## CK-12 Interactive Middle School Math for CCSS

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### Overall Summary

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS partially meet expectations for Alignment to the CCSSM. In Gateway 1, the materials for Grade 8 meet expectations for focus and coherence by meeting expectations for focus and meeting expectations for coherence. In Gateway 2, the materials for Grade 8 partially meet expectations for rigor and practice-content connections by meeting expectations for rigor and partially meeting expectations for practice-content connections.

###### Alignment
Partially Meets Expectations
Not Rated

### Focus & Coherence

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for focus and coherence. For focus, the materials assess grade-level content and spend at least 65% of class time on major work of the grade, and for coherence, the materials have supporting content that enhances focus and coherence, are consistent with the progressions in the Standards, and foster coherence through connections at a single grade.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

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

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for not assessing topics before the grade level in which the topic should be introduced. Overall, the materials assess grade-level content and, if applicable, content from earlier grades.

##### Indicator {{'1a' | indicatorName}}
The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 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 3, Item 1 states, “Diana and Bruce work at different car dealerships. Diana earns a base salary of $20,000 plus a commission of$200 per car sold. Bruce has no base salary but earns a commission of $1,000 per car sold. Set up an equation to represent the number of cars sold for which Diana's total salary will equal Bruce’s. Solve the equation.” (8.EE.7) • In Chapter 4, Item 3 states, “A police department imposes a fine of$15 for every mph (miles per hour) over the speed limit. d. A bill passes to add a base fine of $25 to the$15 for every mph over the speed limit. Graph the new total fine, y, for driving x miles per hour over the speed limit including the $25 base fine.” (8.EE.5) • In Chapter 7, Item 1 states, “While walking through the zoo, you keep track of the number of animals and the number of people at different exhibits. Let the number of animals be the input and the number of people be the output. Each coordinate point represents a different animal exhibit in the form (input, output): (2, 8) (4, 3), (1, 10) (0, 2) (4, 7) a. How many people were at the exhibit with no animals? b. How many animals were in the exhibit being visited by 7 people? c. Graph the coordinate points. Determine whether the relation is a function or not. Explain.” (8.F.1) • In Chapter 8, Item 3 states, “A company wants to transport grain in cylindrical barrels. The barrels have a radius of 11 inches. If each barrel needs to hold 12,705 cubic inches of grain, what must the height of the barrel be? Use ???? = 3.14. Round your answer to the hundredths place if necessary.” (8.G.9) • In Chapter 9, Item 3 states, “There are about 3.2 million public school teachers in the US. The average teacher has 15.9 students. Estimate the total number of students in the US. Express your answer in scientific notation.” (8.EE.3) #### Criterion 1.2: Coherence Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade. The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for devoting the majority of class time to the major work of the grade. Overall, the materials spend at least 65% of class time on major work of the grade. ##### Indicator {{'1b' | indicatorName}} Instructional material spends the majority of class time on the major cluster of each grade. The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for spending a majority of class time on the major clusters of the grade. • The approximate number of chapters devoted to major clusters of the grade is ten out of ten, which is 100%. • The number of lessons devoted to major clusters of the grade (including assessments and supporting clusters connected to the major clusters) is 81 out of 87, which is approximately 93%. • The number of days devoted to major clusters (including assessments and supporting clusters connected to the major clusters) is 91 out of 97, which is approximately 94%. 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 94% of the instructional materials focus on major clusters of the grade. #### Criterion 1.3: Coherence Coherence: Each grade's instructional materials are coherent and consistent with the Standards. The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for coherence. The materials have supporting content that enhances focus and coherence, are consistent with the progressions in the Standards, and foster coherence through connections at a single grade. The materials partially have an amount of content designated for one grade level that is viable for one school year. ##### Indicator {{'1c' | indicatorName}} Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for supporting work enhancing 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 8 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 6.2 connects 8.EE.5 and 8.SP.2. Students identify trends in scatter plots that compare two sets of proportional data. For example, in Activity 1, Inline Questions 1 and 2, students use data from two graphs to answer questions on comparing and identifying trends, “1. Which of the following data sets would have a positive trend? Multiple Choice: The amount of money you make vs the hours you work at a job paying$15 per hour. 2. Imagine drawing a line through the center of the data for MLB Homeruns from 1871 to 2017. Which of the following is true? Multiple Choice: As the x values get larger (increase), the y values get larger (increase).”
• Lesson 8.2 connects 8.G.9 and 8.EE.A. In the warm-up, an energy drink design introduces how the dimensions of a soda can have a significant impact on sales and profit. In the next two activities, students use the formula, which is provided, to find the volume of a cylinder and how cylinders of different height and radius can have the same volume. Activity 3 states, “Imagine that you have been tasked with creating a new energy drink. You are responsible for naming the drink and designing the can. The can needs to be able to hold 12 ounces of liquid which is equivalent to approximately 354.88 cubic centimeters. To add extra space for air in the can, the volume needs to be 360 cubic centimeters. You are responsible for designing the dimensions of the can. Choose the radius first and then solve for the accompanying height. Use 3.14 as a value for pi.”
• Lesson 10.4 connects 8.NS.1 and 8.EE.2. Students use rational and irrational numbers when evaluating square roots. For example, in Activity 2, Inline Question 3 states, “You know that the square root of 9 is 3 and the square root of 16 is 4. You also know that the numbers 10 - 15 lie between 9 and 16, so their square roots will lie between 3 and 4. Knowing this, match the following numbers with their approximate square roots.”
##### Indicator {{'1d' | indicatorName}}
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS partially meet expectations for the amount of content designated for one grade level being viable for one school year in order to foster the coherence between grades.

