unit 4, Lesson 18, Session 4, Apply It, Problem 9, students attend to procedural skill and fluency and conceptual understanding as they compare algebraic solutions and identify the sequence of the operations used in each approach, (7.EE.4). “Damita says the equations 0.8x=0.8=1.6 and \frac{4}{5}(x-1)=1\frac{3}{5} are the same. How can she show this, without solving the equations?”

• Unit 6, Lesson 25, Session 2, Fluency and Skills Practice, Problem 7, students engage with conceptual understanding and application as they solve mathematical problems involving area using unknown side lengths of polygons (7.G.6). In Problem 6, students find the length of one side of a figure when given the area. In Problem 7, students use their understanding of area to apply skills in a new context, “Suppose for problem 6, the unknown side length was the side labeled 34 feet. Could you still solve for x? Explain.”

#### Criterion 2.2: Math Practices

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Indicator {{'2e' | indicatorName}}

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.

The materials reviewed for i-Ready Classroom Mathematics Grade 7 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.” The MPs are embedded within the instructional design. In the Teacher’s Guide, Front End of Book, Standard of Mathematical Practice in Every Lesson, teachers are guided “through a dedicated focus on mathematical discourse, the program blends content and practice standards seamlessly into instruction, ensuring that students continually engage in developing the habits of the mathematical practices.”

The Table of Contents and the Lesson Overview both include the Standards for Mathematical Practice for each lesson. In the Student Worktext, the Learning Target also highlights the MPs that are included in the lesson. MP1 and MP2 are identified in every lesson from 1-33.

There is intentional development of MP1: “Make sense of problems and persevere in solving them”, in the Try It problems, where students are able to select their own strategies to solve the problem. Teachers are provided with guidance to support students in making sense of the problem using language routines such as Co-Craft Questions and Three Reads. Examples include:

• Unit 2, Lesson 7, Session 3, Try It, students make sense of a problem in order to make a generalization about triangles. “Jorge wants to draw two triangles that have the same angle measures and are not similar. Carlos says that is not possible to do. Make or draw two triangles that have the same three angle measures but different side lengths. Are the triangles similar?”

• Unit 3, Lesson 13, Session 1, Try It, students rewrite one quantity so they can compare two quantities as fractions or as decimals. “Lupita and Kevin walk to school. Lupita walks $$\frac{3}{5}$$mi. Kevin walks 0.65 mi. Who walks a greater distance to school? How much greater?” There is a graphic provided with the picture of students walking to school.

