## CK-12 Interactive Middle School Math for CCSS

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## Report for 6th Grade

### Overall Summary

The materials reviewed for CK-12 Interactive Middle School Math 6 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 6 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 6 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.

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

The materials reviewed for CK-12 Interactive Middle School Math 6 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 3 states, “A basketball player makes 84 out of 100 free throw attempts.  a. Find the percent of free throws that the player makes.  b. At this rate, how many free throw attempts should it take to make 210 free throws?” (6.RP.3c)

• In Chapter 6, Item 1 states, “Write and evaluate: the sum of four to the third power and 35.” (6.EE.1)

• In Chapter 6, Item 4 states, “Use the numbers 48 and 30 to answer the following questions:  a. What is the greatest common factor of the two numbers?  b. Use the GCF to write the sum in the form __( __ + __ ).” (6.NS.4)

• In Chapter 7, Item 3 states, “Toby is driving 50 mph on the highway. He wants to know the relationship between how far he drives and how long it takes.  a. What is the independent variable? What is the dependent variable? How do you know?  b. Write an equation to represent the relationship between the two variables. Let x represent the independent variable and let y represent the dependent variable.  c. Create a table and graph. How do the values in the table and graph relate to the equation?” (6.EE.9)

• In Chapter 10, Item 1a states, “You want to create a study about the diet of cats. Write a statistical question for your study. Explain why it is a statistical question.” (6.SP.1)

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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 6 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:

6.RP.A, Understand ratio concepts and use ratio reasoning to solve problems.

• In Lesson 2.2, Activity 3 states, “Students can make up their own kind of sharks with a given number of rows and series of teeth. They can draw pictures of their sharks and give them names. In a small group, students can find the unit rates of teeth per shark and order the sharks from the greatest number of teeth to the least number of teeth.” (6.RP.2)

• In Lesson 2.9, Activity 1, Question 2 states, “A percent is a rate per 100. How would you write 95% and 105% as rates per 100?” (6.RP.3c)

6.NS.C, Apply and extend previous understandings of numbers to the system of rational numbers.

• In Lesson 5.4, Question 4 states, “ Find the distance between -23 and 13.” (6.NS.6a)

• In Lesson 5.10, Activity 2, Question 4 states, “Look at the points (3, 5) and (3, -5). The points have the same x-value, but they are located in different quadrants. How can you find the distance between the two points?” (6.NS.8)

• In Lesson 8.3, the Warm Up states, “Which movement would take you farther left, a vertical movement of -2 or a vertical movement of +2?” (6.NS.7a)

6.EE.B, Reason about and solve one variable equations and inequalities.

• In Lesson 7.1, Activity 2 states, “What variable can we use to represent the distance from each planet to the Sun?” (6.EE.5)

• In Lesson 7.4, Activity 3 states, “If you have \frac{1}{4} of a variable on one side and you add three more fourths to that side of the balance beam, what operation can be used to represent this?” (6.EE.7)

• In Lesson 8.6, Question 6 states, “Write the solution set for the inequality. Include at least three values in your solution set. y ≥ 3” (6.EE.8)

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

• In Lesson 4.4, students are multiplying decimals using the standard algorithm. Activity 2 states, “Rachel has a motorized mini bike with a fuel tank that holds 0.32 gallons. The cost of gas in her neighborhood is $2.859 per gallon. Use the interactive to see how much it costs to fill Rachel's mini bike with gas.” (6.NS.2) • In Chapter 9, there are multiple lessons on finding the area of various shapes, 9.3 Area of Quadrilaterals, Lesson 9.4 Area of Triangles, and Lesson 9.5 Area of Polygons. (6.G.1) #### 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 6 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 6 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 eight out of ten, which is approximately 80%. • The number of lessons devoted to major clusters of the grade (including assessments and supporting clusters connected to the major clusters) is 79 out of 96, which is approximately 82%. • The number of days devoted to major clusters (including assessments and supporting clusters connected to the major clusters) is 87 out of 107, which is approximately 81%. 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 81% 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 6 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 6 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 2.4 connects 6.RP.3 and 6.NS.3. Students divide whole numbers by decimals and use the rate to solve problems. For example, in Activity 3, students find and compare rates, “Usain Bolt also known as ‘Lightning Bolt’, is the fastest sprinter of all time. He ran 100 meters in 9.58 seconds, and he ran 200 meters in 19.19 seconds. Which race was his fastest speed?” • Lesson 6.9 connects 6.NS.B and 6.EE.4. Students factor expressions by finding a common factor and using the distributive property. For example, in Activity 3, Inline Question 5 states, “Look at the expression 12x + 20. Select the equivalent expression. a) 4(3x + 5), b) 6x + 10, c) 2(6x + 10), d) 3x + 5.” • In Lesson 9.2, students find the area by composing triangles into rectangles (6.G.1) and identifying what the formula would be with letters representing numbers (6.EE.2). In Activity 3, Inline Question 1 states, “In general, for a tangram with side length s, what is the area of all the pieces? a) 2s, b) 4s, c) 8s, d) s^2”. • Lesson 9.3 connects 6.G.1 and 6.EE.2. Students use written formulas to find the areas of parallelograms or trapezoids. An example is , “Area of a parallelogram = base x height, where height is the line that forms a right angle between the bases.” • Lesson 9.10 connects 6.G.4 and 6.EE.2. Students find the surface area by evaluating expressions with a letter representing a number. For example, in Activity 2, Inline Question 4 states, “If a cube has a side length of s units, which expression could be used to represent the surface area? a) 6s^2, b) (s^2)^6 c) 6s, d) 4s^2. ##### 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 6 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 6.6 connects 6.EE.A with 6.EE.B as students evaluate expressions and examine how variables can be used in place of numbers. For example, in Activity 1, Inline Question 4, students use a variable in an expression, “Instead of writing out the number of reflected images, replace this phrase with r. Which expression can you use to find the measure between the two mirrors when there are r reflections? a. 360+r, b. \frac{360}{r}, c. 2r, d. \frac{r}{360}.” • Lesson 7.9 connects 6.RP.A with 6.EE.C. Students solve problems involving ratios and identify how the variables are related. For example, in the Activity 3 Interactive, students see the ratio of the toys to actual size and determine what is the independent and dependent variable. The Interactive states, “Use the interactive below and your knowledge of equivalent ratio equations to complete the interactive. Remember that the ratio of the height of toys to the height of the characters is 1:5.” • Lesson 9.7 connects 6.G.A with 6.NS.B as students solve volume problems using decimal operations. For example, in Activity 3, Inline Question 2 states, “(Fill in the Blank) Recall that the volume of the sandbox is 37.5 cubic feet and one bag of sand that fills 0.5 cubic feet costs$4.50. It will cost the school ____________ to fill the entire sandbox.”