As described below, the lessons and assessments provided within the instructional materials can be completed in 97 days. Within each lesson, there is Related Content aligned to the lesson, but there are no instructions for teachers as to when, or how, to assign the Related Content to students. The materials also do not indicate how long completion of the Related Content might take. The suggested amount of time to complete the lessons and assessments is not viable for one school year, and although the Related Content would add to the suggested time, the lack of guidance for teachers regarding the Related Content would require modifications to be made to the materials to be viable for one school year.

• According to the Publisher’s Orientation Video, the average time for a lesson is approximately 50 minutes, and lessons can be completed in one class period. For the majority of the lessons, the length ranges from 40 to 60 minutes, with the majority being 50 minutes in length.
• There are 10 chapters. Each chapter ends with an assessment, and the chapters include varying amounts of lessons.
• No lessons are marked as supplementary or optional.
• There are 87 lessons that would each last for one day, and there are 10 days for 10 chapter assessments, for a total of 97 days.
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Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for being consistent with the progressions in the Standards. The instructional materials clearly identify content from prior or future grade-levels. The instructional materials give all students extensive work with grade-level problems, and the materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The instructional materials clearly identify content from prior or future grade-levels and relate it to grade-level work. Eighth grade standards are identified in a list at the beginning of each lesson and in the Curriculum Guide of the Teacher Edition, in which you can see Standards by Lesson, Lessons by Standard, and Focus Standards for Grade 8 standards. Each lesson lists a grade-level Standard, and for some lessons, there are Additional and Pre-requisite Standards listed, examples include:

• Lesson 2.3, Solving for Missing Angles in Parallel Lines and Triangles, lists 8.G.5, and 7.EE.4a and 7.G.5 are listed as Pre-requisite Standards.
• Lesson 7.2, Domain and Range, lists 8.F.1, and 6.EE.9 and 7.RP.2 are listed as Pre-requisite Standards.
• Lesson 10.9, Solving Problems Using the Pythagorean Theorem, lists 8.G.7, and 6.G.1 is listed as a Pre-requisite Standard.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. 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:

8.EE.C, Analyze and solve linear equations and pairs of simultaneous linear equations.

• In Lesson 3.4, Activity 3 states, “Use the distributive property to solve the equation in the interactive below. $$20(11x + 16 ) = -29$$.” (8.EE.7)
• In Lesson 5.2, Activity 3, Question 5 states, “Why is there no solution to the system: $$5x - 2y = 7$$ and $$5x - 2y = 4$$?” (8.EE.8)

8.F.B, Use functions to model relationships between quantities.

• In Lesson 7.1, Activity 3, Question 1 states, “Find the rule for this function and fill it into the blank. Input: 2, 5, 9, 11, x; Output: -4, -1, 3, 5, x - 6.” (8.F.4)
• In Lesson 7.4, Activity 2, Question 2 states, “The length of a rectangle is 2 more than the width. What equation describes the length as a function of the width?” (8.F.4)

8.G.A, Understand congruence and similarity using physical models, transparencies, or geometry software.