• Unit 4, Math in Action, Session 2, students use multiple strategies to make sense of problems to solve multi-step word problems leading to inequalities of the form px + q > r or px + q < r. “Jorge and Liam went to rent a van for their band to use on a tour around Texas. Read through their notes, and help them finalize their plans.” Information included in the problem is “Rental Company Info table (Company, Daily Rate, Fee for Extra Miles, and Van Gas Mileage) for three companies. Other Info: The tour starts and ends in Houston. Each distance includes how far we will drive to reach each city and other stops we will make. Right now, gas in Texas ranges from $2.39 to$2.63 per gallon. Our budget for renting the van, including gas, is $1,100.” “What we need to do: Choose a rental company.” Determine how many miles we can drive without going over budget for a 5-day tour. Figure out if we can afford to deep Dallas as the last show on our tour or if we should end the tour a day early. If our last show is in Waco, we will drive about 215 miles back to Houston on Day 4.” A map is included showing the route of the 5-day tour with the distances between each city on the tour. In the Reflect section, students discuss how to make sense of the problem. “Make Sense of the Problem - What costs or fees contribute to the total amount the band will pay for the van during the tour?” There is intentional development of MP2: “Reason abstractly and quantitatively, in the Try-Discuss- Connect routines and in Understand lessons.” Students reason abstractly and quantitatively, justify how they know their answer is reasonable, and consider what changes would occur if the context or the given values in expressions and equations are altered. Additionally, some Strategy lessons further develop MP2 in Deepen Understanding. Teachers are provided with discussion prompts to analyze a model strategy or representation. Examples include: • Unit 1, Unit Review, Performance Task, students represent proportional relationships symbolically and make sense of relationships between problem scenarios and mathematical representations. “Janice wants to have the interior of her house and office painted. The total area she needs painted is 3,480 ft2. She wants to choose one company to paint 2,880 ft2 at her horse and a second company to paing 960 ft2 at her office. Janice finds pricing information from four different painting companies, shown below.” Information for each company is provided. One provides a table with area painted in square feet (0, 50, 100, 150, and 200) and cost for each, a second company charges$47.00 for every 20 ft3, a third company charges $2.80 per square foot, and a fourth provides three examples of an area in square feet and the corresponding cost in dollars. “Write an equation to represent each company’s cost per square foot. Then decide which two companies Janice should choose for the lowest total cost. Finally, calculate Janices’ total cost for having her house and office painted.” Students are provided guidance to help them make sense of the relationships between the equations and the numbers in the problem In the Reflect, Use Mathematical Practices section, “Use Reasoning, How is the information from each company related to the equations you wrote?” • Unit 2, Lesson 8, Session 2, Try It, students reason about previous understandings of addition and subtraction to add and subtract rational numbers to solve, “Normally, the freezing point for water is 32$$\degree$$F. A city treats its streets before a snowstorm. On the treated streets, the freezing point for water is changed by -38$$\degree$$F. What is the new freezing point for water on the treated streets?” • Unit 4, Lesson 17, Session 1, Model It, Problem 4, students explain what the numbers or symbols in a multi-step equation represent. “Think about the equation 4w - 8 = 32. a. The value of 4w is 40. How do you know that is true? b. The value of w is 10. How do you know this is true? ##### Indicator {{'2f' | indicatorName}} 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. The materials reviewed for i-Ready Classroom Mathematics Grade 7 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.” In the Discuss It routine, students are prompted with a question and a sentence frame to discuss their reasoning with a partner. Teachers are further provided with guidance to support partners and facilitate whole-class discussion. Additionally, fewer problems in the materials ask students to critique the reasoning of others, or explore and justify their thinking. There is intentional development of MP3 to meet its full intent in connection to grade-level content. Examples include: • Unit 2, Lesson 9, Session 3, Apply It, Problem 2, students critique the reasoning of a claim involving subtracting integers . “Patrick thinks that when a is a negative integer and b is a positive integer, each of the following statements is always true. Read the statements below and decide whether they are true or false. For statements that are true, give an example to support Patrick’s claim. For statements that are false, give a counterexample.a. a - b is positive. b. b - a is positive. c. a - (-b) is negative.” • Unit 3, Lesson 12, Session 2, Try It, Teacher’s edition, Differentiation Extend, provides guidance for teachers to engage students in MP3 as they critique an argument about multiplying integers . “Have students consider this claim: If you know how to find the product of two positive numbers, then you can find the product of related negative numbers by factoring out -1.” A series of questions for the teacher include “How can you rewrite the expression -0.32(2.5) so that it has a factor of -1? Why can you make your first step in simplifying -1(0.32)(2.5) multiplying the two positive factors? How does this show that the claim is reasonable? How can you show this claim is reasonable when multiplying two negative numbers?” • Unit 5, Lesson 22, Lesson Quiz, Problem 3, students construct an argument about the reasonableness of a conclusion made based on a random sample . “Alissa surveys a random sample of 50 students at her school about the country they would most like to visit. The table shows her results. Based on the sample, can Alissa conclude that there are probably fewer students at her school who want to visit Japan than Australia? Explain your reasoning.” A table with the data collected from the random sample is included. • Unit 6, Lesson 25, Session 1, Connect It, Facilitate Whole Class Discussion, provides guidance for teachers to help students reason about problem solving strategies. “Call on students to share selected strategies. As they listen to their classmates, have students evaluate the strategies and agree and build on them. Remind students that one way to agree and build on ideas is to give another example.” • Unit 7, Lesson 30, Session 2, Develop, Model It, students answer, “How do you know an event is equally likely as not?” Students justify their reasoning with other students. “A bag contains 6 red marbles, 6 green marbles, and 12 blue marbles. Paloma reaches into the bag and selects a marble without looking. a. What is the total number of marbles in the bag? b. What is half the number of marbles in the bag? c. Name an event that is possible. d. Name an event that is unlikely. e. Name an event that is equally likely as not. f. Name an event that is likely. g. Name an event that is certain.” Students are then asked: “How do you know an event is equally likely as not?” ##### Indicator {{'2g' | indicatorName}} 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. The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for supporting the intentional development of MP4: “Model with mathematics;” and MP5: “Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.” The materials generally identify MP4 and MP5 in most lessons and can be found in the routines developed throughout the materials. There is intentional development of MP4: “Model with Mathematics,” to meet it’s full intent in connection to grade-level content. Many problems present students with the opportunity to use models to solve problems throughout the materials. Examples include: • Unit 4, Lesson 19, Session 4, Model It, Teacher’s Edition, Differentiation Extend provides guidance for teachers to engage students in MP4 as they discuss using inequalities to model situations. The Model It is showing students how to model a situation using an inequality. “Prompt students to recognize how problem statements can be expressed as mathematical statements and provide information for interpreting the situation. Ask Why is the situation represented by an inequality. Listen For There is more money than the cost for the possible number of stoles that Cameron can buy. He can have money left over. Ask If Cameron did not buy the frame, what inequality could model the problem? List For The problem could be modeled by the inequality 24x<200. Ask Why is the solution to this problem only integers and not other rational numbers? Listen For Cameron can only buy whole numbers of stoles. Generalize Encourage students to describe how they might choose an appropriate model when solving a problem. If the solution is a single value, they might choose to model the problem with an equation. If the solution allows multiple values for the solution they might choose to model the problem with an inequality. If they represent the solution on a number line, they have to consider which values are acceptable for the situation.” • Unit 5, Lesson 23, Session 2, Deepen Understanding, gives teacher guidance for supporting students to consider how they can use double number lines to model data. “Prompt students to think about changing the model to answer different questions. Ask: How could you use the model to make an inference about a similar population with a different number of total students?...How could you change the model to find the number of students who take the bus?...How could you change the model to find the number of students who do not take the subway?” • Unit 6, Lesson 26, Session 2, Try It, students model using the volume of a right square prism to find the volume of a right triangular prism. “Troy uses colored sand to make sand art. The storage container for his sand is shaped like a right square prism. He pours some of the sand into a display container shaped like a right triangular prism. When he is done, the height of the sand left in the storage container is 4 in. What is the height of the sand in the display container?” A storage container with a remaining cube of sand is pictured, along with an empty display container with given length and width dimensions. • Unit 7, Unit Review, Performance Task, students design a probability model. The text presents an online game, Downtown, where students click a button to determine their next move in the game. The moves are: go forward 1 space, go backward 2 spaces, lose a turn, and take another turn. “Delara notes the actions she takes for 350 turns. Find the experimental probability for each action in Downtown using the table below.” A table with the data is included. “Delara wants to create her own version of the game. For her version, she wants to determine the action for each turn by using either a spinner with 12 equal parts or a deck of 40 cards. She wants the theoretical probability for each action in her version to be similar to the experimental probability for each action in the online version. Determine the number of spaces on the spinner and the number of cards for each action that Delara can use to make her version. Use your data to describe whether Delara’s version should use a spinner or a deck of cards to match the experimental probabilities of the online version as closely as possible. Explain your reasoning.” There is intentional development of MP5: “Use appropriate tools strategically to meet it’s full intent in connection to grade-level content.” Many problems include the Math Toolkit with suggested tools for students to use. Examples include: • Unit 1, Lesson 2, Session 2, Connect It, Problem 6 engages students in MP5 as they reflect on the models and strategies in the Try It to find and compare unit rates associated with ratios of fractions. “Think about all the models and strategies you have discussed today. Describe how one of them helped you understand how to solve the Try It problem.” The teacher’s edition includes guidance to teachers, “Have all students focus on the strategies used to solve the Try It. If time allows, have students discuss their ideas with a partner.” • Unit 2, Lesson 8, Session 1, Try It, students have a selection of tools to choose from to solve problems involving adding integers. “The temperature at a mountain weather station is -3℉ at sunrise. Then the temperature rises 5℉. What is the new temperature?” The math toolkit includes: grid paper, integer chips, number lines. • Unit 4, Lesson 18, Session 2, Try It, students select a tool to solve a problem resulting in a multi-step equation. “Noah is designing a set for a school theater production. He has 150 cardboard bricks. He needs to use some of the bricks to make a chimney and 4 times as many bricks to make an arch. He also saves 15 bricks in case some get crushed. How many cardboard bricks can he use to make the arch?” • Unit 5, Lesson 23, Session 3, Analyze It, Teacher’s Edition, Differentiation Extend provides guidance for teachers to engage students in MP5 as they discuss using data displays to make inferences from a sample. The Analyze It section shows students how to use dot plots and box plots to determine mean and median to make inferences about data. “Prompt students to think about what information can be understood about the data set by using different displays; such as a dot plot and a box plot. Ask How does each plot show outliers in the data set? Listen For In the dot plot, there will be numbers that have few or no dots between the main set of data and a number at either end that has dots. The box plot shows a longer whisker between the box and the endpoint when there is an outlier. Ask What aspects of the data set are easier to see in the dot plot? In the box plot? Listen For The number of data points, the symmetry of the data, and the data points that occur most often are easier to see in a dot plot. The median number in the data and the way the data are distributed are easier to see in a box plot. Generalize Encourage students to describe when they might choose each plot to model and solve a problem. Knowing how the data will be analyzed to solve the problem will help them determine which model would be easier to use to find that information.” ##### Indicator {{'2h' | indicatorName}} 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. The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for supporting 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. There is intentional development of MP6: Attend to Precision to meet it’s full intent in connection to grade-level content. Many problems present students with the opportunity to attend to precision within the mathematics and the reasoning of the answer. Examples include: • Unit 3, Session 2, Math in Action, students are asked to reflect as they work through the problem. “Why is it important to label each part of your final solution with units?” The students engage in MP 6 while realizing that being precise with units is important in solving the problem. • Unit 5, Lesson 23, Session 2, Additional Practice, Problem 1, the materials attend to the specialized language of mathematics as students complete problems about making inferences from samples about populations. “Jacob conducts another survey of students in the school in the Example. This time, he surveys a random sample of 30 students. a. In Jacob’s sample, 24 students say they will vote for Garrett. Based on this sample, about how many students in the school should Garrett expect to vote for him? Show your work.” A vocabulary box includes “random sample” with the definition. • Unit 6, Lesson 25, Session 1, Additional Practice, Problem 2 asks students to attend to precision when evaluating the reasonableness of an expression to find surface area. “Muna claims that the expression (8)(16)+(8)(12)+(16)(12) represents the surface area, in square inches, of the right rectangular prism shown. Is Muna correct? Explain.” i-Ready Classroom Mathematics attend to the specialized language of mathematics. The materials use precise and accurate mathematical terminology and definitions, and the materials support students in using them. The Collect and Display routine is described as, “A routine in which teachers collect students' informal language and match it up with more precise academic or mathematical language to increase sense-making and academic language development.” Teacher’s guides, student books, and supplemental materials explicitly attend to the specialized language of mathematics. Examples include: • Unit 1, Lesson 4, Session 2, Discuss It, provides guidance for teachers to support students in attending to precision by correcting a common misconception. “Listen for students who misinterpret the meaning of a specific point in the graph, such as interpreting the point (3,9) as 9 pounds of peppers that cost$3. As students share their strategies, ask them to name the point on the graph using both the value and the unit: 3 pounds of peppers at a cost of 9 dollars. Have students discuss the meaning of the value, the unit, and the point.”