• Lesson 10.4 connects 6.SP.A with 6.SP.B. For example, in Activity 2, Inline Question 3 states, “Here is the test score data again (in ascending order): 77, 83, 83, 85, 87, 90, 93, 94, 99. The median of the test scores is 88.5, since the middle two values are 87 and 90, and the average of those two is 88.5. What is the mean of the whole set?” In Activity 3, Discussion Question 1 states, “How can you use measures of center to describe a data set?”

In the Grade 6 materials, there is not a connection between 6.NS.A and 6.EE.B. In Chapter 3, students multiply and divide fractions, but students do not solve equations with variables. For example, in Lesson 3.10, the Inline Questions for Activity 1 are: “1) If Anna has two bottles of polish and each holds 15 ml, how many total ml of polish does Anna have? 30 2) How can Anna find the total number of manicures she can give with all the nail polish she has? Anna can __ the total number of mL of nail polish by the fraction of a mL it took to give one manicure. Highlight the word that goes in the blank: Reciprocal, Multiply, Divide, Subtract 4) If Anna uses \frac{9}{10} ml for one manicure and she has 30 ml nail polish, how many manicures can she give? a. \frac{3}{10}b. 30 c. 27 d. \frac{100}{3} 4) If Anna uses \frac{4}{5} ml for one manicure and she has 60 ml nail polish, how many manicures can she give? a. 60 b. \frac{1}{75}c. 75 d. 48.”

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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 6 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 are as follows:

• In Lesson 3.1, Dividing a Fraction by a Whole Number, Teacher’s Edition,  Previous Learning Objectives, “recognize and write equivalent fractions ” (4.NF.A.1), the Teacher Notes states, “Students should be comfortable with representing fractions with diagrams.  It will help them visualize the statements they are working on throughout the chapter.”  relating (6.NS.A.1) back to (4.NF.A.1)

• In Lesson 9.1, Break Into Triangles, the Teacher’s Edition, the Teacher Notes states, “...students will review the concept of area and what it is used for. Students should recall how they partitioned shapes into equal parts; they will use this method of decomposing throughout the chapter to understand area and the area formulas.” relating the focus standard (6.G.A.1) back to the previous standard (3.G.A.2).

There are also instances where standards from earlier grades are identified, but there is no connection given. For example, in Lesson 2.6, Introducing Percentages, the Teacher’s Edition lists the Previous Learning Objectives.  For example, one objective states  “Recognize and write simple equivalent fractions (halves, thirds, sixths) (3.NF.A.3.B)”, but there is no connection to the concepts within the lesson.

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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 6 for CCSS can be completed within a regular school year with no modification.

As described below, the lessons and assessments provided within the materials can be completed in 161 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. There are Adaptive Practice problems available for homework. 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 suggested amount of time to complete the lessons and assessments is viable for one school year with no modification.

• Lessons typically follow this format:

• Warm up: Ranging between 5-25 minutes

• Two to Four Activities: Ranging between 10-35 minutes each

• Review Questions: 15 minutes

• The typical lesson length is 90 minutes, but lessons range from 60 to 120 minutes.

• There are 10 chapters. Each chapter ends with an assessment, and the chapters include from nine to eleven lessons.

• No lessons are marked as supplementary or optional.

• There are 106 lessons altogether. The total number of minutes (8275) was divided by an average class period of 55 minutes. This computation resulted in approximately 151 days of instruction. There are 10 days for 10 chapter assessments, for a total of 161 days.

### Rigor & the Mathematical Practices

The materials reviewed for CK-12 Interactive Middle School Math 6 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 6 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,

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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 6 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.

Chapters 1 and 2 provide students with opportunities to develop conceptual understanding of understanding ratio concepts and use ratio reasoning to solve problems (6.RP.A) with the use of Interactives and Inline Questions. Examples include:

• In Lesson 1.2, Activity 2: Tape Diagrams, students manipulate a tape diagram to build a conceptual understanding of how two quantities form a relationship in the form of ratios. The Teacher Notes describe what the students do independently by stating, “This gives students a chance to practice visualizing and identifying ratios.” (6.RP.1)

• In Lesson 1.5, students complete tables of equivalent ratios and use values to answer questions (6.RP.3a). In Activity 2, students complete a table on beats in a sample song. The problem states,  “How many beats are there in this 12 second song sample? Use the table to find the total number of beats for 60 seconds of the song.” Once the table is completed, students answer the following Inline Questions: “1. What is the relationship between 24 seconds and 12 seconds? How can you use this to find the number of beats in 24 seconds? 2. For 12 seconds, the ratio of number beats to number of seconds is ___:12. 3. Since 48 seconds is four times 12 seconds, the number of beats in 48 seconds is ___times the number of beats in 12 seconds. There are ___ beats in 48 seconds. This works because the ratios 25:12 and _____ are equivalent.” Examples of practice questions for students to complete are problem 2, “If there are six campers per tent, how many tents for 30 campers?” and problem 10, “Complete the table 72:48, 36:24, 24:16, ___:12, 12:8.”