• In Lesson 1.2, Activity 1 states, “Previously, you have learned that translations move an image a certain distance in a specific direction without changing the size or shape of the image. Every point of the image is moved the same distance and in the same direction. How can you be sure that the size or shape of the image hasn’t been changed? Use the interactive below to examine whether the corresponding side lengths and angles of both shapes are equal.” (8.G.1)
• In Lesson 2.3, Activity 2 states, “Explore angles, parallel lines, and transversals in architect plans for a bridge in the interactive below.” (8.G.5)

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

• In lesson 2.2, Activity 3 Discussion Question, students create arguments for angles of triangles, “What do you notice about the exterior angles of all triangles?” (8.G.5).
• Chapter 6 has multiple lessons that build upon the use of scatter plots with various data: “Lesson 6.1, Representing Data in Scatter Plots; Lesson 6.2, Linear Patterns in Scatter Plots; and Lesson 6.3, More Patterns in Scatter Plots.” (8.SP.1)

The materials for Grade 8 explicitly relate concepts to prior knowledge from previous grades, and examples include:

• Lesson 2.1 lists a focus standard of 8.G.5 and a pre-requisite standard of 7.G.5. Teacher Directions state, “The lesson kicks off with a review of special angles from 7th grade (vertical, complementary, supplementary). The instruction segues into what happens when two non-parallel lines are cut by a transversal and then, naturally, parallel lines cut by a transversal. Once students see that certain angles end up with the same measurement, move on to introducing the idea that corresponding angles of parallel lines are equal.”
• Lesson 3.1 lists a focus standard of 8.EE.7 and pre-requisite standards of 6.EE.2 and 7.EE.4a. Teacher Directions state, “This lesson picks up from 6th grade and 7th grade standards. The main shift here is to equations with variables on both sides of the equal signs.”
• Lesson 7.1 lists a focus standard 8.F.4 of and pre-requisite standards of 6.EE.9 and 7.RP.2. Teacher Directions state, “In this lesson, the language about input/output/functions is connected to prior learning in 6th grade relating to independent and dependent variables. Students should understand that one way of representing functions is to write a rule to define the relationship between the input and the output and that functions are special types of rules where each input has only one possible output.”
• Lesson 8.1 lists a focus standard of 8.G.9 and pre-requisite standards of 6.G.2 and 7.G.4. Teacher Directions state, “This lesson begins with accessing prior knowledge about volume of prisms. Students should know from past experience that volumes of prisms are found by multiplying the area of the base by the height.”
• Lesson 10.2 lists a focus standard of 8.EE.2 and pre-requisite standard of 6.EE.1. Teacher Directions state, “This lesson starts with the prerequisite knowledge from earlier grades in a discussion of how people found the area of a square and the volume of a cube. From there, students are asked to figure out a missing dimension if only volume or area is given. Only perfect squares and cubes are used in this lesson.”
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Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. The materials include learning objectives that are visibly shaped by CCSSM cluster headings, and the materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade.

Examples of learning objectives visibly shaped by CCSSM cluster headings include:

• In Lesson 10.6, one of the Learning Objectives is, “Understand the relationship between the legs and hypotenuse of a right triangle as Pythagorean Theorem,” and in Lesson 10.7, one of the Learning Objectives is, “Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world problems.” These objectives are visibly shaped by 8.G.B, Understand and apply the Pythagorean Theorem.
• In Lesson 7.3, two of the Learning Objectives are, “Identify whether a relation is a function or not” and “Understand that a function is a rule that assigns to each input exactly one output.” These objectives are visibly shaped by 8.F.A, Define, evaluate, and compare functions.

The materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, and examples include:

• Lesson 4.2 connects 8.EE.B with 8.F.B. In Activity 2, Proportional Relationships in Medicine Continued, “The paramedics and EMTs arrive upon the scene at an emergency, they need to be able to make smart decisions quickly. If they arrive on the scene and a patient has chest pain they might give the patient Diltiazem to relax the muscles and increase blood flow in the patient’s chest. The amount of the medicine they give would depend on the patient’s weight. A graph of this relationship is shown in the interactive below. Use the interactive to populate the table, determine the relationship between weight and medicine dosage and express that relationship as an equation.”
• In Chapter 7, students construct a function to model a linear relationship between two quantities (8.F.4). For example, in Lesson 7.4, Activity 2, Inline Question 1 states, “Rebecca earns $17 per hour at her new job. Which equation describes the total amount of money earned as a function of time, x?” Also, in Lesson 7.8, a Review Question states, “The cost of producing a smartphone is$42.73 per phone. Additionally, the smartphone company pays a flat rate of $175 to ship each store’s order. Write an equation to model the costs for the smartphone company, y, to produce x number of smartphones and ship them to one store.” • In Chapter 8, students know and use volume formulas to solve problems (8.G.9). For example, in Lesson 8.8, Review Question 4 states, “A shipping box measures 16 inches by 12 inches by 8 inches. A second box has a similar shape but each dimension is $$\frac{3}{4}$$ as long. How does the volume of the second box compare to the volume of the shipping box?” The non-routine application problem within instruction is in Chapter 7. In Lesson 7.8, Activity 1, the Discussion Question states, “Think of a real-world example for a nonlinear relationship. Explain how you know the relationship is not linear using a table and graph.” ##### Indicator {{'2d' | indicatorName}} Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade. The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present independently throughout the program materials. Examples include: • In Lesson 4.2, students develop their conceptual understanding of graphing proportional relationships. In Activity 2, students “use the interactive to populate the table, determine the relationship between weight and medicine dosage, and express that relationship as an equation.” (8.EE.5) • In Lesson 5.1, Activity 1 Interactive states, “There are two water bottles that each hold 16.9 fluid ounces. Bottle A is slowly being filled with water at an average rate of 0.8 fluid ounces per second. Bottle B is full and has a small hole poked in it and is leaking water at an average rate of 0.5 fluid ounces per second. If bottle B starts to drain at the same time that bottle A begins to be filled, at what time will bottle A and bottle B have the same amount of water?” Through the interactive, students apply systems of equations to the real-world context. (8.EE.8b) • In Lesson 3.4, Activity 3, students develop procedural skill in solving 1-variable, linear equations. For example, Practice Problem 2 states, “Solve the equation: $$-46 = -4(3s + 4) - 6$$.” (8.EE.7) 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 2.5, Activity 1 Interactive, students develop conceptual understanding of similarity, congruence, and dilations. The materials state, “Recall that when an image is dilated, this causes the side lengths to change, but the angles remain the same. Two shapes that can be produced by dilating one to obtain the other are called similar shapes. Use the interactive below to determine whether the two shapes are congruent, similar, or neither.” In Activity 3, students apply their understanding of similarity and triangles in a real-world context. The materials state, “Thales knew that he had constructed similar triangles. Once the triangles were constructed, Thales used a proportion to compare the sides of one triangle to the corresponding sides of the other triangle to find the distance of the ship from the shore. How far was the ship from the shore in the picture below?” • In Lesson 4.1, Activity 3, students develop conceptual understanding of graphing proportional relationships and the constant of proportionality. The materials state, “The equation for a proportional relationship is $$y = kx$$ where x and y are the related quantities and k is the constant of proportionality. Use the interactive below to graph the relationship between minutes and the number of beats based on the equation.” A Supplemental Question states, “All of the graphs have been straight lines, do you think it is a coincidence? Why?” In the Practice problems, students develop procedural skill in solving direct variation equations. #### Criterion 2.2: Math Practices Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS partially meet expectations for practice-content connections. The materials explicitly attend to the specialized language of mathematics. The materials partially: identify and use the Standards for Mathematical Practice (MPs) to enrich mathematics content; attend to the full meaning of each MP; provide opportunities for students to construct arguments and analyze the arguments of others; and assist teachers in engaging students to construct viable arguments and analyze the arguments of others. ##### Indicator {{'2e' | indicatorName}} The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS partially meet expectations for identifying and using the Standards for Mathematical Practice (MPs) to enrich mathematics content within and throughout the grade-level. The materials state that teachers should use a few MPs in each lesson, but each lesson does not include guidance on which MPs to use. MPs are explicitly identified in the Teacher Notes, but MPs are identified once in Chapter 7 and twice in Chapter 5. Examples of the materials identifying and using the MPs to enrich the mathematics content include: • MP1: In Lesson 4.1, the Introduction includes, “In this lesson, students begin graphing relationships when given a verbal description, and then they move on to graphing from a table (MP1).” • MP2: Lesson 2.3 states, “In this lesson, angle measures are in the form of algebraic expressions (MP2). Students work out problems with parallel lines, triangles, and transversals. Students should use