• Unit 4, Lesson 18, Session 2, Develop Academic Language, teachers are provided with guidance to attend to the specialized language of mathematics by developing understanding of the phrase isolate the variable. “In the second Model It, students explore solving an equation by isolating the x-term. Ask students to use prior knowledge to give a rough definition for isolate. Provide the synonym for separate. Read the second Model It and have students turn and talk with a partner about the steps used to isolate the x-term.”

• Unit 5, Vocabulary Review, Problem 1, provides practice with specialized mathematical vocabulary. Students are provided with a word bank of math and academic vocabulary from the unit including commission, percent decrease, markup, and simple interest. “Use at least three math or academic vocabulary terms to describe a year-end sale at a store. Underline each term you use.”

##### Indicator {{'2i' | indicatorName}}

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.

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for supporting 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 grade-level content standards, as expected by the mathematical practice standards.” The MPs are embedded within the instructional design. In the Teacher’s Guide, Front End of Book, Standard of Mathematical Practice in Every Lesson, teachers are guided “through a dedicated focus on mathematical discourse, the program blends content and practice standards seamlessly into instruction, ensuring that students continually engage in developing the habits of the mathematical practices.”

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

• Unit 2, Lesson 9, Session 2, Close, provides teachers with guidance around MP7 to correct a common misconception around subtraction of negative numbers using structure. “If students think that a subtraction problem with negative numbers always results in a negative answer, then have them simplify -4-(-3) and -3-(-4) and compare the answers.

• Unit 3, Lesson 11, Session 1, Model It, Problems 4, 5, and 6 students use patterns to generalize rules for multiplying integers . Problem 4 asks students to complete three sets of equations. Sets a, b, and c multiply the numbers 3, 2, 1, 0, -1, -2, and -3 by 2, 3, and 4, respectively. Problem 5, a. -4(2) = __, b. 2(-4) = __, c. Does the order of the factors change the product when multiplying negative integers? Justify your answer.” Problem 6, “You have explored how to multiply two integers when one is positive and the other is negative. Is the product of a positive integer and a negative integer always positive or negative? Explain?”

• Unit 4, Lesson 18, Session 3, Connect It Problem 5 students explain the structure within algebraic equations to a strategy for solving . “Consider the equation 12=b(2.5x+15). What values of b might make you want to start solving the equation by distributing b? What values of b might make you want to start solving the equation by dividing by b?”

• Unit 6, Lesson 29, Session 2, Fluency and Skills Practice, Problem 13, students make use of structure in order to determine if, and how many, triangles could be constructed. “A triangle has side lengths of 7 cm and 18 cm. If the length of the third side is a whole number, how many possible triangles are there? Explain your answer.”

There is intentional development of MP8 to meet it’s full intent in connection to grade-level content.  Examples include:

• Unit 1, Lesson 6, Session 2, Try It students notice repeated calculations to make generalizations about the relationship between the circumference of a circle and its diameter . “Look at the circumference of each of the circles below. What do you think would be the circumference of a circle with diameter 1 cm?” There are four circles with the circumference and diameter labeled: D: 2 cm, C6.28 cm, D: 3 cm, C9.42 cm, D: 4 cm, C12.56 cm, D: 2.5 cm, C15.70 cm

• Unit 3, Lesson 13, Session 3, Deepen Understanding, provides teachers with guidance to support students in applying repeated reasoning to understand repeating decimals. “Prompt students to analyze remainders to understand why some rational numbers can be expressed as repeating decimals. Ask: When dividing by 7, what non-zero remainders can you get in any step? Why?...Can you stop dividing after you bring down a zero for any of these remainders? How does this tell you it will be a repeating decimal?...How do you know that when you express a mixed number or fraction with a denominator of 7 as a decimal it will be a repeating decimal?”

• Unit 6, Lesson 26 , Session  3, Teachers are prompted to ask students to apply repeated reasoning to finding the volume of different figures. Ask “What type of prism is the storage bin? How do you know? Alita wants to design a storage bin in the shape of a rectangular prism. How can she make the volume the same in both designs?” Teachers can guide students to discuss how the shape of a prism affects its volume.