• In Lesson 2.8, Activity 2, students further develop their understanding of ratios by using a double number line to fill in the blanks based on a ratio and answering questions. For example, Item 2 states, “There are 4 thousand (4,000) pet tarantulas in the US. The number of turtles is 150% the number of tarantulas. How many pet turtles are there?” (6.RP.3)

Chapter 3 has multiple opportunities for students to work independently to build conceptual understanding of applying and extending previous understandings of multiplication and division to divide fractions by fractions (6.NS.1) through the use of Interactives. Examples include:

• In Lesson 3.3, Activity 3, students develop understanding of dividing a fraction by a fraction using a visual diagram. The teacher directions state how the students will use the Interactive in the activity to build this conceptual understanding. The materials state,  “Students are given a tape diagram and slider and a fraction (starting at 1). Students can use the slider to divide the diagram and the resulting fraction will appear above the slider.” (6.NS.1)

• In Lesson 3.6, Activity 1, students further develop their understanding of division of fractions through an Interactive where students manipulate a scale of a map to connect division with fractions. The Interactive introduces this to students by stating, “Pirate Captain Jim Hawkins designs a treasure map and draws out a 1 mile by 1 mile map of an island. He divides his map into smaller squares to make it easier to read.” (6.NS.1)

• In Lesson 3.9, Warm-Up, students work with an Interactive to divide fractions in the real-world situation of a water gun fight. The directions for the students read, “Use the Interactive to see how many times you can reload the water gun before you have to run to fill the bucket up with more water. Through this lesson, you will use tape diagrams to model fraction division and find the quotients.” (6.NS.1)

Chapters 6 and 7 have multiple opportunities for students to work independently to build conceptual understanding of applying and extending previous understandings of arithmetic to algebraic expressions and reasoning about and solving one-variable equations and inequalities (6.EE.A,B) through the use of Interactives. Examples include:

• In Lesson 6.9, Activity 3, students factor expressions using the distributive property. Inline question 4 states, “Write an equivalent expression for 20x + 30 by dividing both terms by 5,” and question 5 states, “Look at the expression 12x + 20. Select the equivalent expressions.” (6.EE.3)

• In Lesson 7.4, Activity 1, students develop understanding of solving equations in the form of 20x + 30 through an Interactive. In the Interactive, students use numbers to try to isolate and solve for x. The student directions state, “Answering the question above will require knowledge of multiplication equations. Multiplication equations have many similarities with addition equations. Use the Interactive below to explore these similarities and to practice solving multiplication equations visually.” (6.EE.7)

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

The materials reviewed for CK-12 Interactive Middle School Math 6 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 (6.NS.2,3; 6.EE.1,2).

In Chapter 4, the materials develop and students independently demonstrate procedural skill and fluency in adding, subtracting, multiplying, and dividing multi-digit numbers and decimals with standard algorithms (6.NS.2,3). Examples include:

• In Lesson 4.2, “There are widget interactives that will guide students through the standard method of adding and subtracting decimals. Students can work an unlimited amount of times, so they should practice the method until they are comfortable before moving onto the real-world examples” (purple text). The first CK-12 Widget Interactive gives students step-by-step procedures on adding decimals, for example “8.153 + 1.535.” Students independently practice with numerous problems before moving onto the second part of the Interactive where they now have to “carry over/borrow” a 1, for example “7.242+1.846,” but the same step-by-step procedures are followed. Again, the student can practice independently as much as needed. The second CK-12 Widget Interactive focuses on subtracting decimals, again giving the same step-by-step procedures. The problems get increasingly more difficult,  for example, “2.972 - 1.141; 6.268 - 1.948,” and students can practice independently with an unlimited amount of problems. (6.NS.3)

• In Lesson 4.4, Activity 2 Interactive, students multiply multi-digit numbers. The teacher directions state, “This Interactive gives students a walk through for multiplying two decimals. Use the text boxes to evaluate the product one step at a time, after a student has typed in their answer they should press the enter key to see if it is correct. If it is wrong, it will turn red, and students can try again. Once a correct answer is entered it will turn black, and a new text box will appear.” In Multiplying Decimals with the Standard Method, students independently demonstrate procedural skill with multiplying decimals in all of the Review Questions. For example, Review Question 7 states, “ 1.7 × 9.691 = ____.” (6.NS.3)

• In Lesson 4.6, the Warm-Up: Practice Long Division “gives the student practice dividing with the standard method.” The Interactive provides the student step-by-step procedures on long division with problems such as 679 divided by 7. In Activity 1, Practice More Difficult Long Division increases the level of difficulty, for example “9460 divided by 43” but still gives the same step-by-step procedures. In Lesson 4.6, Activity 1 Interactive, students demonstrate fluency in dividing multi-digit numbers as students, “Use these Interactives to practice some more challenging and advanced long division problems! Can you answer the most difficult ones? 180482 = ? and 8692505 = ?” (6.NS.2)

In Chapter 6, the materials develop and students independently demonstrate procedural skill in writing and evaluating numerical expressions (6.EE.1) and writing, reading, and evaluating expressions in which letters stand for numbers (6.EE.2). Examples include:

• In Lesson 6.1, Activity 1: Can you make the math?, students write an expression from a word phrase. For example, Inline Question 1 states, “Which of the following correctly displays ‘one-third of the sum of a number and 5’?” answer choices: a. \frac{1}{3}(x+5); b. \frac{1}{3}+x+5; c. \frac{1}{3}x+5; d. \frac{1}{3x}+5.” Practice Questions 2 states, “Choose an expression for the following phrase: Four less than a number.” (6.EE.2)

• In Lesson 6.2, Activity 2 Interactive, students evaluate expressions involving whole-number exponents using sliders to see how the exponent is used to represent multiplication. The teacher directions state, “For this Interactive, students can experiment with different values raised to an exponent and see the resulting expanded expression. Students can use the red and blue slider to adjust the values of the exponent.” (6.EE.1)

• In Lesson 6.3, Activity 3 Interactive, students demonstrate fluency in writing expressions involving whole-number exponents using the Interactive to determine how many lights are needed and identifying it as an expression with exponents. The student directions state, “Use the Interactive below to figure out how many strings of LED lights you would need to decorate the Christmas tree on an ugly Christmas sweater.” (6.EE.1)

• In Lesson 6.4, Activity 3: What picture does connect the dots make? states, “This Interactive helps students practice evaluating expressions using order of operations with an added bonus of drawing a picture. An expression is given and students can use the buttons at the bottom of the window to choose which operand that should be used next.” For example, Inline Question 1 states, “Which order of operations would you do FIRST in this type of problem? 2(4 + 3)2 ÷ 7.” (6.EE.1)

