## CK-12 Interactive Middle School Math for CCSS

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### Overall Summary

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS 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
Partially Meets Expectations

### Focus & Coherence

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS 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 CK-12 Interactive Middle School Math 7 for CCSS 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.

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for assessing grade-level content. Overall, assessments are aligned to grade-level standards, and the instructional materials do not assess content from future grades. Each chapter has an End of Chapter Assessment in both Word and PDF formats.

Examples of End of Chapter Assessment items aligned to grade-level standards include:

• In Chapter 2, Item 1 states, “There is a wall in your living room that is 13 feet wide. Your TV is centered on the wall. You want to hang up two pictures on either side of the TV. Each picture should be 4.25 feet away from the center of the TV.  a. Label where the center of the TV is on the number line above.  b. Write two expressions to calculate where each picture will go. Then label their positions on the number line.” (7.NS.1)

• In Chapter 3, Item 4 states, “Gary’s birthday is coming up! He wants to book the party room at his favorite restaurant. The restaurant requires him to spend a minimum of $200 in order to book the party room. Each person’s meal costs$12.50. He also plans to buy a cake from the restaurant for $45. a. Using the minimum requirement, write an inequality to represent the total amount he will spend at the restaurant for p people. b. Solve the inequality for p. Graph the solution on a number line. c. What is the least number of people you can have at your party? Show your Reasoning. Hint: Remember that you can’t have a fraction of a person.” (7.EE.4b) • In Chapter 4, Item 2 states, “At a restaurant, a burger is$10.99 and a drink is $2.00. a. The tax rate is 8.5%. What is the cost of a burger and drink including tax? Round your answer to the nearest cent. b. If you want to tip your waiter 20% of the total cost, including tax, how much should you tip? Round your answer to the nearest cent.” (7.RP.3) • In Chapter 7, Item 2 states, “Jessie is playing a game where a red ball, a blue ball and a gold ball are each placed under a cup. Then the three cups are shuffled around. If Jessie correctly guesses which cup has a gold ball underneath it she wins the game. a. If Jessie has no idea which cup the ball is under, what is the probability that she guesses correctly? Write your answer as a fraction in simplest form. If Jessie plays the game 12 times, how many times would you expect her to guess correctly?” (7.SP.6,7) • In Chapter 8, Item 1a states, “A news reporter wants to estimate how many of the 900,000 registered voters in Rhode Island plan to vote for the candidate Fiona Rodriguez in the state senatorial race. The reporter goes to a mall in a major city and surveys 50 people. He finds that 35% of people plan to vote for Fiona Rodriguez. Why might this sample not be representative of the population?” (7.SP.1) ##### 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 CK-12 Interactive Middle School Math 7 for CCSS meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. All lessons contain a Warm-Up, two or more activities, Extension Activities, Inline Questions, and Review Questions that are at grade level. Inline Questions range in number, and lessons generally contain around 10, which are used throughout the lesson to check for understanding. Also, there are Supplemental Questions and Extension Activities. These questions and activities are only seen in the Teacher’s Edition. The Review Questions are mostly multiple choice, and there are approximately 10 per lesson. Examples include: 7.RP.A, Analyze proportional relationships and use them to solve real-world and mathematical problems. • In Lesson 1.6, Activity 1, Question 2 states, “If c = 0.79s is the equation that represents the proportional relationship in the interactive, what is k?” (7.RP.A) • In Lesson 4.2, Activity 2, Question 2 states, “Jake also has a monthly car note of$575. About what percent of his income is this?” (7.RP.3)

7.NS.1, Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.

• In Lesson 2.3, the Warm Up states, “Think about the three cases of integer addition: when the addends (the two numbers that are being added) are both positive, both negative, or one of each. Discuss how you approach an addition problem differently in each of these cases and what sign the answer has.” (7.NS.1)

• In Lesson 2.6, Question 7 states, “Solve -4 + 5 - 7” (7.NS.1)

7.EE.B, Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

• In Lesson 3.10, Activity 2 states, “Are there any values of n such that n + 1 < n?” (7.EE.4b)

• In Lesson 6.7, Activity 1, Question 4 states, “If you are looking at a square pyramid that has a base length of x, a slant height of y, and the pyramid height of z, which of the following are true?  a)The area of the base is 4x.  b) The area of the base is x^2c) The area of a triangular face is 12xy.  d) The area of a triangular face is 12xz.” (7.EE.4a)

The full intent of the standards can be found in the progressions of the chapters and lessons, for example:

• In Lesson 4.2, students solve multiple word problems related to percentages. For example, in Activity 1, Question 1, students identify how percent is found, “Which of the following can be used to find 60% of 450 customers?  A. 450 - (45 + 45 + 45 + 45)  b. 225 + 45  c. 45 + 45 + 45 + 45 + 45 + 45  d. 225 - 45”. In Activity 3, Question 1, students use ratios and percentages to solve the problems, “Jake pays $1625 per month in rent. He makes$6735 per month. Which equations can be used to correctly calculate the percent of Jake's salary on rent each month?” (7.RP.3)

• In Lesson 7.10, students solve multiple problems involving probability. In Activity 2, Question 4, students reason about the likelihood of probability by frequency. The question states, “The outcomes are not equally likely because the likelihood of getting a hit is less than 0.5. About one-third (0.333) of the time, the batter will hit the ball, and two-thirds of the time, he will not. Using a die roll to simulate an at-bat, what will the numbers 1 through 6 represent?” (7.SP.7)

#### Criterion 1.2: Coherence

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

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for coherence. The majority of the materials, when implemented as designed, address the major clusters of the grade, and the materials have supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. The materials also 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 partially have content from future grades that is identified and related to grade-level work and relate grade-level concepts explicitly to prior knowledge from earlier grades.

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

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

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of chapters devoted to major clusters of the grade is four out of eight, which is approximately 50%.

• The number of lessons devoted to major clusters of the grade (including supporting clusters connected to the major clusters) is 53 out of 80, which is approximately 66%.

• The number of days devoted to major clusters (including assessments and supporting clusters connected to the major clusters) is 58 out of 88, which is approximately 66%.

A day-level analysis is most representative of the instructional materials, because this calculation includes assessment days that represent major clusters. As a result, approximately 66% of the instructional materials focus on major clusters of the grade.

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

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

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major standards/clusters of the grade. Lessons in Grade 7 incorporate supporting standards in ways that support and/or maintain the focus on major work standards. Examples of the connections between supporting and major work include the following:

• Lesson 1.9 connects 7.G.1 and 7.RP.A. Students work with scaled drawings and solve problems with the use of proportions. For example, in Activity 1, the Teacher’s Edition directions are, “Discuss with students why scale drawings are proportional relationships. Why are they included in this chapter?... Also we can write the scale factor into an equation of proportionality.” Also, in the Activity 2 Interactive, students use proportions to create a scaled drawing. The problem states, “Tiana wants to rearrange the furniture in her bedroom. She knows that it is 12 feet by 10 feet, with a door and window on the opposite wall. In her bedroom, she needs her bed, a desk, bookshelf, dresser, and chair. She is drawing a scale mapping on graph paper and decides to make 1 foot = 2 squares (0.50 inch). Use the interactive to rearrange her furniture.”

• Lesson 4.10 connects 7.G.1 and 7.RP.3. Students use proportional relationships to solve problems involving scale and percent. For example, in Activity 1, Inline Question 1 states, “Which methods correctly convert a scale factor of 45 to a percent?” In Activity 2, students scale an image, “A scale model of a car was built at 12.5% scale. If the width of the model car is 9.75 inches, what is the width of the real car?”

• Lesson 7.6 connects 7.RP.2 and 7.SP.7. Students find the probability of possible outcomes with objects that have constant proportions. For example, in Activity 1 Interactive, students use the proportions of a dart board to predict probability. The problem states, “Below is a very basic dartboard, without a bullseye. There are 20 sections on the dartboard, and you have an equal likelihood of hitting any of them. The numbers around the circle represent the point values for each section if you are keeping score. Find probabilities for different sets of numbers (numbers less than 8, multiples of 3, etc) by clicking on the sections. The fraction will adjust accordingly.”

• Lesson 8.10 connects 7.SP.2 and 7.RP. Students examine samples to make generalizations using ratio understanding. The Warm Up states, “You will be using sample proportions to estimate the population proportions. A sample proportion is the ratio of members in the sample with a certain attribute to the total number of members in the sample.”

##### 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 CK-12 Interactive Middle School Math 7 for CCSS meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Examples include:

• Lesson 2.3 connects 7.NS.A with 7.EE.B. For example, in Activity 3, Stock Market states, “A particular stock started at $11.15 at the beginning of the day. After 3 hours, it was up$0.67 and at the end of the day it was down $2.25. What was the value of the stock at the end of the day? Use the number line interactive below to help you find the answer.” Also, Inline question 5 states, “On Monday, a stock rose$.50. On Tuesday, it dropped $.15. On Wednesday, it dropped$.12. Thursday it rose $.42. Friday it fell$.07. What was the overall loss?”