• Unit 7, Lesson 33, Session 3, Teacher’s Edition, Differentiation Extend provides guidance for teachers to engage students in MP8 as they notice repeated reasoning to make generalizations about finding the sample space for a compound event. Try It, “Lucia has a four-digit passcode on her phone. You know her code only uses the digits 0 and 1. What is the probability of guessing her passcode on the first try?” Model It shows an organized list to model the sample space. It is organized by numbers with four zeros, three zeroes, two zeros, one zero, and zero zeros. The Differentiation Extend provides guidance for the teacher to help students understand the patterns in the list. “Prompt students to identify the structure and patterns in the list of possible passcodes. Ask What pattern do you see in the outcomes with three 0s? The outcomes with two 0s? Listen For In the line for the three 0s, the 1 starts in the last place and then moves to the left one digit at a time. In the line for two 0s, the 0s start in the first two places. The second 0 moves to the third and then the fourth place. Then the first 0 moves one digit to the right and the process repeats. Ask How does using patterns help you find the sample space for a compound event? Listen For It gives you a way to check that you have found all the possible outcomes. Ask There are 16 possible passcodes. How could you use multiplication to show this number? Listen For There are two possible digits, 0 and 1, in each of the four places in the passcode. So the total number of passcodes is 2×2×2×2 or 16.”

### Usability

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports, partially meet expectations for Criterion 2, Assessment, and meet expectations for Criterion 3, Student Supports.

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Teacher Supports

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 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' | indicatorName}}

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials.

• The Program Overview provides the teacher with information on program components and description about i-Ready classroom Mathematics implementation.

• Each unit has a Math Background document that provides the teacher with information to unpack the learning progressions and make connections between key concepts.

• Each Unit has an Unit Opener that provides the teacher with Unit Big Ideas and describes the themes of the unit.

• Each Unit has a Unit Flow and Progression video that describes how concepts are developed in the unit.

• Each Unit has a Professional Development document that provides guidance on instructional strategies, such as Supporting Math and Academic Vocabulary Development, Establishing Classroom Environments That Support Mathematical Discourse for ALL Learners, Knowing and Valuing Every Learner: Culturally Responsive Mathematics Teaching.

• Each Unit has a Unit Overview that provides the teachers with pacing, objectives, standards, vocabulary and lesson-level differentiation for each of the lessons in the unit.

• The Teacher’s Guide provides in-class instruction and practice included in the teacher’s edition.

• The Teacher’s Guide for Assessments and Reports supports whole group/partner discussion, ask/listen fors, common misconceptions, error alerts, etc.

• DIfferentiation strategies are included before and during the unit/lesson for the teacher. There are recommended resources to support students’ learning needs that are highlighted in the Prerequisites report.

• Unit and Lesson Support includes information about prerequisite lessons to focus on, and identifies the important concepts within those lessons.

• On the Spot Teaching Tips suggest additional scaffolding to support students with unfinished prerequisite learning as they engage with on-level work.

• Digital Math Tools contain support videos that explain how to use their digital tools.

• Ready Classroom Central is an online teacher portal with resources for professional support such as training videos, planning tools, implementation tips, whitepapers, and discourse support.

• Language Expectations identify examples of what English learners at each level of language proficiency can do in connection with a one grade-level standard.

• The Unit Prepare For provides teachers with guidance to support students when completing the graphic organizer in the beginning of the unit, Prepare for Unit. There is additional guidance to Build Academic Vocabulary through the use of identified cognates and specified academic terms.

• The Unit Review includes problem notes for teachers identifying the Depth of Knowledge level of each problem and the standard, along with suggested strategies, and possible misconceptions based on the selected answer.

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Throughout each lesson planning information, there is narrative information to assist the teacher in presenting student materials throughout all phases of the unit and lessons. Examples include:

• Unit 1, Lesson 4, Session 1, Discuss It “Support Partner Discussion After students work on Try It, have them respond to Discuss It. Listen for understanding of: the relationship between distance and time and the use of ordered pairs to model a relationship between quantities.”

• Unit 2, Lesson 9, Session 1, Model It, provides Differentiation guidance after students have solved problems including adding and subtracting with negative integers. “If students are unsure that subtracting a negative integer has the same result as adding the opposite of that integer, then use this activity to reinforce understanding of the concept.”

• Unit 4, Unit Review, Problem 1 includes teacher notes to support assessing student knowledge. “A, B, D are correct. Students could solve the problem by writing an equation for the perimeter of the square and comparing the different forms of the equations to find which are equivalent.” The materials go on to explain why the other answer choices are incorrect.

• Unit 5, Lesson 22, Session 2, Develop, Discuss It, students work with random sampling. Teachers are asked to support partner discussion. “After students complete problems 1 and 2, have them respond to Discuss It with a partner. Support as needed with questions such as: Why is it important that every member of the population has an equal chance of being selected? If some individual or group did not have a chance of being selected, how would that affect the resulting sample?”

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

In the Teacher’s Guide, a Lesson Progression table is provided that links each lesson within the current unit to a prior and future grade level lesson. Within the Math Background section, detailed explanations of the mathematical concepts in each lesson are provided. For example, in Unit 1, Math Background, Understanding Content Across Grades, insights are provided for prior knowledge, current lesson, and future learning in starting Lesson 1:

• Prior Knowledge, “Insights on: Understanding Multiplication as Scaling. Students learn about resizing a quantity by multiplication as scaling. Common Error - Students may assume that when they multiply the answer will always be a larger number. Experience with visual models of scaling situations will help them see that multiplying a fraction means taking a fractional part of the starting amount. If you multiply a fraction less than 1 whole, you will find a part less than the whole of the starting amount.” This information is included with a visual model of scaling.

• Current Lesson, Insights on: Scale and Scale Drawings. For example: “A scale describes the relationship between lengths in the original figure and lengths in the scale drawing. A scale factor is the number you multiply an original length by to the corresponding length in the scale drawing.” This information is included with a visual example of scale drawings and scale factors.

• Future Learning, Proportional Relationships, “Students will move on to extend and apply their understanding of proportional relationships and scale drawings. Students will: apply proportional reasoning to solve problems involving percents, random samples, and probability. Students will: understand similar figures and dilations in the coordinate plane. Students will: develop an understanding of slope to work with equations and functions.”

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level/series.

• The Correlations Document describes lesson correlation to the CCSSM through multiple lenses. The document identifies the major and supporting areas of focus within the CCSSM and the lessons address those standards. There is a table correlating each lesson with the standards covered, designating standards as “Focus”, “Developing”, or “Applied” within each lesson. The Correlations Document also identifies the Standards of Mathematical Practice that are included in each lesson. One table is organized by MP while the other is organized by lesson. The Unit Review Correlation identifies the associated standard and lesson to each problem within the Unit Review, along with their Depth of Knowledge level.