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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 6 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 Chapter 1, students engage in routine real-world scenarios and demonstrate the application of ratio and rate reasoning. Lesson 1.3, Equivalent Ratios & Tape Diagrams, Activity 4, Inline Question 1 states, “You mix 12 cups of brown paint by using 3 cups of yellow paint to 4 cups of red paint to 5 cups of blue paint. After painting a portion of a fence you realize that you need more of the same color paint to finish the fence. This time you want to make 26 cups. How many cups of each color do you need?” (6.RP.3)

• In Lesson 7.8, Making Tables and Graphs, students write and solve routine equations of the form x+p = q and px=q and use variables to represent two quantities that change in relationship to one another. In Activity 1, students use the distance = rate times time equation to complete a table: “Complete the table for the Cheetah. The Cheetah travels at 105 feet per second. Write an equation for the Cheetah’s distance d over time t.” (6.EE.7 & 6.EE.9)

• In Lesson 9.4, Area of Triangles, Activity 2, students apply their knowledge of the area of a triangle in routine real-world contexts as they answer the following prompt, “Marielle wants to paint a triangular section of her house. One gallon of paint covers 400 square feet. Use the Interactive below to find the dimensions of the triangle section.” (6.G.1)

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 8.5 Inequalities with a Variable, in the Review Questions, students are asked to solve the following problem:  "After 3 dozen cookies, Anna has fewer than 24 to make. Describe the total number of cookies." (6.EE.8)

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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 6 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 1, students develop conceptual understanding of division of fractions with the interactive, Can You Design a Flag?. The materials state, “Students are given an adjustable flag that measures 1\frac{1}{5} m. Students can change the thickness of each portion by clicking and dragging the red points at the bottom of the flag. As the sections are adjusted, the fractions at the bottom will change, showing how much of the flag that portion is taking up. Students can toggle between a flag with 6 stripes and 3 stripes by clicking the button at the bottom right hand corner of the screen.” (6.NS.1)

• In Lesson 4.7, students demonstrate fluency with dividing decimals by decimals. For example, the practice problems include, “Find the quotient 31.93÷3.1. a) 10.3 b) 9.4 c) 12.6 d) 14.7.” (6.NS.3)

• In Lesson 1.5, Activity 3, Inline Questions, students demonstrate application of ratios in the Interactive about bicycles. Some examples include: “1. What is the relationship between 16 teeth in the back gear with 8 teeth in the back gear? How can you use this to find the number of teeth in the front gear for every 8 teeth in back gear?  A. Since 8 back teeth is half the number of 16 back teeth, you can divide 44 by 2 to get the number of front teeth associated with 8 back teeth.  B. Since 16 back teeth is two times 8 back teeth, you can multiply 44 by 2 to get the number of front teeth associated with 8 back teeth.  C. Since 8 back teeth is 16 back teeth minus 8, you can subtract 8 from 44 to get the number of front teeth associated with 8 back teeth.  D. Since 16 back teeth divided by 2 is 8 back teeth, you can divide 44 by 2 to get the number of front teeth associated with 8 back teeth. 2. Since 12 is halfway between 8 and 16, the number of teeth in the front gear will be halfway between 55 and the number of teeth associated with 8 back teeth. True/False” (6.RP.3)

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 1.3, students develop a conceptual understanding of equivalent ratios through tape diagrams. For example the Warm Up states,” What does “miles per gallon” mean?,” students use the Interactive to adjust miles and gallons to create equivalent ratios. Inline Question 1 states, “Which ratio of miles to gallon would a person driving the truck like to have?” Activity 4 states, “ How can you mix the color brown with paints?,” students apply their understanding of equivalent ratios to mixing paint. Inline Question 1 states, “You mix 12 cups of brown paint by using 3 cups of yellow paint to 4 cups of red paint to 5 cups of blue paint. After painting a portion of a fence you realize that you need more of the same color paint to finish the fence. This time you want to make 26 cups. How many cups of each color do you need?”

• In Lesson 2.6, students develop a conceptual understanding of percentages being a ratio per 100 in the Interactive in Activity 1, How Much of a Century Have You Lived? The materials state, “To start, students are given a number line with dates from 200 to 2100 in ten year increments. Below there is a text box where students can input their birthday (must be between 2000 and the current date) and press the enter key. Students will see a red line on the timeline showing the imputed date to today, and above that, the percent.” Inline Question 5 states, “(Fill in the blank) When you are 20 years old you will have lived __% of a century. When you are 50 years old you will have lived __% of a century. When you are 100 years old you will have lived __% of a century. When you are 101 years old you will have lived __% of a century.” In Practice, students develop procedural skills as they independently determine percentages as numbers out of 100. The materials state, “Write the following percent as a ratio out of 100. 3% a) \frac{4}{100} b) \frac{3}{100} c) \frac{2}{100} d) \frac{1}{100}.”

#### 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 6 for CCSS meet expectations for practice-content connections. The materials intentionally develop all of the mathematical practices to their full intent except for use appropriate tools strategically (MP5), which is partially developed.

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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 6 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 2.3, Price Unit Rates, students are asked to determine how much a veterinarian earns in a day. Since there are multiple variables, students must persevere to find a solution. Activity 2: How much does a veterinarian get paid each day? states, “Veterinarians, or vets, provide medical care to pets and other animals.  In 2015, (6.RP.3b) veterinarians normally got paid about \$88,490 per year. Vets often work 6 days a week and get as much as 20 days off of work a year (not including weekends), Use the interactive to determine how much money a veterinarian makes each work day.”

• In Lesson 4.6, Long Division, Activity 3, students are given a long division problem consisting of letters.  Two of the letters are given numeric value as shown below.  The students must figure out the remaining letters’ values.

?   ?   ?  O   ?   ?   L   ?    ?   ?