• Lesson 3.4 connects 7.EE.A with 7.EE.B. Students rewrite expressions in different forms while using variables to represent numbers. For example, Activity 3 Interactive states, “Your math teacher, Miss Nomer, gives you an extra credit problem to figure out her age. Half of her age three years ago is equal to one-third of her age nine years from now. How old is she currently? All the pieces to figure out Miss Nomer's age are in the box below. Your job is to make two equivalent expressions from the clues above. Set them equal to each other so you can determine her age and get extra credit.”

• Lesson 4.3 connects 7.NS.A with 7.RP.A. Students use operations to solve real-world problems involving percentages. For example, Warm-up Inline Question 1 states, “The original value of a house is $300,000. The house is now worth$600,000. Which of the following statements are true?  a. The new price is 200% of the old price.  b. The new price is 2 times the old price.  c. The new price is 300% of the old price.  d The amount of increase was $300,000.” • Lesson 4.6 connects 7.RP.A with 7.NS.A. Students interpret and calculate percent error and absolute error. In Activity 1, Inline Question 3 states, “Which of the following statements are true about the distance between -4 and 7?” Review Question 5 states, “A student determines the volume of a cube to be 4.6cm^3. What is the percent error if the correct volume of the crystal is 4.3cm^3?” ##### 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 CK-12 Interactive Middle School Math 7 for CCSS partially 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. The materials do not clearly identify content from future grades, but the materials do relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples where grade-level concepts are explicitly related to prior knowledge from earlier grades: • In Lesson 2.7, Multiplying Rational Numbers, the Teacher’s Edition, lists the Previous Learning Objectives: “Use positive and negative numbers to represent quantities in real-world contexts. (6.NS.C.5)’ to connect to the lesson’s focus standards 7.NS.A.2.a and 7.NS.A.2.c. In the Teacher Notes, it says “Students should know how to multiply fractions and decimals, having learned it in 6th grade. This text will review that a little, but the main focus is on multiplying when the numbers have different signs.” • In Lesson 6.7, Surface Area of Pyramids, the Teacher’s Edition, lists the Previous Learning Objectives: “Represent three-dimensional figures using nets made up of rectangles and triangles. (6.G.A.4)” and “Use nets to find surface area in the context of solving real-world problems. (6.G.A.4)”, the Teacher Notes states: “This lesson expands on the surface and addresses pyramids. The bases of the pyramids students will see will be either triangles or quadrilaterals. Students will use their previous work with nets throughout the lesson.” Relating the focus standard 7.G.B.6 to these 6th grade standards. • In Lesson 7.1, Understanding Likelihood, the Teacher’s Edition, list Previous Learning Objectives: “Recognize and write equivalent fractions. (4.NF.A.1)” and “Compare two fractions with different numerators and different denominators. (4.NF.A.2)”, the Teacher Notes states: “Students will use their understanding of fractions as they work with probabilities for example when they write or compare probabilities.” relating the focus standard 7.SP.C.5 to these 4th grade standards. There is one instance that alludes to content related to future grades, but the future grade-level content is not identified. In Lesson 3.7, Solving Two-Step Equations, the Teacher’s Edition, the Teacher Notes references future learning: “Solving equations is one of the most important lessons for 7th-grade students. It is the foundation of 8th-grade math and Algebra”, but there are no specifics given of how the lesson connects to future learning. ##### 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 CK-12 Interactive Middle School Math 7 for CCSS can be completed within a regular school year with some modifications. As described below, the lessons and assessments provided within the materials can be completed in 121 days. An average lesson is 90 minutes with additional material available through Related Modalities and practice problems. In addition, lessons include a daily 15 minute review problem session which could easily be modified. Related Modalities content is included within each lesson, but there is no instruction for teachers as to how or when to utilize it. For homework assignments, the materials state, “It is the expectation that the Adaptive Practice will be used as homework. The students must correctly answer ten questions to receive full credit.” The material is viable for one school year with some modification. • Lessons typically follow this format: • Warm up: Ranging between 5-25 minutes • One to four Activities: Ranging between 10-25 minutes each • Review Questions: 15 minutes • Most lessons are 90 minutes long, but lessons range from 60 to 120 minutes. • There are eight chapters. Each chapter ends with an assessment, and the chapters include from six to eleven lessons. • No lessons are marked as supplementary or optional. • The total number of minutes (6235) was divided by an average class period of 55 minutes. This computation resulted in approximately 113 days of instruction. There are eight days for eight chapter assessments, for a total of 121 days. ###### Overview of Gateway 2 ### Rigor & the Mathematical Practices The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also 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 CK-12 Interactive Middle School Math 7 for CCSS meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and do not always treat the three aspects of rigor together or separately. The materials partially meet expectations for spending sufficient time working with engaging applications of mathematics, ##### 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 CK-12 Interactive Middle School Math 7 for CCSS meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The materials include problems and questions that develop conceptual understanding throughout the grade level. Chapter 1 has multiple opportunities for students to work independently to develop conceptual understanding of analyzing proportional relationships and using them to solve real-world and mathematical problems (7.RP.A) through the use of Interactives. Examples include: • In Lesson 1.6, Activity 1, students use the Interactive to develop understanding of proportional relationships by manipulating numbers to see a total cost based on the amount being bought. The student directions state, “A website offers music downloads for$0.79 per song. Use the slider to see how the cost changes as you increase the number of songs you buy. Use the record button to mark different price points on the table below, then use the data given.” (7.RP.2)

• In Lesson 1.8, Warm-up, students manipulate the sliders in the Interactive to solve proportional relationships involving percents by finding out the discount on the amount being spent. The student directions state, “Use the Interactive and slide the tape diagram to adjust for each fraction. This will help you determine the discount. Then, subtract the discount from the original price to get the sale price.” (7.RP.3)

Chapter 2 has multiple opportunities for students to work independently to build conceptual understanding of applying and extending previous understandings of operations with fractions (7.NS.A) through the use of interactives. Examples include:

• In Lesson 2.3, Activity 3, students develop a conceptual understanding of the distance between numbers by manipulating the sliders on the Interactive activity and answering questions such as, “Which equation models the situation in the problem? A. 11.15 + (-.67) + (-2.25) B. 11.15 + .67 + 2.25 C. 11.15 + .67 + (-2.25) D. 11.15 + (-.67) + 2.25”. (7.NS.1)