• The Program Overview provides teachers and explanations for how the standards are addressed in each unit. One section identified is the coherence section titled “Lesson Progression.”

• At the beginning of each Unit, Lesson Progression shows how each standard connects to and builds upon the previous grade levels. Each standard is identified in each lesson. It is arranged in a flow chart, and connects lessons to future grade levels.

• In the lesson overview, prior knowledge is identified, so teachers know what standards are linked to prior work. Future grade level content is also identified.

Explanations of the role of specific grade-level mathematics are present in the context of the series.

• Grade Level Support, Learning Progression identifies prerequisite skills for each lesson and their related standards for the two prior grade levels, when applicable, in a flow chart. For example, Unit 6, traces the learning for Solve Problems Involving Volume 7.G.6 with the prerequisite skill of Understanding and finding volume. The identified standards are Understand Volume 5.MD3, Find Volume with Formulas, 5.MD.5, and Solve Volume Problems with Fractions, 6.G.2.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 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.

In the lesson overview, Connect to Family and Community, a letter is provided for students to take home to their family. This letter includes learning in the unit and ways to encourage family involvement in the lessons. The family letter is provided in the following languages: Arabic, Korean, Mandarin, Russian, Spanish, Tagalog, and Vietnamese. For example:

• Unit 6, Lesson 26, School to Home Connection, “Do this activity together to investigate volume in the real world. Have you ever wondered where firefighters get the water they used to put out fires? Some fire engines have a water tank to store water. When the water supply in the tank runs, firefighters can use other sources of water, like fire hydrants. Water tanks need to hold as much water as possible while fitting in the space available in the fire engine. Not all fire engines use tanks with the same shape. The most common shape is a rectangular or T-shaped tank, which is made of right rectangular prisms. Some water tanks can hold 134 cubic feet, or 1,000 gallons, of water!  Where else do you use volume in the real world?”

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Materials explain the instructional approaches of the program. Examples include:

• The Teacher’s Guide and the Program Implementation area in the digital platform contains a section “Understanding the Try-Discuss-Connect Routine.” This routine is embedded throughout the program. This document explains how the routine is used. “Ready Classroom Mathematics empowers all students to own their learning through a discourse-based instructional routine. Lessons are divided into Explore, Develop, and Refine sessions and are taught over the course of a week. In Explore and Develop sessions teachers facilitate mathematical discourse through a Try-Discuss-Connect instructional routine.”

• “Using a Session” in the Teacher’s Guide describes the planning and support features within the Teacher’s Guide. This includes each component of the lesson and teacher’s guide and describes why it is important in the lesson. For example, “SMPs are infused throughout the instructional model. Deepen Understanding is a consistent opportunity to build understanding of a key lesson concept by extending mathematical discourse. The content connects a particular aspect of lesson learning to an SMP, showing how it might look in the classroom.”

• Integrating Language and Mathematics identifies and explains the six language routines embedded within the curriculum. It identifies each routine, why a teacher may use it, the process and what part of the Try-Discuss-Connect Routine it can be used within. For example, for Say It Another Way, “What: A routine to help students paraphrase as a way to process a word problem or other written text and confirm understanding. Why: Paraphrasing helps students figure out whether they have understood something they have read or heard...How: Students read or listen to a word problem or other written text. One student paraphrases the text. Other students give a thumbs-up to show that the paraphrase is accurate and complete.”

Materials reference relevant research sources. Examples include:

• Boaler, (2016), Mathematical Mindsets

• Council of the Great City Schools, (2016), A Framework for Re-Envisioning Mathematics Instruction for English Language Learners

• Kersaint, (2016), Orchestrating Mathematical Discourse to Enhance Student Learning

• National Council of Teachers of Mathematics, (2010), Teaching and Learning Mathematics

• National Council of Teachers of Mathematics, (2014), Principals to Action

• National Council of Teachers of Mathematics, (2014), Using Research to Improve Instruction

• Richhart, (2009), Creating Cultures of Thinking

Materials include research-based strategies. Examples include:

• “Collaborative learning (partner or small group) encourages students to present and defend their ideas, make sense of and critique the ideas of others, and refine and amend their approaches.” Examples include, “Ready Classroom Mathematics lessons provide multiple opportunities for collaborative learning, such as Discuss It prompts where students explain and justify their strategies to each other and Consider This prompts where students compare problem-solving approaches, solutions, and reasoning.” The research included to support this is, “Research tells us that when students work collaboratively, which also gives them opportunities to see and understand mathematics connections, equitable outcomes result.” (Boaler, 2016)

• Professional Development, contains an adapted excerpt from Reimagining the Mathematics Classroom, co authored by Dr. Mark Ellis for teachers. The excerpt explains “funds of knowledge” to teachers and how they can apply this knowledge using the materials. “Connect to Culture in the Teacher’s Guide for each lesson offers suggestions for tapping into students’ funds of knowledge and connecting the knowledge to Try It and other problems.”

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

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

he materials reviewed for i-Ready Mathematics Grade 7 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. The Teacher’s Guide includes an Activity Sheet in the Table of Contents which provides a list of printable tools and resources. “Dot Paper, Frayer Model 2, Fraction Bars are available to print and copy for each student.” Materials include a Manipulatives List by Lesson for each grade level. For example:

• Unit 1, Lesson 6: 1 meter stick for the whole class, 1 compass per group, and 1 ruler per pair.

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

This is not an assessed indicator in Mathematics.

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

This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 partially meet expectations for Assessment. The materials partially include assessment information in the materials to indicate which standards are assessed and partially provide multiple opportunities throughout the grade to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. The materials provide assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Within the Teacher’s Guide, Teacher Toolbox, Assess, Lesson Quizzes and Unit Assessments are provided. In the Teacher version, Lesson Quizzes identify: tested skills and content standards, DOK levels, Problem Notes, Short Response Scoring Rubric with points and corresponding expectations, worked out problems, and Differentiation suggestions. While the Lesson Quizzes identify the content standards, they do not identify the mathematical practices. For example:

• Unit 4: Algebraic Thinking: Expressions, Equations, and Inequalities, Lesson 19, Lesson Quiz, Tested Skills, assesses 7.EE.4 and 7.EE.4b, “Problems on this assessment require students to be able to solve real-world and math problems involving inequalities using models, properties, and inverse operations....” Problem Notes, Problem 5, “Students could check that the inequality is true by substituting values in for c. (2 points) DOK 2, 7.EE.4b.”