0   1   2   3   4    5   6   7   8   9

“In Activity 3, the students are presented a challenging problem for which they must analyze givens, constraints, relationships and goals.  The students are specifically encouraged to look for entry points and plan a solution pathway rather than guessing and checking values.” The challenge and scaffolding encourage student perseverance. (6,NS.2)

• In Lesson 6.2, Using Exponents, students work with fractal trees to figure out how many branches there are at each step and how it changes from step to step. In Activity 1, “the students use the Interactive to make conjectures about the relationship displayed.”  The challenging nature of this task encourages perseverance. (6.EE.1)

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 3.2, Dividing into Groups, students “use visuals to represent how repeated addition can be used to solve the division of a fraction by a fraction.” In Activity 1: Can you fill the video game health bar?, students experiment with a “health bar” for a video game, dividing it into different fractional parts, reasoning both abstractly and quantitatively.  The problem states, “Every time Maria drinks her health potion, she gets a health boost and a fraction of her health is returned to her health bar.  Find out how many health boosts it takes to fill her health bar.” (6.NS.1)

• In Lesson 5.5, Absolute Value on Number Line, MP2 is intentionally developed throughout the lesson using the Interactives and Inline Questions. During Activity 3: Making a Robot Part 4, students reason quantitatively and abstractly as they “develop a system for using absolute value to write a command which will count the number of steps a robot took.” (6.NS.7) Then students answer such Inline Questions as the following, “2. Look at the robot interactive again, If the robot takes 5 steps forward and 3 steps backward, how many total steps has he taken?” (6.NS.7)

• In Lesson 7.1, Equivalent Expressions, MP2 is intentionally developed throughout the lesson using Inline Questions. Following the Warm Up Activity: How Much Do Beaded Bracelets Cost?, students reason quantitatively and abstractly by answering Inline Questions such as, “2. Create an expression to represent the cost of 5 bracelets with 4 stars and 9 ovals each.” Also following Activity 2: Astronomical Relationship, students answer the Inline Question, “1. How can you describe the relationship between the distance from each planet to the sun and the planet’s orbital period based on the information at the bottom of the Interactive?” (6.EE.3)

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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 6 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 5.9, Distance on the Coordinate Plane, Standards for Mathematical Practice: “MP3: In the Introduction and Activity 1, the Discussion Questions provide the students the opportunity to form arguments and to analyze the arguments of their classmates.”  Warm - Up: Maps, Teacher Notes state: “This Interactive introduces distance on the coordinate plane within a real world context. Students can simply click and drag the red point at Dave’s House to count the distance between his house and the school. Either have students look up the distances between two places on Google Maps or use the map above to answer the questions below. Allow the students to construct an argument in small groups. Follow the small group discussions with a full class discussion to allow the students the opportunity to analyze the arguments of their classmates.”  (6.NS.8)

• In Lesson 7.4, Solving Multiplication Equations, Standards for Mathematical Practice: “MP3: The Discussion Questions in Activity 3 give the students the opportunity to form an argument and to analyze the arguments of their classmates.” Activity 3: Division Equations, in the Discussion Questions, Teacher Notes state: “Allow the students to discuss these questions using Turn and Talk or in small groups to allow them to construct viable arguments. After an argument has been formed, begin a full class discussion to allow students the opportunity to analyze the arguments of their classmates.” Discussion Questions; “1. How did you determine the value of x in the Interactive?  2. If you have \frac{1}{4} of a variable on one side and you add three more fourths to that side of the balance beam, what operation can be used to represent this? 3. How can you check that a value is an answer to an equation? 4. Becky claims that both multiplication and division problems can be solved using multiplication. Is she correct? Support your answer with evidence.”  (6.EE.7)

• In Lesson 8.4, Comparing with an Unknown, Standards for Mathematical Practice: “MP3: In Activity 2, the students develop an algorithm for identifying mystery number as fast as possible. The students share their algorithms and discuss the relative effectiveness, using evidence, of each algorithm.” Activity 2: Guess the Number, Discussion Question asks, “Which strategies were more effective in helping to identify the mystery number in the fewest guesses?  Write out a series of steps that you believe should be followed to find the answer as quickly as possible.” The Teacher Notes state: “Answers may vary. Ask the students to write an algorithm to formalize their steps as much as possible. The students will likely come up with different algorithms. Allow the students to share their algorithms in a class discussion. The students should analyze the different algorithms and use evidence to support which they feel would be most effective.”  (6.EE.6)

• In Lesson 10.5, Measures of Center and Variability, Standards for Mathematical Practice: “MP3: In activity 3, the students are given the opportunity to analyze an argument about the effect of outliers on the interpretation of a dataset.” Activity 3: 100 Meter Hurdles, the Discussion Question states: ”After the completion of Helena’s 18 meet season, her 18 hurdle times are listed: 17.99, 18.25, 17.50, 35.55, 17.42, 17.85, 17.33, 16.98, 32.43, 17.88, 18.10, 17.32, 17.09, 30.45, 17.64, 17.82.  The mean time is 20.475 seconds.  The median time is 17.835 seconds.  Philip claims that the median is the better measure of center because Helena appears to have fallen down making that time an outlier.  Do you agree or disagree? Support your stance with evidence.”  (6,SP.3 & 6.SP.5)

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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 6 for CCSS partially 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 1.5, Completing Tables of Equivalent Ratios, students use a table of equivalent ratios to model mathematical relationships in authentic contexts. In Activity 3: Which gears are best for bike riding? students virtually model with mathematics the ratios among gears. Activity 3 states, “Bicyclists change gears on their bikes to change the speed. Many bicycle enthusiasts say that 44:17 is the perfect gear ratio for normal bike riding. Using the next Interactive, observe how different gears will move by adjusting the ratio between them.” Students then answer the Discussion Question which states, “Which gears do you think are usually better for biking up steep hills, low or high? Why? Discuss in class or in the CK-12 Cafe. Do others agree? Critique their answers and defend your position!”(6.RP.3)

• In Lesson 5.3, Points on the Number Line, students use negative numbers to model quantities in real-world contexts of sea-level, money, and robotics. In Activity 3, Making a Robot Part 2, students model with mathematics as they move a robot in positive and negative directions. Students are tasked with developing a command to identify the location of the robot relative to its starting position. (6.NS.5)