• In Lesson 2.7, students multiply rational numbers. In Activity 1, the context is owing friends money, and students answer, “Annie owes $6 to 3 friends. How much money does she owe? Remember owing money means you have a negative amount.” In Activity 2, the context is rewinding to the beginning of a TV show. Both of these contexts develop an understanding of multiplying signed rational numbers. (7.NS.2a) Practice questions at the end of the lesson in the student materials include problem 1, (-9) × (+8), and problem 2, (-5) ×(3), and practice questions from the teacher materials include problem 1, (2)(-8)(-3), and problem 4, 4 ×(-50). • In Lesson 2.10, Activity 2, students convert fractions to decimals in the Interactive to develop understanding of multiplying and dividing rational numbers. The student directions state, “Use the Interactive to match the fractions and decimals in the table. Then, select either T for terminating decimals or R for repeating decimals in the last column.” (7.NS.2) Chapter 3 has multiple opportunities for students to work independently to build conceptual understanding of using properties of operations to generate equivalent expressions and solving real-life and mathematical problems using numerical and algebraic expressions and equations (7.EE) through the use of Interactives. Examples include: • In Lesson 3.3, Activity 2, students manipulate the Interactive to sort expressions that are equivalent to the given expression, which develops their understanding of equivalent expressions. The Teacher Notes describe how the students will be independently working by stating, “For this Interactive, students practice matching equivalent expressions to the expression given at the top. Students can click and drag the expressions on the right into the yes or no column.” (7.EE.2) • In Lesson 3.7, Activity 1, students develop the conceptual understanding of solving multi-step problems with the Interactive by balancing the equations to solve for x. The student directions state, “The Interactive will tell you if it is not balanced and when the equation is solved correctly. Click on the buttons at the top of the Interactive to add and subtract ones and x's. At the end, division buttons will appear, so that you can isolate x”. (7.EE.3) ##### Indicator {{'2b' | indicatorName}} Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency. The instructional materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for attending to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level, especially where called for by the standards (7.NS.1,2; 7.EE.1,4a). In Chapter 2, the materials develop and students independently demonstrate procedural skill in adding and subtracting (7.NS.1) and multiplying and dividing (7.NS.2) rational numbers. Examples include: • In Lesson 2.3, Activity 2 Interactive, students demonstrate procedural skill in adding rational numbers written as decimals. The directions state, “You may remember adding decimals and fractions from last year. Adding decimals is not that much different than adding whole numbers, just make sure you line up the decimal point. As with integers, whichever rational number has the greater absolute value, the answer will have that sign. You may use the Interactive below to brush up on adding decimals.” (7.NS.1) • In Lesson 2.4, the Warm-Up: Subtracting Integers states, “Subtraction is taking away a value from another. Adding -4 would mean moving 4 units to the left. With subtraction it is the opposite. Subtracting -4 would mean moving 4 units to the right. Therefore subtraction can also be defined as adding the opposite. 2 - (-4) + 2 + 4. When doing subtraction problems, change the problem to adding the opposite before starting.” Students complete practice problems, for example, Activity 1: Diving Depths, Inline Question 2 states, “If -5 - 12 models Fatima’s diving depth, what is another way to write this problem?” (7.NS.1) • In Lesson 2.7, students multiply rational numbers. In Activity 1: Annie’s Debt and Activity 2: TV Show Skip Back, students see the results of multiplying numbers with different signs. In Activity 3: Are you -8?, students determine which expressions are equal to -8. For example, Inline Question 1 states, “How would you multiply -\frac{2}{3}×2\frac{3}{4}?” The practice questions at the end of the lesson, such as “$$(-5) ×(3)$$ ,” give independent practice on multiplying integers. In Lesson 2.9, Review Questions, students demonstrate procedural skill in multiplying rational numbers, and some examples include, “6. Multiply the following rational numbers. \frac{1}{11} ×\frac{22}{21} × \frac{7}{10}” and “9. Multiply: \frac{1}{3} ×\frac{4}{12} × \frac{2}{9}.” (7.NS.2) In Chapter 3, the materials develop and students independently demonstrate procedural skill in applying properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients (7.EE.1) and writing equations of the form px + q = r and p(x + q) = r to solve word problems (7.EE.4a). Examples include: • In Lesson 3.2, Review Questions, students demonstrate procedural skill in applying properties of operations to expressions with multiple examples. Some examples include, “1. Simplify the expression using the distributive property and combining like terms until there are two terms. -5(6t-8)-6(t+3)” and “4. Use the distributive property to write an equivalent expression. (-x+4).” (7.EE.1) • In Lesson 3.3, Activity 2: Are You Equivalent?, students develop procedural skill in applying properties of operations to determine equivalent expressions. The materials state, “Analyze the expression 4(x-3) - 2(5x+6)+10. In the box, there are several other expressions that may or may not be equivalent to it. Sort them depending on if they are equivalent or not to 4(x-3) - 2(5x+6) +10.” Also, students develop skill in the practice questions at the end of the lesson, for example, “8. Simplify the expression \frac{4x}{2} - 2(x+13)-5^2.” (7.EE.1) • In Lesson 3.7, students independently demonstrate procedural skill in solving two-step equations in the Review Questions, for example, “10. 13 - 8x = -3.” (7.EE.4a) ##### 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 CK-12 Interactive Middle School Math 7 for CCSS partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics. The materials include multiple opportunities for students to independently engage in routine application throughout the grade level, but the materials include limited opportunities for all students to engage, collectively or independently, in non-routine application problems. Examples of students engaging in routine application of grade-level skills and knowledge, within instruction and independently, include: • In Lesson 2.4, Subtracting Integers and Other Rational Numbers, students solve routine money problems. For example, Activity 2 states: “Gina has a savings account with$23.64 in it. She makes a withdrawal of $15.67 and then a deposit of$6.78. How much money is in her account?” (7.NS.3)

• In Lesson 3.5, Solving Multi-Step Problems with Rational Numbers, students solve routine multi-step problems posed with positive and negative rational numbers. Activity 2: “A new skatepark, Sk8er L8er, is putting in two kickers, with a grind box in the middle, like the picture. To make the feature ready to skate on, the skatepark must also put a layer of Skatelite over the surface to make it smooth and perfect for tricks. The skatepark needs to figure out how many linear feet of Skatelite to buy for this feature. The ramp on each kicker is x feet long, and the grind box is \frac{3}{4}x feet long. The height is \frac{1}{2}x feet.” (7.EE.3)

• In Lesson 4.2, Problem Solving with Percents, students use proportional relationships to solve multi-step percent problems . Activity 2 Interactive states, “Jake is renting an apartment for $1,800 a month, and his monthly income is$5,625. What percent of Jake’s monthly income is his rent? Begin by using a tape diagram to estimate the percent of Jake’s monthly income that his rent is.” (7.RP.3)

• In Lesson 6.3, Solving Problems involving Circles, students use the formula for a circle to solve problems: Activity 3, Inline Question 3 states, “Sherry wants to put some decorative tile around the pool (circular pool with a diameter of 20 feet). If each tile is 6 inches long, how would she determine how many tiles she needs?”  (7.G.4)

The materials provide limited opportunities for students to independently engage with non-routine application throughout the grade level. An example where a student would engage in a non-routine application is shown below.

• In Lesson 7.11 Using Simulations to Estimate Probabilities of Compound Events,  Activity 3: Make a Simulation states,  "In the previous lesson you chose an event and created a simulation to model its probability. Appropriate tools were chosen to model the probability of the event. Either extend your scenario to model a compound event or choose a new scenario. Aim for a minimum of 3 simple events. Consider whether the events are dependent or independent. State the scenario, the probabilities, the research you did, and the simulation tools you chose." (7.SP.7)

##### 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 CK-12 Interactive Middle School Math 7 for CCSS 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. Examples include:

• In Lesson 3.1, Activity 2, students develop conceptual understanding of combining like terms. Students sort different parts of expressions in the Interactive Activity. Teacher directions state, “This Interactive is a visual example of combining like terms, given expressions with variables. The instructions mention the blue box on the graph represents 7x. Students will also see four yellow boxes each with their own values. Students can click and drag the red points at the corner of each of the boxes to move the boxes around. Students can add to the blue box by stacking the yellow boxes on top of the blue box ... Students can also visualize subtraction by placing the yellow boxes in the blue box.” (7.EE.2)

• In Lesson 2.4, Interactive 3, students develop procedural skill by practicing subtraction with decimals. For example, Inline question 1 states, “Calculate: -56.902 - 12.45 - (-13.58) - (-27.9).  a) -41.567 b) -16.945 c) 33.124 d) -27.872.”  (7.NS.1)

• In Lesson 1.6, Review Questions, students represent and solve proportional relationships presented through different real-world scenarios. For example, Question 5 states, “The amount of money Sebastian spends on shoes can be represented by the equation y = 50x , where x is the number of pairs of shoes he owns, and y is the total cost. How many pairs of shoes does Sebastian own if he's spent $650?” (7.RP.2) Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples include: • In Lesson 1.9, Activity 1, students develop understanding of the effects of scale factors in geometric shapes. The materials state, “Take Brainy’s photo and enlarge it and shrink it. See what sort of conclusions you can make about scale drawings. Determine what the scale factor would be if he started with an 8” by 8” photo and made a duplicate of 6” by 6”.” Later in the lesson, students build procedural skill in finding scale factors in the Review Questions. Review Question 4 states, “A map has a scale of 1 inch = 3 feet. What is the scale factor of the map?” • In Lesson 4.5, Activity 1: Mark Ups Interactive, students develop a conceptual understanding of using equations for percent problems. The materials state, “Use the Interactive below to explore how markup rates affect the sale price of a product. In this Interactive, students will get to experiment with markups and item prices, and see how that will affect the resulting purchase price.” Inline Question 3 states, “Change the markup rate to 160%. At this rate, what will you multiply each purchase price by to get the selling price?” In the Review Questions at the end of the lesson, students apply their knowledge of percents and equations to solving real-world problems. Review Question 2 states, “The marked price of a sweater at the clothing store was$24. During a sale a discount of 25% was given. A further 15% discount was given to the customers who have the store’s credit card. How much would a member customer need to pay for the sweater during the sale if the customer paid with the store's credit card? Round your answer to the nearest cent.”

• In Lesson 6.3, students develop procedural skill in finding the circumference and area of circles. Activity 2 states, “Use 3.14 for \pi to determine the area and circumference of the circles in the interactive.” Inline Question 1 states, “The area of a circle is 81\pi. What are the steps to find the circumference?” In Activity 4: Room for pi?, students apply their understanding of circles to real-world situations. For example, Inline Question 3 states, “Sherry wants to put some decorative tile around the pool. If each tile is 6 inches long, how would she determine how many tiles she needs?”