The Teacher version of the Unit Assessments, which have Form A and Form B, identify: Problem Notes, worked out problems, DOK levels, content standards and mathematical practices, Scoring Guide, and Scoring Rubrics. Within the Scoring Guide, “For the problems in the Unit 4 Unit Assessments (Forms A and B), the table shows: depth of knowledge (DOK) level, points for scoring, lesson assessed by each problem, and the standard addressed.” Examples include:

• Unit 4: Algebraic Thinking: Expressions, Equations, and Inequalities, Unit Assessment, Form A, Problem 6, “Which solutions, if any, do the inequalities -5(x +4) >10 and x + 3< -7 have in common? Show your work.” The Problem Notes state, “(2 points), DOK 3, 7.EE.4” Within the Scoring Guide, Problem 3 is identified as aligning to 7.EE.4 and SMP3.

• Unit 4: Algebraic Thinking: Expressions, Equations, and Inequalities, Unit Assessment, Form B, Problem 6, “Which solutions, if any, do the inequalities -8(x + 9) > 24 and x + 8 < -1 have in common? Show your work.” The Problem Notes state, “(2 points), DOK 3, 7.EE.4” Within the Scoring Guide, Problem 3 is identified as aligning to 7.EE.4 and SMP3.

Digital Comprehension Checks “...can be given as an alternative to the print Unit Assessment. For this comprehension check, the table below provides the Depth of Knowledge (DOK), standard assessed, and the corresponding lesson assessed by each problem.” While the Comprehension Checks identify the content standards, they do not identify the mathematical practices.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 partially meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The assessment system provides opportunities to determine students’ learning. Examples include:

• Lesson Quizzes contain Choice Matrix and Select Scoring Rubric and Short Response Scoring Rubric. The Choice Matrix and Select Scoring Rubric contains points and expectations for the quiz. 2 points if all answers are correct, 1 point if there is 1 incorrect answer and 0 points if there are 2 or more incorrect answers. The Short Response Scoring Rubric contains points and expectations for the short response question. Students earn 2 points if the “Response has the correct solution(s) and includes well-organized, clear and concise work demonstrating thorough understanding of mathematical concepts and/or procedures.”

• Unit Assessments contain the Extended Response Scoring Rubric (if there is an extended response question included in the assessment), Short Response Scoring Rubric, and a rubric for Multiple Select, Fill-in-the Blank and Choice Matrix questions (depending on which question types are on the assessment) that provides guidance for scoring each type of problem on the assessment. For example, the Extended Response Scoring Rubric, a response should earn 4 points if, “Response has the correct solution(s) and includes well-organized, clear and concise work demonstrating thorough understanding of mathematical concepts and/or procedures.” This same expectation scores a 2 on the Short Response Scoring Rubric. The Multiple Select, Fill-in-the Blank and/or Choice Matrix  Scoring Rubric contains points and expectations for the assessment. 2 points if all answers are correct, 1 point if there is 1 incorrect answer and 0 points if there are 2 or more incorrect answers.

The Lesson Quizzes provide sufficient guidance to teachers to follow-up with students; however, there is no follow-up guidance in the Unit Assessments or Comprehension Checks. For example:

• Unit 7: Probability” Theoretical Probability, Experimental Probability, and Compound Events, Lesson 33, the Lesson Quiz provides three types of differentiation: Reteach, Reinforce, and Extend. “Reteach: Tools for Instruction, Students who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction. Grade. Reinforce: Math Center Activity, Students who require practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities (available in on-level, below-level, and above-level versions). Extend: Enrichment Activity, Students who have achieved proficiency with concepts and skills and are ready for additional challenges will benefit from group collaborative games and activities that extend understanding.” The Reteach section directs teachers back to Lesson 33, Compound Events. The Reinforce section directs teachers back to Lesson 33, Compound Event Bingo. The Extend section directs teachers back to Lesson 33, Design a Simulation.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. Assessments include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.

The formative and summative assessments include a variety of item types to measure grade-level standards. For example:

• Fill-in-the-blank

• Multiple select

• Matching

• Graphing

• Technology-enhanced items, e.g., drag and drop, drop-down menus, matching

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

#### Criterion 3.3: Student Supports

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 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' | indicatorName}}

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics

• At the end of the Lesson Quiz in the Teacher’s edition, there is a section for differentiation that provides suggestions for Reteach (Tools for Instruction), Reinforce (Math Center Activity), and Extend (Enrichment Activity). Reteach, “Students who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction.” Reinforce, “Students who require practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities (available on-level, below-level, and above-level versions).” Extend, “Students who have achieved proficiency with concepts and skills and are ready for additional challenges will benefit from group collaborative games and activities that extend understanding.” The digital platform contains these activities for each lesson.

• In Refine lessons, the teacher’s edition provides suggestions to Group & Differentiate, “Identify groupings for differentiation based on the Start and problems 1-3. A recommended sequence of activities for each group is suggested below. Use the resources on the next page to differentiate and close the lesson.” Resources are suggested for groups Approaching Proficiency, Meeting Proficiency, and Extending Beyond Proficiency. The resources are found in the digital platform (Reteach, Reinforce, Extend). The following pages also contain descriptions of additional activities in the teacher’s edition for Reteach, Reinforce, and Extend.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Refine sessions provide recommendations for students that demonstrate understanding “Extending Beyond Proficiency” to engage in problems for reinforcement and a challenge. The number of problems is the same as students who are considered to be “Meeting Proficiency”. Additional Enrichment Activities can be found online in the Small Group Differentiation Extend section.

In Explore and Develop sessions, the materials contain a Deepen Understanding section to extend understanding of the lesson’s key concepts through the use of discourse with students. The section contains teacher prompts and suggestions for what ideas to look for from students. Each Deepen Understanding is labeled with an embedded mathematical practice. Examples include:

• Unit 1, Lesson 4, Enrichment Activity Constant Graphing, students are provided with a challenge question at the beginning and multiple opportunities to draw and explain their answer. “Can you find the constant of proportionality and the equation of a proportional relationship that passes through a given point on a graph?”

• Unit 2, Lesson 8, Session 4, Challenge extends student thinking at the end of a lesson on adding with negative numbers, with a multi-step addition problem. “Students extending beyond proficiency will benefit from solving multi-step problems involving unknown addends. Describe this problem: An airplane flies 82.5 ft above sea level. It descends about 3 ft and then rises about 8 ft. Its new height is 87.1 ft above sea level. What could have been the two exact changes in height?...Have students propose and then solve similar problems.”

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 provide varied approaches to learning tasks over time, and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The Teacher’s Guide provides a lesson structure and instructional routine for the lessons by implementing the Try It-Discuss It-Connect It Routine. “Ready Classroom mathematics empowers all students to own their learning through a discourse-based instructional routine. Lessons are divided into Explore, Develop, and Refine sessions and are taught over the course of a week. Students develop greater understanding of mathematical representations and solution strategies using think time, partner talk, individual writing, and whole class discourse.“

Units begin with a single page consisting of the unit number, title, and subtitle. A self-check list of student friendly skills is included where students can check off skills they know before and after each lesson. Each unit concludes with a Self-Reflection, Vocabulary Review, and Unit Review.