• In Lesson 7.6, Writing Equations, students write equations to model authentic scenarios in computer programming and business. In the Warm-Up, students model with mathematics as they figure out how to represent buying multiple items of clothing. It states, “Camryn is a website developer who is developing a website for a retail store. She needs to write a program that will allow the user to buy more than one item at once. When this program is finished, it will work similar to the program below. What mathematical rules would allow this program to function?” (6.EE.9)

MP5 is identified, but it is not intentionally developed to meet its full intent in connection to grade-level content. Examples include, but are not limited to:

• In Lesson 5.2, Rational Number Line, students must create their own units of measure. In the  Activity 1: Rational Numbers, in the Interactive, the students are given a ruler. In Activity 2: Measuring Force, the students are given a spring scale. In Activity 3: Out in the Cold Part 2, the students are given a thermometer. Students are not given the opportunity to choose from a variety of tools or to work with a variety of tools to discover which would be the best to use. (6.NS.6)

• In Lesson 5.9 Distance on the Coordinate Plane, students discuss which tool would be the most appropriate for measuring a long distance. In the Warm-up: Maps, the Discussion Questions ask the students to determine the distance from the library to the post office. The Teacher Notes remind the teacher to be sure to point out the challenges of using tools except for Google Maps. The next two questions discuss how a GPS calculates distance. There are no other tools used. (6.NS.8)

• In Lesson 9.1, Break Into Triangles, in Warm-Up: Area, Discussion Question 5, it states, “You want to measure the area of a large rectangular field in square feet. How could this be done with a single piece of paper that is 1-foot by 1-foot? What other tools would be more effective, and would you use them to find the area of the field?” In subsequent activities, they are given the strategy of decomposing shapes. Students are not given the opportunity to use appropriate tools strategically. (6.G.1)

• In Lesson 9.7 Volume of Prisms, students discuss the efficacy of the various tools which could be used to find volume. In all the activities the students use unit cubes to determine volume. There is no choice of other tools. There is one Discussion Question that asks the students to speculate on what other tools may be used. (6.G.2)

• In Lesson 9.2, Compose into Rectangles, students are asked questions regarding tools as they estimate the area of a circle. This is not 6th grade level content. (7.G.4)

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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 6 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 1.1, Introducing Ratios, the Teacher’s Edition includes, “In this lesson, students will learn that a ratio is used to describe the relationship between two quantities. They will use ratio language to describe quantities involving recipes, colored blocks, and butterflies. Throughout the lesson, it would be helpful to allow students the time to practice using ratio language to describe things in the classroom” (6.RP.1)

• In Lesson 5.6, The Four Quadrants, at the beginning of the lesson, the Teacher Notes state, “It would be helpful to define the terms horizontal and vertical, so students can use these terms throughout the lesson to describe an object's location on a coordinate plane.” (6.NS.C.6)

• In Lesson 5.7, Points on the Coordinate Plane, the Warm-Up states, “We can describe the position of an object by the location on the x-axis number line and the y-axis number line. The location of the object can be written using the coordinate (x, y) where x is the location of the object along the x-axis and y is the location of the object along the y-axis. Use the Interactive below to practice using coordinate notation.” (6.NS.6)

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 1.1, Introducing Ratios, Activity 1, Inline Questions 2 state, “Angie wants to bake cookies for a bake sale. The recipe says, ‘for every 1 cup of butter use 3 cups of flour.’” You can use the word ratio to show the relationship between quantities. What is the ratio of butter to flour in one batch of cookies?” (6.RP.1)

• In Lesson 5.5, Absolute Value on Number Line, Activity 1 states, “The absolute value of a number is the distance of that number from zero. The absolute value of 23 is 23, because it is 23 units from zero. The absolute value of -12 is 12, because it is 12 units from zero. The absolute value symbol is written using a straight vertical line on either side of the number or expression. The absolute value of 5 is written \left|5\right|.” (6.NS.7)

• In Lesson 10.4, Mean, Median, Mode, and Range, the Warm Up states: “A measure of center is a single number used to describe a set of numeric data. It describes a typical value from the data set. Measures of the center include the mean and the median. The mean (or what is more commonly referred to as the average) of a data set is the sum of the data values divided by the number of data values in the set. As you saw in the Warm-Up, the mean can be thought of as "evening out" the data values. The range is a measure of spread. You can find the range by taking the greatest data value and subtracting the least data value. In other words, it is the difference between the maximum and minimum data point.” Activity 2 includes, “The median represents the middle value of an ordered data set. It is another measure of center.” (6.SP.2 & 6.SP.5)

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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 6 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 2.7, Percentages with Tape Diagrams, MP7 is intentionally developed throughout the lesson as “students break percentages down to increments and use increments of ten percent to find and estimate percentages.” The Warm Up directs students to, “Use the interactive to find the percent of the field a sprinter runs with a parachute. Find the distance she runs at 10%, 20%, 25%, and 50% of the field.” Students use the structure of percentages to determine the answer. (6.RP.3)

• In Lesson 3.5, Finding Rectangle Dimensions, Warm Up,  students use the interactive to create a visual model of fraction division.  The model’s structure is then tied to the equivalent fraction multiplication expression. The Inline Questions help students make the connection between division and multiplication of fractions. For example, Question 3: “What are some ways to rewrite \frac{1}{3}\div5 ? a) \frac{1}{3}\times\frac{1}{5} b) \frac{1}{5}\times\frac{1}{3} c) 3\times5 d) \frac{1}{3}\div\frac{1}{5} (6.NS.1)

• In Lesson 9.5, Area of Polygons, students make use of structure as they “use their existing knowledge of area formulas to derive formulas for the areas of regular and irregular polygons.” For example, in Activity 1, students decompose irregular polygons into known shapes in order to determine their area. (6.G.1 & 6.EE.2)

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

• Lesson 1.3, Equivalent Ratios & Tape Diagrams, In Activity 1, the students are asked to use repeated reasoning to make a conjecture about the relationship between arrangements of objects and the number of objects.” Activity 1: How many boxes of gel pens do we need to buy?  Discussion Questions: “#1 The teacher needs at least one pen each student for a full class of 18 students.  How many different ways can you get 18 pens?  #2 How many different ways can you get 24 pens?  #3 Is there a general method you could use to find the different ways to get a given number of pens if you didn’t know the class size? #4 Are all the arrangements you found ideal in a real-world context?” (6,RP.3)