#### Criterion 2.2: Math Practices

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

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

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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 CK-12 Interactive Middle School Math 7 for CCSS 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 materials intentionally identify and develop MP1 in connection with grade-level content by providing opportunities for the students to make sense of problems and persevere in solving them. Examples include:

• In Lesson 4.4, Finding the Whole Given the Percent, MP1 is intentionally developed as they use an Interactive. During Activity 2: Increase and Decrease, “students are asked to find multiple methods for solving for the whole in an increase/decrease problem” as they use proportional relationships to solve multi-step percent problems. Students are asked to prove their method is equivalent using algebraic skills they have learned. (7.RP.3)

• In Lesson 6.11, Volume of Composite 3D Solids, students intentionally develop MP 1 as they “look for an entry point (for finding volume of composite solids) and consider similar problems which may guide them.” In Activity 1: Step Stool Storage, the Teacher Notes explains, “In this Interactive, students will adjust the dimensions of a step stool to figure out its volume and how much storage it has. Students will start with a small step tool with three red points and dimensions, 8\times6\times5. Once students resize the stool to the correct dimensions, a slider will appear at the top of the screen so students can see how the step stool can be broken up into smaller shapes.” (7.G.6)

The materials intentionally identify and develop MP2 in connection with grade-level content by providing opportunities for the students to reason abstractly and quantitatively. Examples include:

• In Lesson 3.4, Equivalent Expressions Within a Context, students intentionally develop MP 2 throughout the lesson using the Interactives and Inline Questions. Activity 3: Mystery Age, states, “Your math teacher, Miss Nomer, gives you an extra credit problem to figure out her age. Half of her age three years ago is equal to one-third of her age nine years from now. How old is she currently? All the pieces to figure out Miss Nomer’s age are in the box below. Your job is to make two equivalent expressions from the clues above. Set them equal to each other so you can determine her age and get extra credit.” (7.EE.4)

• In Lesson 7.3, Discerning Between Equally Likely and Non-Equally Likely Outcomes, students intentionally develop MP2. For example in Activity 1: Rolling the Dice, students are given this situation: “Sai and his friend Kai are rolling dice to see who gets the higher number. They each roll a six-sided die and whoever gets the higher number wins the round. If they roll the same number, then it is a tie and no one wins the round.” Students then are posed the following Discussion Questions, “Look at your results, is this what you expected? Are both boys equally likely to win? Why or why not?” as they use data to determine whether the simulation was fair or unfair. (7.SP.7)

##### 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 CK-12 Interactive Middle School Math 7 for CCSS meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials intentionally identify and develop MP3 in connection with grade-level content by providing opportunities for the students to construct viable arguments and critique the reasoning of others. Examples include:

• In Lesson 2.9, Multi-Step Multiplication & Division Problems involving Rational Numbers, the materials help students to intentionally develop MP3 to its full intent. In the Discussion Question following Activity 1: Switch the Order, students critique the reasoning of a student and form an argument. “Jack claims that the expressions -8 ÷ 2 ÷(-5) ÷ 2 and -8 ⋅ \frac{1}{2} ⋅ (-\frac{1}{5}) ⋅ \frac{1}{2} are the same, do you agree or disagree? Provide evidence for your argument? Can you apply the Commutative or Associative Properties to one and not the other?” (7.NS.2 & 7.NS.3)

• In Lesson 3.8, Using Two-Step Equations to Solve Problems, Activity 2, the Discussion Question asks, “Looking back at the answers for some of the inline questions, are any of the answers not possible? Could you automatically eliminate any?” The Teacher Notes state, “ The answer is, yes, some of the answers could definitely be eliminated. Ultimately, all students will have to take a standardized test at the end of the year, and it is always a good test-taking technique to learn how to eliminate answers that are not possible. In the case of 2, 3, and 5, seconds cannot be negative, so those "distractors" can automatically be eliminated, thus making the selection choice smaller and a greater likelihood of selecting the correct answer. For similar reasons, you could discuss with the class why some of the equations are incorrect in #1 and #5. For example, 160t cannot be positive in the equation because Alex is falling, meaning that 160 needs to be negative.” (7.EE.4)

• In Lesson 4.4, Finding the Whole Given a Percent, Standards for Mathematical Practice: “MP3: In Activity 1, the students are asked to develop an argument around which approach they prefer to help understand a pie chart. The students are given the opportunity to analyze the arguments of their classmates.“ Activity 1: A Slice of Pie, Discussion Question: “When solving the problem above, Donna found it easier to start with smaller percentages, and Ellie found it easier to start with multiples of 10. Who do you side with and why?  Use evidence or an example to support your answer.” The Teacher Notes state, “Answers may vary. Students may have leaned toward small percentages or multiples of 10 for easy calculation. However, finding smaller percentages may be a more effective strategy if the smaller percentages are factors of larger percentages. Allow students to share their strategies.” (7.RP.3)

• In Lesson 8.2, Visually Comparing Two Data Distributions, Activity 3, the Teacher Notes encourage the teacher to have students discuss mean and median in relation to visual data sets. The Discussion Questions asks, “Based on the data taken, which angle do you believe produced the most solar energy?” The Teacher Notes then state, “Allow students to discuss with a classmate and then share with the class. Encourage them to discuss how the mean, median, MAD and IQR influenced their conclusion. After several students have shared their results with the class, allow the groups to put all of their findings together to determine which angle produced the most solar energy.”(7.SP.3)

##### 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 CK-12 Interactive Middle School Math 7 for CCSS meet expectations for supporting 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 intentionally identify and develop MP4 in connection with grade-level content by providing opportunities for the students to model with mathematics. Examples include:

• In Lesson 2.5, Finding the Distance Between Two Numbers, students model the rise and run of slope with mathematics. In Activity 2: Getting around Washington DC, students use an online map of Washington, D.C. set in a grid to investigate distances between various landmarks. The Inline Questions state, “1. How many blocks is the Spy Museum for Union Station?  2. Select the two routes Cheryl could take to get to the Spy Museum from 3rd and C SW.  3. The DMV is located at Half St and K in SW. What would be the coordinates on our map?” The Teacher Notes state, this “Interactive is a real-world application of finding the distance between two points when they are not collinear.” (7.NS.1)

• In Lesson 4.9, Solving Problems Involving Taxes, Commissions, and Fees , Activity 4: Big Tipper Continued, students are encouraged to use a variety of strategies to determine a 20% tip, such as multiplying by \frac{1}{5}, using 10% times 2, etc. Then they model with mathematics.  Students are given a sample meal check and are directed as follows: “Put a tip in the input box. Aim for a tip that is around 20%. Click the ‘Check’ button to check your answer. Click the ‘New Amount’ button to try a new bill.” (7.RP.3)

• In Lesson 7.9, Solving Problems Involving Compound Probability, Activity 1: Deal or No Deal, the students model with mathematics the probability of getting a certain prize in a ‘Deal or No Deal’ type game. It states, “You start with four cases, and in each 'round,' choose one case to remove from the table. The goal is to try to leave the case with $10,000 for last. Play the "Deal or No Deal" game in the Interactive below several times. Review the tree diagram and the probability of each final outcome at the end of the game. Once you have a feel for the probabilities of each prize, answer the Inline Questions that follow. 1) How can you find the probability of winning$10,000? 2) Look at the tree diagram. Which of the following statements is true? 3) Look at the completed tree diagram. Select the true statements.” (7.SP.8)

• In Lesson 8.8, Understanding Sampling Variability, Activity 3: Collecting Data, students collect data and analyze data on reaction time, using the Interactive to model with mathematics. The directions on the Interactive are as follows: “You will be recording the time it takes you to catch a bug on the screen 5 times. Then do so with three other classmates and observe the statistics for your results. Press the buttons to release the bug. Tap the bug to catch it, and stop the timer. Observe the results for each student in the given table.”  Students are directed to, “collect data from yourself and from 4 other classmates. Each classmate should provide 5 samples. Display each sample in a spreadsheet. Find the mean and MAD for each person’s data.” (7.SP.2)

The materials intentionally identify and develop MP5 in connection with grade-level content by providing opportunities for the students to choose tools strategically. Examples include:

• In Lesson 5.2, Triangle Construction,  students do the following:  “In Activity 1, students choose their own tools to create a conjecture about the restrictions on the side lengths of a triangle. The students can come up with a conjecture and provide examples and counterexamples to support their arguments. The students share the experience of how their choice of tool helped or hurt their conjecture.” Activity 1: Three Sides; Discussion Question states: “Can any three lengths create a triangle? Create a conjecture about the side lengths of a triangle.” Then the Teacher Notes state the following:  “For this question, the students will need physical tools to practice constructing triangles based on a chosen number of sides. Allow the students to choose their own tools to practice constructing triangles. The students can choose rulers, graph paper, string, etc. The students should choose three side lengths and then attempt to construct a triangle using those dimensions. If the sum of any two sides is not greater than the third side, the triangle sides will not connect. The students should work in small groups to maximize the data collection and to compare their tool choices with their peers. At the end of the activity, the students should share their conjectures and discuss how their choice of tools assists or hinders their efforts.” (7.G.2)

• In Lesson 6.2, Area and Circumference of Circles: “ In Activity1, the students explore the challenges of using various tools to measure the circumference of a circle.” Activity 1 states, Parts of a Circle; Discussion Question: “What tool do you think would be best for measuring the circumference of a circle? What challenges would you have measuring the circumference with a circle?” After students discuss the questions with their classmates, the Teacher Notes instruct the teacher to print the circle below and allow the students to use real tools like rulers and measuring tape to make the activity more tangible.  (7.G.4)

• In Lesson 7.10, Using Simulations to Estimate Probabilities of Simple Events states, “ In each Activity, the students must choose the appropriate tools to simulate the scenario presented in the Activity.” For example, in Activity 2: Batting Average; Discussion Questions state: “1. What other tools could you have used to simulate a 0.333 batting average, a 1-in-3 chance of getting a hit.  2. Would the tools you chose for the previous question still apply if the batting average was 0.3000 or 0.320? Which tools would work in these situations.” Activity 3: Make a Simulation states, “Choose an event and create a simulation to model its probability. Choose the appropriate tools to model the probability of the event. It may require research to find the probability of the possible outcomes. State the scenario, the probabilities, the research you did, and the simulation tools you chose.” (7.SP.6 & 7.SP.7)

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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 reviews for CK-12 Interactive Middle School Math 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.