Prompts in the Teacher's Guide suggest appropriate places to give students individual time to think. Discuss It provides students opportunities to share in a small group before whole-class discussion. Students work independently before sharing in small or large groups.

Each lesson has an area for supporting partner discussion. There are suggested questions the teacher can ask to provide students with oral feedback as to their understanding. Examples include:

• “Why did you choose the model or strategy you used?”

At the end of each unit is the Self Reflection page where students can work in pairs to respond to the prompts. Prompts include: 1. Three examples of what I learned are… 2. The hardest thing I learned to do is ____ because… 3. A question I still have is...

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 provide opportunities for teachers to use a variety of grouping strategies.

In the Program Overview, guidance for teachers includes the first step is finding where the students are and what content they should be learning. A chart shows how to use data to differentiate instruction with a list of differentiated resources. During a lesson, teachers should informally observe student work and offer resources to use and where to find them. There is no teacher guidance on how to identify students who need a specific grouping strategy.

In the Teacher’s Guide, each lesson contains information to support partner discussion and facilitate whole class discussion. Guidance is provided for differentiation-reteach, reinforce, or extend to help struggling students understand the concepts or skills being taught in the lesson. The Teacher’s Guide also includes a “Prepare For” section of each lesson. This section includes guidance for the teacher on how and when to use grouping strategies. For example:

• Unit 2, Lesson 8, Session 1, Prepare for Adding with Negative Numbers, “Ask students to consider the term integers. Begin by writing the number -1, 0, and 1 on the board. Ask students to name other integers. Discuss how the integers continue forever in both the positive and negative direction. Have students work in pairs to complete the graphic organizer. Invite pairs to share their completed organizers and use them to prompt a whole-class comparative discussion of definitions, examples, and non-examples.”

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for providing strategies and support for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Materials consistently provide strategies and supports for students who read, write, and/or speak in a language other than English to meet or exceed grade-level standards through regular and active participation in grade-level mathematics. Examples include:

• Each Lesson Session includes differentiated support for various levels of English proficiency with level 1-3, levels 2-4, and levels 3-5 identified. Support for Academic language is used during the “Try-Discuss-Connect Language” routines in each lesson.

• In the Program Overview, language expectations charts are provided that describe the language English Learners can understand and produce in connection with students’ levels of English proficiency. Teachers can use the examples to help meet the needs of English Learners.

• Each Unit Overview connects with one of the CCSS addressed in the unit and shows an example of how language expectations can help to differentiate instruction to meet the needs of English learners.

• In the Program Overview, there is an Integrate Language and Mathematics section. “Scaffolded language support for a specific problem is outlined. These suggestions for scaffolding and amplifying language can be applied to other problems as well.”

• Language objectives are included and students are expected to understand and produce language as they work on lesson objectives. Graphic organizers are used to help students access prior knowledge and vocabulary they build on in the lesson.

• Discourse cards are available in the Teacher Digital Experience under the Ready Classroom Mathematics Toolbox. These cards provide sentence starters and questions to help students engage in conversations with their partners, small groups or the whole class.

• All classroom materials are available in Spanish.

• Multilingual Glossary is available in Arabic, Chinese, Haitian Creole, Portuguese, Russian, Tagalog, Urdu, and Vietnamese. There is a Bilingual glossary in the student textbook that includes mathematics vocabulary in English and Spanish.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials feature a balance of images and information about people representing various demographic and physical characteristics. Problems represent a balance of settings and ethnic traditions. Examples include:

• Unit 5, Lesson 20, Session 3, Try It uses the Persian New Year as context for the problem. “Cyrus is hosting a dinner to celebrate Nowruz, the Persian New Year. His groceries cost $150 before he uses a 10%-off coupon. He also orders$60 worth of flowers. Sales tax on the flowers is 6.25%. What is the total amount Cyrus spends?” Photographs depict the symbolic dishes traditionally served, and two females in traditional clothing at a Nowruz celebration. Connect to Culture provides additional context and explanation about Nowruz celebrations, along with an opportunity for students to share their own experiences.

• Unit 6, Math in Action features engineers and a manager as subjects in the tasks. The engineers referenced are three females and one male with the names Anica, Paulo, Jessica and Carolina. The name of the manager is Carlos.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials contain a cognate support routine in the Teacher’s Edition “for students who primarily speak Spanish or other Latin-based languages.” In the Prepare For Unit _, “Academic vocabulary for each lesson is listed in the Lesson Overview. The chart below includes the Spanish cognates for academic vocabulary introduced in the unit and in each lesson. To support students whose primary language is Spanish, use the Cognate Support routine as described in the Unit 1 Professional Learning. Support students as they move from informal language to formal academic language by using the Collect and Display routine. Have students refer to the chart during discussion and writing.” A table with the academic words from the unit and Spanish cognates is included. The “Cognate Support Routine” provides instructions for teachers:

1. Ask students to identify terms that look or sound similar to words in their home language.

2. Check to see if the identified terms are cognates.

3. Write the cognates and have students copy them next to the English terms.

4. Pronounce the English term and its cognate or ask a volunteer to do so. Have students repeat.

Each lesson includes Family Letters which, “provide background information and include an activity.” They are designed to be distributed after the Explore Session, to inform them of their students’ learning and create an opportunity for family involvement. Letters available include English, Spanish, Arabic, Korean, Mandarin, Russian, Tagalog, and Vietnamese.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Connect to Culture “provides teachers with ideas to increase engagement and encourage connections among students from a wide variety of backgrounds.”

• Unit 3, Lesson 12, Overview, Connect to Culture, “Use these activities to connect with and leverage the diverse backgrounds and experiences of all students. Engage students in sharing what they know about contexts before you add the information given here.”  There is a box on the page called Cultural Connection, Alternate Notation - “Latin American countries use all the same symbols for division that are used in the United States, but they sometimes use another symbol as well. The colon may also be used to indicate division, as in 12:2 = 6. Encourage students who have experience with this notation for division to share what they know with the class.”

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 provide support for different reading levels to ensure accessibility for students.

The Unit “Prepare For” section provides academic words and phrases that students will use in the unit. It is suggested for teachers to use the “Academic Vocabulary” routine described in the Professional Learning to provide explicit instruction and active engagement. Another suggestion to support students to move from informal to more formal academic language is by using the “Collect and Display” routine. Students can refer to the chart throughout discussions and writings.