• In Lesson 4.8, Using Greatest Common Factor, MP8 is intentionally developed as the students play the "mystery number" game more than once and use repeated reasoning to look for general methods and shortcuts when playing the game.”  Activity 3: “Can you guess the number? See if you can guess the mystery number in the game below!  The number is between 1 and 100. After your guess, you will see the GCF between the mystery number and your guess.  Can you find the number in 20 tries?” Teacher Notes “Students are given an empty table with columns labeled Common factors, Guess, GCF. Students can guess the mystery number by typing in a value at the bottom and clicking Guess. The value will be inputted into the table as well as the GCF of the guess and actual value.”  (6.NS.4)

• In Lesson 9.5, Area of Polygons, students intentionally develop MP8. In this activity, students use an interactive to explore breaking a polygon into triangular pieces and, “use repeated reasoning to construct a general expression for the area of a regular polygon using triangles.” The  Discussion Questions ask, “1. How could an expression for the area of the hexagon in the interactive be written as the sum of triangles? 2. How could an expression for the area of a pentagon be written as the sum of triangles? 3. How could an expression for the area of an octagon be written as the sum of triangles?” (6.G.1 & 6.EE.2)

### Usability

The materials reviewed for CK-12 Interactive Middle School Math 6 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 6 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 6 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 6.9, Distributive Property, the Introductory Teacher Notes states, “Students will continue to work with expressions in this lesson, specifically using the distributive property. Students should remember what they have learned about finding the greatest common factor. While working it may help to remind them that the process will be similar; they want to find the greatest common factor between two values. To start, students will review factors and then move on to writing equivalent expressions within a context. It might be helpful to remind students of the definition of equivalent expressions and provide some examples. If students are having trouble writing expressions within the given contexts, give them some simple expressions to practice using the distributive property.” (6.EE.3; 6.NS.3; 6.NS.4)

• Answers to all Inline Questions

• Instructions for help with the Interactives. For example, in Lesson 9.10, Nets, Activity 1, the Teacher Notes state, “This Interactive helps students think about different ways nets can be arranged. To start, students are given a rectangular prism (the birdhouse) on a 2D rectangle (the wooden board). Students can use the red circles to rotate and move the rectangle. Use the sliders at the bottom to open the prism into a net and see different arrangements of the net. Students can click and drag anywhere on the plane to rotate the polyhedra. Zoom using a mouse wheel or two fingers on a trackpad. Students should see if they can find a net arrangement that can be cut from the given rectangle.” (6.G.1-4)

• Possible answers, further questions, and discussion ideas for the Discussion Questions are in the following examples.  In Lesson 10.5, Measure of Center and Variability, Activity 3, Discussion Question, the Teacher Notes say, “The students should notice that Helena falling over a hurdle is not an outlier. She falls down regularly, approximately 1 out of every 6 races. The data is becoming bimodal, meaning that there are two underlying scenarios, races where Helena falls down and races where she does not. The median gives us a clearer idea of what time Helena can expect if she completes the race cleanly. Her coach is likely interested in both: the mean because it gives an indication of how likely Helena is to complete the race cleanly while the median gives a clear idea of where Helena fits, in terms of her speed, relative to other members of the team.” (6.SP.3; 6.SP.5d)

• 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 lesson-planning:

• 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 with.

• Learning Objectives—goals for each lesson.

• Agenda—here 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 6 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 6 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 3.1, Dividing a Fraction by a Whole Number, lists the following as Previous Learning Objectives: Write a fraction that represents a given diagram or picture (3rd); Recognize and write simple equivalent fractions (halves, thirds, sixths) (3.NF.3b); and Recognize and write equivalent fractions (4.NF.1).

• Lesson 4.5, Dividing Decimals in Diagrams, lists the following as Previous Learning Objectives: Compare two decimals to the hundredths place (4.NF.7) and Use visual models to multiply multi-digit decimals (6.NS.2-4).

• Lesson 6.4, Order of Operations, lists the following as Previous Learning Objectives: Identify parts of an expression using mathematical terms (sum, product, quotient) (6.EE.2b); View one or more parts of an expression with parentheses as a single entity (6.EE.2b); and Understand that exponents represent repeated multiplication (6th).

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 3.1, Dividing a Fraction by a Whole Number, the Adaptive Practice Teacher Notes state, “Students should be comfortable with representing fractions with diagrams, it will help them visualize the statements they are working with throughout the chapter.” (6.NS.1)

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

• In Lesson 5.1, Positives and Negatives, 6.NS.5 and 6.NS.6c are listed as Focus Standards, 6.NS.6a is listed as an Additional Standard, and the standards for mathematical practice listed with the lesson are MP2, and MP4. The Learning Objectives are the following: Understand that positive and negative numbers are used together to describe quantities having opposite values, recognize that the opposite of the opposite of a number is the number itself, explain the meaning of 0 in situations with positive and negative numbers, position integers on a vertical number line diagram, and use positive and negative numbers to represent quantities in real-world contexts.

• In Lesson 8.2, Comparing Absolute Values, 6.NS.7d is listed as a Focus Standard, 6.NS.7 is listed as an Additional Standard and the standards for mathematical practice listed with the lesson are MP1 and MP2. The Learning Objective is, “Distinguish comparisons of absolute value from statements about order.”

• In Lesson 10.9, Using Box Plots, 6.SP.4 and 6.SP.5 are listed as Focus Standards, and the standards for mathematical practice listed with the lesson are MP2 and MP3. The Learning Objectives are the following: Identify the components of box plots, and answer questions about a data set using a box plot.

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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 6 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 6 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 6 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 1.3, Equivalent Ratios & Tape Diagrams, Activity 2, How is a ruler sort of like a tape diagram?: Blank Paper (1 Sheet), Ruler, and Pencil.

• In Lesson 4.8, Using Greatest Common Factor, Activity 1, What shapes can you make shapes on a clock?: 1 Blank Sheet of Paper, Pencil, and Ruler.

##### 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 6 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 6 for CCSS partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.