The materials intentionally develop MP6 through providing instruction on communicating mathematical thinking using words, diagrams, and symbols. Examples include:

• In Lesson 3.2, Rewriting Expressions Using the Distributive Property, Activity 1, students are asked to expand expressions such as \frac{1}{2}(4a-5). The Teacher Notes state, “For questions #4 and #5, discuss what it means to be a factor. Students commonly get the words ‘factor’ and ‘multiple’ confused. It might be hard for students to see that a number with a + sign is a factor. If that’s the case, show them this example; if a = 2, b = 3, and c = 5, then 2 and 8 b+care factors of their product, 16. Notice that 3 nor 5 are factors, but their sum is.” (7.EE.1)

• In Lesson 5.1, Special Angle Pairs, students learn about supplementary, complementary, adjacent, and vertical angles.  The Teacher Notes at the beginning of the lesson states, “Start by reviewing some important terminology: lines, line segments, types of angles, etc. Some of these terms may be new to students, like complementary and supplementary. If students are having difficulty with all the new vocabulary, you can provide them with a vocabulary toolkit or encourage them to make flash cards.” (7.G.5)

• In Lesson 6.3, Solving Problems Involving Circles, Activity 2, students attend to precision as they are asked to, “Use 3.14 for \pi to determine the area and circumference of the circles in the Interactive. Repeat several times until you are comfortable with the two formulas. Remember the 3.14 is an estimation of \pi, but it does enable you to get a numerical answer, and not one in terms of \pi.“ (7.G.4)

The materials use precise and accurate terminology and definitions when describing mathematics, and the materials also support students in using the terminology and definitions. There is no separate glossary in these materials, but definitions are found within the units in which the terms are used. The vocabulary words are in bold print. Examples include:

• In Lesson 3.3, Identifying Equivalent Expressions,  Introduction, students read the definition of equivalent expressions. The definition is as follows: “Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other. In addition, you can also determine if two expressions are equivalent when values are substituted in for the variable and both arrive at the same answer.” In Activity 1 Interactive, students see an example of identifying equivalent expressions to help them understand the proper use. This is introduced to the students as, “In this Interactive, there is a column of expressions and a box with other expressions. Your job is to drag the expressions in the box to its equivalent expression in the column. The first one is done for you.” (7.EE.1)

• In Lesson 5.1, Special Angle Pairs, Activity 1, students read and apply the exact definitions of terms relating to angles: “A line is composed of infinitely many points, but you only need two points to define a line. Three points are used to define an angle, where the middle point is always the vertex.”  Students are supported in using the terms to answer Inline Questions where they must identify angle terms from a diagram: “1. (Highlight) Based on the data in the image, select the points collinear with point A. 2. (Drag and Drop) Sort the terms below into the correct categories using the image for reference. Remember multiple items may use the same points. For example, points C and D could describe both a line segment and a ray. 3. Angles are labeled in the form ∠ABC, where the middle letter always describes the vertex. The other two letters may be in either order. Select all the correctly labeled angles below.”  (7.G.5)

• In Lesson 8.5, Introduction to Sampling, Activity 1 states, “Sampling is the practice of using data obtained from a group to represent a population. A population is a group of objects with a common characteristic. The group selected from the population is called a sample. By studying small groups of a larger population, you can identify trends that might apply to the entire population. Throughout this chapter, you will explore what makes a good sample and how it can be used to make estimates about large populations.”(7.SP.1)

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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 CK-12 Interactive Middle School Math 7 for CCSS 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 materials intentionally identify and develop MP7 in connection with grade-level content by providing opportunities for the students to look for and make use of structure. Examples include:

• In Lesson 2.4, Subtracting Integers and Other Rational Numbers, Activity 1, students develop MP7 as they use an Interactive to “explore the link between adding a negative and subtracting a positive number.”  The Teacher Notes state, “This interactive shows an application of how negative values are used; in this case, it is how deep a diver dives. Students will see a body of water with a diver, boat and some fish. There are also two number lines; the horizontal line ranges from -20 to 0 and the vertical line ranges 0 feet to 20 feet. The horizontal line has a red point that students can click and drag to make the diver dive. While the student moves the point in the negative direction the father down the diver will go. The arrow on the vertical line will travel down with the diver showing the student how many feet down the diver is.”  Discussion Question: “Why is subtracting a negative integer the same as adding a positive integer?” (7.NS.1)

• In Lesson 2.11, Using Arithmetic Methods to Solve Multi-Step Problems, students intentionally develop MP7 as they “explore how parentheses placement can affect the simplification of an expression.” In Activity 1, students make use of structure as they investigate an equation. “See the equation with blue parentheses. Below is the expression from the left side of the equation.  Depending on which operation is performed first, the value of the expression changes.  For example, if you add 3 + 4 before performing any other operations in the first equation, then the expression equals 37. 1) Move the red points to change which operation is performed first. 2) Move the red point so the second expression equals 18. 3) Move the red point so the third expression equals 1.” (7.NS.2a & 7.NS.3)

• In Lesson 3.9, Writing Two-Step Inequalities, Activity 1, MP7 is intentionally developed as students compare the structure of inequalities to the written expression that matches them.  In this interactive, you will practice matching inequalities to phrases.  Try to notice any keywords that help you match the phrase to the inequality.” In the Inline Questions, students continue to use the structure of inequalities and their expression in words. For example, Question 2: “How could the inequality -3>-2+\frac{1}{2}z be expressed differently than it was in the interactive? a) -3 is less than -2 and half a number. b) -3 is greater than -2 and half a number.  c)  -3 is less than half a number and 2 d) -3 is greater than -2 less than half a number. (7.EE.4)

• In Lesson 6.2, Area and Circumference of Circles, Activity 2, Students use an interactive to determine the revolutions of a bowling ball as it rolls down an alley. Students apply their measurements as they use the ratio of circumference to diameter to help derive the circumference of a circle” guided by  Inline Questions: “1). Use the interactive. Approximately how many inches does the ball travel in on revolution?  2) How can we mathematically find the number of revolutions it takes the ball to reach the pins, 3. The number \pi is defined as the ratio of the circumference, C, to the diameter, d.  For the ball, this is \frac{27}{8.5}\approx 3.14 and 4) How can we rewrite the formula  as a formula to find the circumference? r represents the radius in the formulas.” (7.G.4)

The materials intentionally identify and develop MP8 by providing opportunities for the students to look for and express regularity in repeated reasoning. Examples include:

• In Lesson 1.4, Identifying Proportional Relationships, students intentionally develop MP8 as they “use repeated reasoning to develop a conjecture about the properties of graphs of proportional relationships.” Activity 1’s Discussion question asks, “What do you notice about this graph and the graph from the Driving Away interactive?” (7.RP.2)

• In Lesson 6.10, Volume of Triangular Prisms, in the introduction, students compute the area of a triangle using a one square unit grid and then use that result to compute the volume of a one unit high triangular prism.  The Discussion Questions 3 and 4 lead them to use repeated reasoning to derive the formula for the volume of a triangular prism of any dimensions: 3) How many cubes would there be in 2 of these figures? 4) How many cubes would there be in n of these figures?” (7.G.6)

### Usability

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS partially meet expectations for Usability. The materials partially meet expectations for Teacher Supports (Criterion 1), meet expectations for Assessment (Criterion 2), and do not meet expectations for Student Supports (Criterion 3).

##### Gateway 3
Partially 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 CK-12 Interactive Middle School Math 7 for CCSS partially meet expectations for Teacher Supports. The materials provide: teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; explanations of the instructional approaches of the program and identification of the research-based strategies; and a comprehensive list of supplies needed to support instructional activities. The materials contain adult-level explanations and examples of concepts beyond the current grade so that teachers can improve their own knowledge of the subject, but do not contain adult-level explanations and examples of the more complex grade-level concepts. The materials partially include standards and correlation information that explains the role of the standards in the context of the overall series.