Use of “Three Reads'' is suggested as a support to MP1, Make Sense of the Problem. In the Teacher's Guide there are places to develop academic language throughout the lessons. Examples include:

• Unit 1, Lesson 1, Session 2, in the Teacher's Guide, Develop Academic Language, - “Why? Reinforce understanding of actual through synonyms and antonyms. How? Have students find the work in Model It. Ask them to tell the differences between a town represented on a map and the actual town. Then have them discuss the meaning of actual using synonyms and antonyms. (For example, actual is the same as real and the opposite of unreal.)” Make a T-chart for students to list synonyms and antonyms as they work in the lesson.”

• Unit 3, Lesson 11, Session 3, Problem 4, includes directions for read-aloud and verbal rephrasing of information to support students to make sense of a multi-part, grade-level problem. “Before students begin, read the first part of the problem aloud. Select students to repeat the information to be sure that everyone hears and notes it. Then have students read the directions for Part and Part B. Call on one or more students to rephrase the directions to confirm that they understand each part of the task.”

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Digital tools are available for students. These tools include Counters and Connecting Cubes, Base-Ten Blocks, Number Line, Multiplication Models, Perimeter and Area, and Fraction Models. Geometry, Scientific Calculator and Graphing Calculator are also included but cannot be reviewed as these tools are powered by Desmos. Support videos are available for each of the digital tools, explaining how they may be used and their functions. For example:

• Grade 7 Standard Manipulative Kit includes the most commonly used manipulatives. Manipulatives include Algebra Tiles, plastic rulers, centimeter cubes, base ten blocks, number cubes, geometric solids, two color counters and protractors. A la carte items are available. The materials state that these items may only be used once, may be common to classrooms, or print options are available. A la carte items include fraction tile sets, compasses, geoboards, meterstickes, transparent circle spinners, and transparent counters.

• Visual models such as number lines, graphs, or bars, are also available but cannot be manipulated.

The “Try-Discuss-Connect” routine embedded throughout every lesson provides students the opportunity to connect and transition from the use of manipulatives to written methods. Inside of the digital platform, Program Implementation, Try-Discuss-Connect Routine Resources, Understanding the Try-Discuss-Connect Instructional Routine, the guide describes how the routine helps students transition from manipulatives to written methods. In the Try It activity, “students have access to a variety of tools and manipulatives to use to represent the problem situation. During the Discuss It activity , “Students present and explain their solution methods and listen to and critique the reasoning of others, models and representations.” “The class then looks at the strategies highlighted in the Picture It and Model It, and students make connections between strategies, their own strategies, and the strategies discussed as a class.” During the Connect It activity, “Students apply their thinking during the lesson to new problems.” The routine integrates the CRA model in the:

• Try It, “Students use concrete, representational, or abstract strategies to solve the problem, based on their understanding of the problem or mathematical concept.

• Discuss It, “Students who use more concrete approaches begin to make connections to representational or abstract approaches as they engage in partner discussions.”

• Connect It, “Through the Connect It questions, students connect concrete and representational approaches to more abstract understanding as they formalize their connections.”

#### Criterion 3.4: Intentional Design

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7: integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, have a visual design that supports students in engaging thoughtfully with the subject, and provide teacher guidance for the use of embedded technology to support and enhance student learning. The materials do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 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.

All aspects of the materials can be accessed digitally. Some components are only digital such as the Interactive Tutorials, Digital Math Tools Powered by Desmos, Learning Games, and Comprehension Checks. Adaptive diagnostic assessment, lesson quizzes, mid-unit, unit assessments, and assignable comprehension checks are all available online for students to complete. The digital materials do not allow for customizing or editing existing lessons for local use.

At the beginning of each unit, the Unit Resources includes the digital tools available in the student digital experience, “Engage students with digital resources that provide interactive instruction, practice, assessment, and differentiation.” These tools include:

• Interactive tutorials

• PowerPoint slides

• Learning games

• Digital practice

• Diagnostic assessment

• Lesson and unit comprehension checks

In the digital platform, Program Implementation, Digital Resource Correlations, there are Prerequisite Interactive Tutorial Lesson Correlations. This document shows to which lesson the tutorial is aligned. There are Comprehension Check Correlations for each unit that show to which standard and lesson each question on the digital comprehension check is aligned.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials do not provide an opportunity for students and teachers to collaborate with each other.

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

Lesson routines are consistent in grades 6-8. Each lesson follows the same pattern of “Try It, Discuss It, and Connect It.” Session Slides begin with Learning Targets and a Start slide. The sections of each session are labeled at the top, including “Try It”, “Model It”, “Discuss It”, or “Connect It”. The session slides conclude with a Close: Exit Ticket and Vocabulary.

“Math in Action” sections include one student’s solution as an exemplar model of a possible strategy, use of good problem solving, and a complete solution. Each section is written in first person language explaining each step they took to solve the problem, including completed work and relevant images. Notice That boxes provide important information about that student’s solution. A Problem Solving Checklist textbox can be used by students when writing their own solutions based on the model

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

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

The materials reviewed for i-Ready Classroom Mathematics Grade 7 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

At the beginning of each unit, the Unit Resources includes the digital tools available in the student digital experience and the teacher digital experience, “Engage students with digital resources that provide interactive instruction, practice, assessment, and differentiation.” There are digital tools included for:

•  In-Class Instruction and Practice

• Interactive tutorials

• PowerPoint slides

• Independent Practice for School or Home

• Learning Games

• Digital Practice

• Assessments and Reports

• Diagnostic Assessment

• Lesson and Unit Comprehension Checks

• Prerequisites Report

• Comprehension Check Reports

• Differentiation

• Interactive tutorials

• Learning Games

In the digital platform, Program Implementation, Digital Resource Correlations, there are “Prerequisite Interactive Tutorial Lesson Correlations” for each lesson that has a corresponding interactive tutorial. This document provides guidance on how these can be used, “Interactive Tutorials can be shown before an Explore session to build background knowledge on a topic. The chart below shows which Interactive Tutorial can serve as a prerequisite to each lesson, along with which objectives that interactive Tutorial covers. Additionally, there are Digital Math Tools Support Videos for students or teachers to watch to learn how to use the Digital Math Tools.

Ready Classroom Central, Program Overview, Student Bookshelf is a video explaining to teachers how students access and use the Student Bookshelf in Student Digital Experience.

## Report Overview

### Summary of Alignment & Usability for i-Ready Classroom Mathematics | Math

#### Math 6-8

The materials reviewed for i-Ready Classroom Mathematics Grades 6-8 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for Usability. Within Gateway 3, the materials meet expectations for Teacher Supports (Criterion 1), partially meet expectations for Assessment (Criterion 2), and meet expectations for Student Supports (Criterion 3).

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

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### Overall Summary

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###### Usability
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