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 3.9, Dividing Fractions with Diagrams, Warm-up, Inline Question 2, “Create a diagram to represent 1\frac{3}{7}+\frac{5}{7}. How many sections will there be in a diagram?” and Review Question 6: “Divide the following fraction. Be sure to convert any improper fraction to a mixed number. \frac{3}{4}\div\frac{1}{2}”

• Chapter 2, Rates and Percentages, Question 1: “(6.RP.A.2, 6.RP.A.2, 6.RP.A.3.b) Ken drove 80 miles in 2 hours. Assume he drove at a constant speed. a. Write a ratio between Ken’s distance and time.”

• Chapter 6, Expressions, Question 2: “(6.EE.A.2.c, 6.EE.A.3) Use the expression 4x-2*3+5^2 to answer the following questions. a. Write an equivalent expression.”

##### 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 6 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 6 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 6 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 6 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 6 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 6 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 5.4, Symmetry on the Number Line, 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, The distance between the points 4 and -6 is -2.“ (6.NS.6)

• In Lesson 8.2, Comparing Absolute Values, 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 2, Identify the Absolute Value of \left|-144\right|.” (6.NS.7)

##### 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 6 for CCSS 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 2.4, Constant Speed Unit Rate, Activity 1,  students use an Interactive to “track the distance that a train goes over time.” The Teacher Notes state, “Students can use the PLIX to model speed along a number line. They begin with a single rate and then experiment with changing speeds.” (6.RP.3)

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

• In Lesson 1.4, Double Number lines & Equivalent Ratios, Activity 4 asks, “How do you mix brown paint?” The Discussion Question asks, ” When do you think you would prefer to use a tape diagram and when would you prefer to use a number line? Discuss with your class or in the CK-12 cafe!” The Teacher Notes on this question state, “Answers may vary. Some students may prefer to use a tape diagram when each numerical increment has an associated value. Allow the students the opportunity to discuss their answers as a class. A class discussion will provide students the opportunity to analyze the arguments of their classmates.” (6.RP.3)

• In Lesson 5.10, Absolute Value as Distance on the Coordinate Plane, Making a Robot Part 8, Activity 3, the Discussion Question asks, “The next step is to build the function which will return the number of steps taken by the robot. What would this function look like in two dimensions? How would the function return the number of steps taken both horizontally and vertically? Allow students to discuss how absolute value can be used to find the total number of steps taken by the robot. The students should realize that every time a number is entered into either the stepsX(n) function or the stepsY(n), the absolute value of the number entered will need to be added to the total number of steps taken. “ (6.NS.7 & 6.NS.8)

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 6 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 5.6, The Four Quadrants, Activity 3, Making a Robot Part 5, Discussion Question, the Teacher Notes direct teachers to “allow students to discuss the questions above. The goal is for the students to determine that the current forward and backward notation will not be sufficient, and a left and right command with similar notation will be necessary.” (6.NS.6) While the goal of the discussion is stated, there is no suggestion as to how to form the small groups based on the student needs.

• In Lesson 10.5, Measures of Center and Variability, Activity 1, Determining the Difference - Center or Variability? The Teacher Notes state, “This activity could be used as the basis of a classroom discussion in order to help students see that some questions are answered by considering variability rather than the center. The activity might be difficult for students if it's the first time they have thought about statistical questions that could focus on variability too. Thus, it might work best in a small group setting or as a whole group class discussion.” (6.SP.3 & 6.SP.6) While there is the suggestion that this be done small or whole group, there is no guidance as to how to form the small groups based on the student needs.

##### 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 6 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 6 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 1.5, Completing Tables of Equivalent Ratios; Activity  2, the picture is of males racing bikes. Then in the Extension Activity for the same lesson the picture is that of a male riding a recumbent bike. (6.RP.3)

• In Lesson 7.5, Defining Independent and Dependent Variables, Activity 1 states, “Noreen is an engineer who ran a test to determine whether solar panels produce more energy at warmer or cooler temperatures.” (6.EE.9)

• In Lesson 7.6, Writing Equations,  Activity 2, the example given states, “Darius and three friends go out to dinner. They decide to split the bill between them equally. Write an equation to represent this relationship. Use x to represent the independent variable and y to represent the dependent variable.” (6.EE.9)

##### 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 6 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 6 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 backgrounds 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 6 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 6 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 1.4, Double Number Line & Equivalent Ratios, Warm-up Activity, students solve problems as they use ratio reasoning. It states, “With the following Interactive, practice labeling points by where they belong on the number line.”  (6.RP.3)

• In Lesson 8.5, Inequalities with a Variable, Activity 1, students are learning about inequalities that include a variable. It states, “For this Interactive, students will practice matching inequality symbols to their meaning. Students should read the directions and click ‘Start’ when they are ready. They will have 15 seconds to match as many inequalities as they can. If they get an answer incorrect, it will turn red and students can guess again.” Following this activity, there are three Inline Questions which are all multiple choice. (6.EE.8)

#### 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 6 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 Math6 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 6 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 6 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 6 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 3.11, Comparison Division, Activity 1, the Teacher Notes on the Interactive state, “Students get a chance to work with fractions within the context of time and scheduling. Students can type in the amount of hours (between 0-24) they spend on a certain activity in the text boxes. Once students have entered a number they can see the fraction of the day that that activity takes up. Students can type in their own activity in the bottom row of activities. The total row will show how many total hours they have used and the fraction of the day that is taken up by an activity. If students use all of their 24 hours and try to input more hours for another activity they will get a notification at the bottom of the screen that says: ‘There are only 24 hours during the day.’”(6.NS.1)

• In Lesson 8.9, Multiple Inequalities, Activity 1, the Teacher Notes on the Interactive state, “For this Interactive, students will practice graphing compound inequalities on a number line. Students drag the red points along the number line to plot the solutions to the given inequality. Students then click the points to create an open circle or closed circle. Once students have graphed the inequality, they can click the 'Check' button. If the graph is correct, it will turn green and students can try another inequality.” (6.EE.5, 6.EE.6, 6.EE.7, & 6.EE.8)

## 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

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### Overall Summary

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###### Usability
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