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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 CK-12 Interactive Middle School Math 7 for CCSS 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 to assist teacher delivery of student materials. The Teacher Edition of the materials contains Teacher Notes throughout to assist the teacher in presenting the student lessons.  Examples include:

• Important information about student learning at the beginning of lessons. For example, in Lesson 7.4, Theoretical Probability Models, the Introductory Teacher Notes states, “In this lesson, we shift from experimental probability to theoretical. Students will continue to learn how to calculate theoretical probabilities and use these probabilities to estimate and predict the likelihood of outcomes. Students should continue to use what they have learned about probabilities as they work through the examples to answer questions and make predictions. (7.SP.5 & 7.SP.6)

• Answers to all Inline Questions

• Instructions for help with the Interactives. For example, in Lesson 1.8, Solving Multi-Step Ratio Problems, Warm-Up, the Teacher Notes for the Interactive states, “This Interactive is intended to help with the discount problem in the text above. It has three sliders: A green slider to adjust price (of the item being discounted), a red slider to change the numerator of the fraction, and a blue slider to change the denominator. As the students change the fraction, an equivalent number of boxes will appear next to the fraction to help the student visualize the percentages. The denominator dictates how many boxes appear, and the numerator dictates how many boxes are colored.  Students can set these values to match the product price and discounts in the text above, and they will see how much was discounted (ex: set the Interactive fraction to \frac{1}{4} and price to $1,200 to find the price of the discount on the refrigerator -$300 off.) (7.RP.3)

• Possible answers, further questions, and discussion ideas for the Discussion Questions are in the following examples. In Lesson 6.1, Area and Perimeter of Scale Drawings, Activity 2, the Discussion Question Teacher Notes state, “Students need to convert the scale so that both are in inches before determining the size of the model. Once the scale is all in inches, then also convert the measurements of the actual building into inches. Once everything is all in the same units, then it can be scaled down. As for the scale factor, it is reasonable. It might be a little big to bring a nearly 5-foot tall model to school, but it could work. As an extension, you could have students determine a more “reasonable” scale and then determine the dimensions of their model. Students need to explain why they chose their scale.” (7.G.1)

• Specific learning standards and objectives for each lesson

• Lesson-specific Teacher Notes

• A scope-and-sequence at the end of the Teacher Edition

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. In the Teacher Edition at the beginning of each lesson, there is an overview of the lesson to assist the teacher in planning lessons:

• Common Core Standard—the focus and prerequisite standard(s) for each lesson is listed.

• Standard for Mathematical Practice—the mathematical practice(s) for each lesson is listed as well as where in the lesson it is developed.

• Previous Learning Objectives —a majority of the lessons list these objectives and the standard(s) or grade(s) the objective is connected.

• Learning Objectives -goals for each lesson.

• Agenda - there is an agenda listed for each lesson with the allotted times for the Warm-Up, the Activities, Review Questions, Related Modalities and Adaptive Practice.

• Introductory Teacher Notes—located at the beginning of the lesson after the agenda, these notes describe what the students will be doing in the lesson. Some have helpful hints.

• Interactives—Teacher Notes for the Interactive activities give the teacher direction on how the students are to use the Interactive and helpful hints.

• Discussion Questions -  Teacher Notes for Discussion Questions  provide possible answers and/or possible questions to ask to further the discussion.

• Extension Activities—some of the lessons give extension activity ideas that can enhance the learning.

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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 CK-12 Middle School Interactive Math 7 for CCSS partially meet expectations for containing adult-level explanations, 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.

The Teacher Edition does not contain any adult-level explanations and examples of the more complex grade-level concepts so that teachers can improve their own knowledge of the subject.  In the Subjects Menu, Math Flexlets are available for 6th, 7th and 8th Grade Math Essentials. These are shortened versions of some key lessons intended for review.  For example, Interactive 6th Grade Math Essentials states, “This Flexlet is a great resource to prepare for or review Middle School Math 6. It is a collection of only the 'key' lessons in CK-12 Interactive Middle School Math 6. Additional detailed support for concepts introduced here is available in the full CK-12 FlexBook 2.0.” This resource does not offer adult-level explanations and examples of the more complex grade-level concepts since it addresses only key lessons and not more complex concepts.

Additionally, Study Guides can be found under the Explore menu, and are intended as a “Quick review with key information for each concept.” The math content covered in the Study Guides is beyond the current course and offers math high school courses Algebra and Geometry. These Study Guides can be used so that teachers can improve their own knowledge of the subject. However, not all Study Guides are connected to High School standards or standards at all.

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

The materials reviewed for CK-12 Middle School Interactive Math 7 for CCSS partially meet expectations for including standards and 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. However, there are few, if any, explanations of the role of the specific grade-level mathematics in the context of the series and no connection to future learning.

Previous learning objectives are listed on most of the lessons. There are limited instances of objectives connecting to previous grade levels, and the remaining previous learning objectives listed are related to grade-level standards. Examples include:

• Lesson 2.7, Multiplying Rational Numbers, lists the following as Previous Learning Objectives: Use positive and negative numbers to represent quantities in real-world contexts (6.NS.5). The Introductory Teacher Notes state, “Students should know how to multiply fractions and decimals, having learned it in 6th grade. This text will review this a little, but the main focus is on multiplying when the numbers have different signs. Students should use their knowledge of positive and negative values when working through some of the examples. For instance, when adding, the order does not matter.”

• Lesson 3.1, Combining Like Terms, lists the following as Previous Learning Objectives: Identify terms, factors, and coefficients in an express (6.EE.2b) and Apply properties of operations as strategies to add and subtract rational numbers (7.NS.1d).

• Lesson 6.1, Area and Perimeter of Scale Drawings, lists the following as Previous Learning Objectives: Solve real-world problems involving area of a special quadrilateral (6.G.1); Solve mathematical problems involving area of a special quadrilateral (6.G.1); Understand for what values of k will a scaled drawing be bigger or smaller than the original (7th); and Compute the actual lengths from a scale drawing (7.G.1).

Future learning objectives are seldom present and are usually referred to later in the grade level and not to a concept in future grade levels or courses. For example, in Lesson 6.11, Volume of Composite 3D Solids, the Introductory Teacher Notes state, “This lesson combines the volumes of different types of prisms.  Even though the surface area of pyramids was explored earlier, the volume of one is not covered until 8th grade.”

Mathematics standards, practices and learning objectives are listed throughout the grade level at the beginning of each lesson. Examples include:

• In Lesson 3.11, Using Two-Step Inequalities to Solve Problems, the Focus Standard is 7.EE4b, and the standards for mathematical practice listed with the lesson is MP4. The Learning Objectives are the following: Use inverse operations to solve two-step inequalities, solve inequalities in the context of real-world problems and interpret the solution of an inequality within the context of the problem.

• In Lesson 4.7, Changing Percents, the Focus Standard is 7.RP.3 and the standards for mathematical practice listed with the lesson are MP2 and MP4. The Learning Objective is, “Solve problems involving a percent where quantities change in a real-world context.”

• In Lesson 7.3, Discerning Between Equally Likely and Non-Equally Likely Outcomes, the Focus Standards are given as 7.SP.7a and 7.SP.7b, and the standards for mathematical practice listed with the lesson are MP2 and MP6. The Learning Objectives are the following: Understand what an outcome is, understand what an event is, develop a uniform probability model by assigning equal probability to all outcomes, and use this model to determine probabilities of events, understand the difference between a fair and unfair event and develop a non-uniform probability model by observing frequencies in data generated from a chance process.

##### 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 CK-12 Interactive Middle School Math 7 for CCSS do not provide strategies for informing all stakeholders, including students, parents, or caregivers, about the program and suggestions for how they can help support students’ progress and achievement. Although the materials support teachers with planning, instructions, and analysis of student progress, there are no specific resources for parents or caregivers. While students are able to access their reports, there are no strategies provided to assist their progress or achievement. There are no explanations for parents or caretakers on the place to create an account to help support in-class learning or home instruction.

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

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

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Instructional approaches of the program and identification of the research-based strategies can be found on the homepage, the citations for this research can be found under the “Resources” tab on the homepage. The materials state the following, “The CK-12 Interactive Middle School Math series promotes exploratory learning (Stein 2010). Each lesson contains interactive applets which actively engage students in the learning process and allow them to explore concepts in an open-ended environment (Cocea & Magoulas, 2015; Hoyles, 2018; NCTM, 20115). Inline question sets Socratically guide students to discover connections present in the interactive applets, and a list of Works Cited includes:

• Stein, R. G. (2010). Math for Teachers: An Exploratory Approach. Kendall Hunt

Publishing Company.

• Cocea, M., & Magoulas, G. D. (2015). Participatory learner modeling design: a

methodology for iterative learner models development. Information Sciences, 321,

48-70.

• Schunk, D. H. (2012). Learning Theories: An Educational Perspective. Pearson.

• Hoyles, C. (2018). Transforming the mathematical practices of learners and teachers

through digital technology. Research in Mathematics Education.

• Hoyles, C., & Lagrange, J. B. (Eds.). (2010). Mathematics education and technology:

Rethinking the terrain. New York: Springer.

• National Council of Teachers of Mathematics. (2014). Access and equity in mathematics

education: A position of the national council of teachers of mathematics. National

Council of Teachers of Mathematics.

• National Council of Teachers of Mathematics. (2015). Strategic use of technology in

teaching and learning mathematics: A position of the national council of teachers of

mathematics. National Council of Teachers of Mathematics.

• Wolf, D., Lindeman, P., Wolf, T., & Dunnerstick, R. (2011). Integrate Technology with

Student Success. Mathematics Teaching in the Middle School, 16(9), 556-560.”

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

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

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

The Interactives in the lessons are designed to replace any extra materials. There is a comprehensive list of supplies needed for the optional activities included at the beginning of the Teacher Edition under the Resources tab. The materials listed are provided for the lessons that need extra supplies for optional activities  (Note: the quantity listed is per student unless otherwise noted.) Examples include:

• In Lesson 1.7, Interpreting Graphs of Proportional Relationships, Warm-up Activity, Proportional Relationships in Art: Ruler and Tape Measure.

• In Lesson 6.2, Area and Circumference of Circles, Activity 1, Parts of a Circle: Ruler Access, Tape Measure Access, and Access to other measuring tools if desired.

##### 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 CK-12 Interactive Middle School Math 7 for CCSS meet expectations for Assessment. The materials include an assessment system that provides multiple opportunities throughout the grade to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up, and the materials provide assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices.  The materials partially include assessment information in the materials to indicate which standards are assessed.

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

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

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS partially meet expectations for having assessment information included in the materials to indicate which standards are assessed. The materials sometimes identify the standards and mathematical practices addressed by formal assessments.

Formative assessments, including Inline Questions, Review Questions/Quiz, and Adaptive Practice are located in each lesson, however the materials only identify the standards and practices assessed for some of the formal assessments. In the Teacher Edition, at the beginning of each lesson, standards and mathematical practices are clearly listed, but specific standards and practices are not listed for each question on the Inline Questions, Adaptive Practice and Review Questions/Quizzes. The end of chapter assessments identify the standards for each question, but do not identify the mathematical practices. Examples include, but are not limited to:

• In Lesson 3.1, Combining Like Terms,  Activity 2, Inline Question 4, “Simplify the expression: 8x+3x+6x-7 ” Answer choices a) 10x+7, b) 17x+7, c) 17x-7, d) 11x-7

• Chapter 2, Operations with Rational Numbers, Question 2: “(7.NS.A.1.a, 7.NS.A.1.c) The value of A is 5. a. What value, call it B, can you add to 5 to make 0? Write an equation using subtraction to show this. How could you represent this using addition?”

• Chapter 7, Probability, Question 4: “(7.SP.C.8) Alex, Bianca, and Cameron are racing canoes. Assume that each racer has an equal chance of winning. a. (7.SP.C.8.b) Create a tree diagram to represent the number of ways each racer can finish.”

##### 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 CK-12 Interactive Middle School Math 7 for CCSS meet expectations for including an assessment system that provides multiple opportunities throughout the grade to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The assessment system provides multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance and most of the assessments provide sufficient suggestions for following-up with students. Examples include:

• Every lesson has Adaptive Practice Questions which generate a report with the number correct, difficulty of the questions, time spent and mastery level.

• Answer keys are provided for all Inline Questions, Discussion Questions, and End of Chapter assessments.

• Each of the End of Chapter Assessments contains a rubric to assist the teacher in scoring student work. Each problem is given a 1-5 score and is correlated with the CCSS. Rubrics are provided for End of Chapter Assessments only. Scoring rubrics provide information on student performance but do not include suggestions for the teacher to follow up.

• Statistics are given through reports to the teacher on each assessment component students take. The Skill Meter gauges student understanding and skill based question-by-question and is color-coded so teachers can quickly ascertain student understanding:

• Beginning - new to concept (red)

• Exploring - starting to understand (orange)

• Developing - demonstrating familiarity (yellow)

• Proficient - understands core concept (light green)

• Mastery - deep, demonstrated understanding (dark green)

• The Class Insights function uses the Skill Meter to give information on individual students and the entire class, by placing students on a quadrant analysis graph based on their skill level and engagement. The Class Insights function also has the Teacher Assistant which, “uncovers your students’ learning gaps and misconceptions, giving you (the Teacher) personalized insights on where you (the Teacher) can intervene effectively.” The Teacher Assistant provides suggestions for following-up with students through the “Insights and Recommendations” section. Examples of suggestions include:

• Recommending specific “PLIX” activities to help students with low skill levels improve their skill levels.

• Noting which students are doing exceptionally well on the current concept, and suggesting new concepts to keep those students challenged.

• Information about the top question(s) students answered incorrectly, with the recommendations for students to review the following question(s) and the related paragraphs.

• Information on which students are not reaching the goal of 10 correct answers on the Adaptive Practices, and recommending to remind students to complete that goal.

##### 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 CK-12 Interactive Middle School Math 7 for CCSS meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

The assessments regularly provide opportunities for students to demonstrate the full intent of grade-level standards and practices through a wide variety of assessment types, such as multiple choice, drag and drop, matching, short answer, true/false, computational response, and discussion response. Students use different types of modalities to demonstrate their understanding in assessment, including short answer explanations and multi-layered questions. The Inline Questions and Review/Quiz Questions are connected to standards and practices. The End of Chapter Assessments have the content standards identified on the answer keys.

##### 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 CK-12 Interactive Middle School Math 7 for CCSS partially provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials have accommodations that are built into every Review Questions/Quiz. Teachers can set the number of attempts allowed, adjust the time limit, allow students to pause and resume, show hints, show solutions, or shuffle the questions. Teachers are able to alter these quizzes by choosing from item sets or adding their own questions. As a result, these items have the potential to alter grade-level expectations due to the fact that these are teacher-created itemsA Word version of the End of Chapter Assessments is included, making these assessments customizable. Both assessments are only available in English.

#### 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 CK-12 Interactive Middle School Math 7 for CCSS do not meet expectations for Student Supports. The materials provide manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials partially 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, and partially provide extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity. The materials do not provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

##### 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 CK-12 Interactive Middle School Math 7 for CCSS do not meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics. The materials have some general strategies, but they do not explicitly provide specific strategies and supports for differentiating instruction to meet the needs of students in special populations or support their regular and active participation in the learning of grade-level mathematics.

##### 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 CK-12  Interactive Middle School Math 7 for CCSS partially meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

The program provides occasional opportunities for students to engage with grade-level mathematics at higher levels of complexity through Adaptive Practice and Review Questions.  However, these are additional to the lesson so not all advanced students would be provided access to them. The advanced students would be completing more assignments than their classmates. Examples include, but are not limited to:

• In Lesson 2.3, Adding Integers and Other Rational Numbers,  Review Questions, the Teacher Notes state, “To customize the questions click here:” Under Assign to Class, Customize, Add question set, various “hard” questions may be assigned. For example, in “Set 1, Question 4, Simplify \frac{14}{70}+\frac{74}{35}.” (7.NS.1)

• In Lesson 7.4,  Theoretical Probability Models,Review Questions, the Teacher Notes state, “To customize the questions click here:” Under Assign to Class, Customize, Add question set, various “hard” questions may be assigned. For example, in “Set 1, Question 1, Steve was asked to pick a number from 1 to 100. The probability of obtaining a prime number is 0.12.” (7.SP.5 & 7.SP.6)

##### 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 CK-12  Interactive Middle School Math 7 for CSS 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.

Students can demonstrate learning through Inline Questions, Review Questions, and Adaptive Practice. The Interactives offer additional opportunities for students to demonstrate their learning. Some of the Discussion Questions offer multiple solution paths, and the Inline and Review Questions give immediate feedback to the student. Student reports provide levels of mastery: beginning, exploring, developing, proficient or mastery. These reports give the students an idea of how well they are doing on a specific concept.

Throughout the materials students work through Interactives that have a variety of outcomes. Students also answer Inline and Review Questions and have discussions that build off of the Interactives. For example, in Lesson 1.3, Identifying Proportional Relationships in Tables, Activity 2, the Teacher Notes state, “This Interactive shows 12 tables, each with 4 x-y values. Students are instructed to click on the tables that show proportional relationships. Once students click the tables they believe are correct, there is a button at the bottom labeled ‘Check.’ Once students click this button, a message will appear telling them whether or not they selected the correct tables, correct tables will turn green, and incorrect tables will turn red. At this point, you can encourage students to persevere in solving the Interactive. Students can click the red tables again to un-select them and can ‘check’ again if they wish.” (7.RP.2)

Students have opportunities to share and compare their thinking with others. In many lessons, students discuss their findings during the Interactives and following Inline Questions. Sometimes students are asked to compare their thinking with others. Examples include:

• In Lesson 1.5, Unit Rate and The Constant of Proportionality, Activity 1, the Discussion Question asks, “Jamal comes to the conclusion that the unit rate and the constant of proportionality are the same thing. Do you agree with Jamal or disagree? How are the constant of proportionality and the unit rate of a relationship similar and how are they different?” The Teacher Notes state, “This question has been designed to help students analyze the arguments of others and construct a viable argument. Encourage the students to look through previous activities and lessons to build evidence that supports the differences and similarities that they will use to either support or disprove Jamal's argument.” (7.RP.2)

• In Lesson 2.1, Combining Opposite Numbers,  Activity 3, the Discussion Question directs students to, “Discuss other types of situations that you could use a number line to help you with.” The teacher notes state, “This question is open-ended, designed to get students to think beyond the typical number line.“ (7.NS.1)

Students are able to reflect on their work and understand where they are in their learning through different reports, like the Heat Map. The reports that the student receives on the Adaptive Practice give feedback based on the difficulty level of each question answered, but there is no self-reflection.

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

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

The materials reviewed for CK-12 Interactive Middle School Math 7 for CCSS partially provide opportunities for teachers to use a variety of grouping strategies. The program does include materials designed for each child’s regular and active participation in grade-level content. However, the majority of the lessons are based on individual instruction. Lesson instructions in the Teacher Notes provide teachers with suggestions for grouping strategies that include small-group options, working with partners and individual instruction. However, there is no guidance provided to the teacher on how to assign partners or on how to form the group based on the different needs of the students. Examples include, but are not limited to:

• In Lesson 3.5, Solving Multi-Step with Rational Numbers, Activity 1, Shopping Discounts, Discussion Question, Teacher Notes suggest, “The students should begin with a turn and talk or small group discussion to help form their arguments. The discussion should then transition into a full class discussion to allow the students the opportunity to analyze the arguments of their classmates.” (7.EE.B) There is no guidance as to how to form the small groups.

• In Lesson 4.9, Solving Problems Involving Taxes, Commissions, and Fees, the Warm Up’s Extension Activity gives a recommendation in the Teacher Edition. It states, “Allow students to pair up and write questions in the format of the previous two questions where they provide a sales price and either an amount of tax or a price after taxes. Their partner will have to guess in which state they could have purchased the item. Students can take turns.” There is no guidance as to how to form the pairs. (7.RP.3)

##### 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 CK-12  Interactive Middle School Math 7 for CCSS partially meet expectations for providing 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 provide a means to change the language of the main text to any of the supported languages, which includes the directions for the Interactives. However, the text within the Interactive will not change, and the video content will still be in English. Additionally, the Adaptive Practice, which is expected to be homework, is available in two languages: English and Spanish. The materials do not provide any other strategies or support for students who read, write, and/or speak in a language other than English beyond changing the language of the text.

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

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

The materials reviewed for CK-12  Interactive Middle School Math 7 for CCSS partially provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials do not contain many images depicting people. The Interactives have images of things or shapes.  Students with disabilities are not included. Since this is a digital series, the names in the text can be changed to make it more relatable to students. Many of the questions do not use names, just non-specific gender terms such as the following: you, the student, the class, ... etc.  Although athletes in pictures are generally male, an equal number of male and female names are used. However, only a few names appear to represent different races. Examples include:

• In Lesson 2.1, Combining Opposite Numbers, Activity 2, it begins, “Peter is painting his wooden fence white.” (7.NS.1)

• In Lesson 2.6, Multi-Step Addition & Subtraction Problems Involving Rational Numbers, Activity 2, it explains, “Cheryl's friend Annika is visiting her in Washington DC.” (7.NS.2)

• In Lesson 7.3, Discerning Between Equally Likely and Non-Equally Likely Outcomes, Activity 1, it states, “Sai and his friend Kai are rolling dice to see who gets the higher number.” (7.SP.C.7)

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

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

The materials reviewed for CK-12  Interactive Middle School Math 7 for CCSS do not provide guidance to encourage teachers to draw upon student home language to facilitate learning. There is no evidence of promoting home language knowledge as an asset to engage students or purposefully utilizing student home language in context with the materials.

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

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

The materials reviewed for CK-12  Interactive Middle School Math 7 for CCSS do not provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning. While there is some culture implied by names or problem contexts, specific guidance on how to connect students' cultural and/or social background to facilitate learning or motivate students is not found.

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

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

The materials reviewed for CK-12  Interactive Middle School Math 7 for CCSS do not provide supports for different reading levels to ensure accessibility for students. While there are some videos and other tools available under the Related Content section, they do not identify strategies to engage students of different reading levels to ensure accessibility. Some of the Teacher Notes suggest that teachers encourage the students to use the proper vocabulary, but the materials provide no specific strategies for supporting students at different reading levels or grouping students by reading levels.

##### 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 CK-12  Interactive Middle School Math 7 for CCSS meet expectations for providing manipulatives, both virtual and physical. They are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials provide suggestions and/or links for virtual and physical manipulatives that support the understanding of grade-level concepts. Manipulatives are accurate representations of the mathematical objects they represent and are sometimes connected to written methods. Physical manipulatives, while not included with the series, are listed in the beginning of the Teacher Edition under the Resource tab. The use of physical manipulatives is minimal.

Each lesson contains several Interactives where students use virtual manipulatives to gain an understanding of the math standard they are learning. They include a variety of manipulatives such as: graphs, x-y tables, number lines, coordinate planes, GeoGebra Interactives, word matching problems, tape diagrams, dice and playing cards. Examples include:

• In Lesson 1.1, Unit Rate and Proportionality, Activity 3, students are understanding rates as a ratio. It states, “If a car travels 300 miles in 5 hours, how far does it travel in 1 hour? How far does a car travel in 1 hour if it travels 350 miles in 5 hours? Drag the car back and forth to determine how many miles the car drives in one hour.  When looking at the point value for the car, the x-value is the hours, and the y-value is the miles.“ (7.RP.1)

• In Lesson 6.2, Area and Circumference of Circles, Activity 1, students use the Interactive to discover parts of a circle. It states, “Students will be practicing labeling the parts of a circle: radius, center, diameter, and circumference. At the bottom are draggable words that students can place on the black line next to the appropriate part. If a work is placed in the wrong spot, it will turn red.” (7.G.4)

#### 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 CK-12 Interactive Middle School Math 7 for CCSS integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, and the materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

##### 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 CK-12 Interactive Middle School Math 7 for CCSS integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, when applicable.

The materials integrate technology in ways that engage students in the grade-level standards and are aligned to the standards and the Mathematical Practices. Third party programs such as Geogebra are used to assist with simulations and the data collection tool. Insight is available for teachers to use to gauge engagement and performance. Each lesson includes Interactives that relate to the concept and engage students in the process of learning. However, the Interactives cannot be customized.

##### 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 CK-12 Interactive Middle School Math 7 for CCSS include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

Students can collaborate with other students through the CK-12 Cafe, Math, and PLIX Corner. The Math Corner is for students to ask questions or help other students. The PLIX Corner is where students can discover and discuss the Interactives found throughout CK-12 concepts. Teachers are also able to collaborate with students through the Math and PLIX Corner.

Teachers can collaborate with other teachers through the CK-12 Cafe, Jumpstart for Educators, which allows all teachers with access to the materials, to “ask questions, collaborate, and explore CK-12 in this forum for educators.”

##### 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 CK-12 Interactive Middle School Math 7 for CCSS have a visual design that supports students in engaging thoughtfully with the subject and is neither distracting nor chaotic.

The lessons follow a consistent format and the print, as well as any graphics, are easy to follow and do not detract from the math. Each lesson starts with a Warm Up and is followed by activities that contain Interactives with Inline Questions and sometimes Discussion Questions. At the end of each lesson is a set of Review Questions for students. This format is consistent in each chapter throughout all grade levels. The graphics are visually appealing and support student understanding of the concepts. The font size, directions and text are appropriate for the grade level.  The format is engaging, and the Interactives have clear directions that make them easy to use.

##### 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 CK-12 Interactive Middle School Math 7 for CCSS provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

All lessons include embedded technology in the form of Interactives. The Teacher Notes give guidance on how to use the technology to enhance student learning. Inline and Discussion Questions often follow these Interactives. Examples include:

• In Lesson 4.8, Calculating Simple Interest, Activity 3, the Teacher Notes on the Interactive state, “This Interactive helps students practice finding the interest, given the principle amount, rate and amount of time. First is the scenario, next the breakdown of what each value is, and lastly, the text box for the answer. When the student types in their answer and presses Check, they will find out if their answer was correct or not and if they are correct, they can either move on or try a new number.” (7.RP.3)

• In Lesson 8.1, Analyzing Data Sets Visually and Numerically: Review, Activity 2, the Teacher Notes on the Interactive state, “In this Interactive, students will get to experiment with how changing data affects the mean and mean absolute deviation. In this data set, there are five values that can range from one to nine. Below that are the mean and mean absolute deviation of the current data set. Students can use the sliders above each number to change its value. The mean and MAD will automatically be calculated as each value changes. “ (7.SP.4)

## Report Overview

### Summary of Alignment & Usability for CK-12 Interactive Middle School Math for CCSS | Math

#### Math 6-8

The materials reviewed for CK-12 Interactive Middle School Math 6-8 for CCSS 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 partially meet expectations for Usability. Within Gateway 3, the materials partially meet expectations for Teacher Supports (Criterion 1), meet expectations for Assessment (Criterion 2), and do not meet expectations for Student Supports (Criterion 3).

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

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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