facts about all the angles formed when parallel lines are cut by a transversal. Additionally, students should use facts about angles that they learned in Grade 7, such as vertical, complementary, and supplementary angles.” • MP4: Lesson 8.6 states, “The interactive shows that the volume of the cylinder contains the volume of the cone and the sphere. Students should already know that the volume of a cone is $$\frac{1}{3}$$ the volume of the cylinder (see Volume of Cones). After this, you can move to helping them derive the equation. From there, students use the formula to calculate the volume of spheres in real-world and mathematical problems (MP4).” • MP5: Lesson 8.1 states, “Interactives and questions should help students derive the formula for the volume of a prism (MP5).” • MP6: Lesson 4.8 states, “This lesson focuses on how an equation in the form y = mx+b is a translation of the equation y = mx. Furthermore, two lines with the same slope but different y-intercepts, are also translations of each other. Attend to precision when discussing and defining b; b is not the y-intercept (MP6). Rather, b is the y-coordinate of the y-intercept. Students must understand that the x-coordinate of the y-intercept is always 0.” • MP7: Lesson 8.6 states, “In this lesson, interactives and questions help students understand the relationship between the volume of the cylinder and the sphere. They will look at a sphere inside a cylinder and a cone (all with the same radius and height). The questions help students see which dimensions (of the three shapes) are the same and get to the idea of the ratio relationship (MP7).” • MP8: This MP was identified in one lesson. Lesson 9.8 states, “This lesson also includes some problems that use addition/subtraction as a way to revisit the preceding lesson (MP8).” There are some instances in which the Mathematical Practices are labeled but do not enrich the content. For example, in Lesson 1.5, MP6 is identified in the Teacher Notes with, “Congruence is defined and students connect corresponding sides to congruent sides (MP6).” While congruence is defined, students are not prompted to use precise language and definitions. ##### Indicator {{'2f' | indicatorName}} Materials carefully attend to the full meaning of each practice standard The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of two MPs. Examples of the materials not attending to the full meaning of MP5 include, but are not limited to: • In Lesson 8.1, Teacher Notes, “This lesson begins with accessing prior knowledge about volume of prisms. Students should know from past experience that volumes of prisms are found by multiplying the area of the base by the height. They should make connections from these learnings to intuiting how the volume of a cylinder would be found. Interactives and questions should help students derive the formula for the volume of a prism (MP5). Once the formula is established, students should practice finding the volume in mathematical and real examples.” Students do not select which tools to use as they are provided. • In Lesson 8.6, Activity 1, the materials include, “As with the other shapes, you are going to have to be clever to determine how many cubic units can fit in a sphere. You can use the cube’s relation to a circumscribed cylinder to determine its volume. Circumscribed means constructed around a shape touching as many points as possible. Use the interactive below to explore this relationship.” Students do not select a tool for this investigation. Examples of the materials not attending to the full meaning of MP8 include, but are not limited to: • In Lesson 9.8, Teacher Notes, “This lesson is similar to the last one in that students must attend to precision with units in this lesson (MP6). They work through multi-step word problems that involve multiple operations (MP4). This lesson also includes some problems that use addition/subtraction as a way to revisit the preceding lesson (MP8).” Students do not express regularity in repeated reasoning to develop rules for multiplying and dividing numbers written in scientific notation as the rules are provided. • In Lesson 10.4, Activity 1, students read, “As you saw above, an irrational number is a number which cannot be written as a fraction. While you cannot write a fraction or decimal to express the number, you can estimate it’s value. Use the interactive below to explore this idea.” Students also answer the following four Inline Questions: “1. The square root of 71 is between what two whole numbers?; 2. The square root of 20 is between what two whole numbers?; 3. Choose the FALSE statements. (1) The square root of 33 us closer to 5 than 6. (2) The square root of 68 is closer to 9 than 8; and 4. Fill in the Blank: Since the square root of 100 is 10, the square root of 101 will be a (little or lot) larger than 10.” In Activity 2, “Irrational numbers have non-terminating and non-repeating decimals. Even though you cannot write non-terminating decimals in their entirety, you can place them on a number line. In the case of irrational roots, you can use perfect squares to help narrow down the location of the irrational value on a number line. Example: The $$\sqrt{95}$$ is between what two whole numbers? The largest square root that is less than 95 is 81. The smallest square root that is greater than 95 is 100. Since $$\sqrt{81}=9$$ and $$\sqrt{100}=10$$, you can say that the $$\sqrt{95}$$ is between 9 and 10. Use the interactive below to practice this strategy for approximating irrational numbers.” The materials present continuous guidance, and students do not look for and express regularity in repeated reasoning. ##### Indicator {{'2g' | indicatorName}} Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by: ##### Indicator {{'2g.i' | indicatorName}} Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS partially meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. The materials provide opportunities for the students to construct arguments about the content, and examples include: • In Lesson 1.6, Activity 2, Discussion Question, students identify if the images are congruent and construct an argument on why that was their answer. The Question states, “Is the image produced by a series of rigid motions congruent to its pre-image? How do you know?” • In Lesson 7.8, Activity 1, Discussion Question, students use their understanding of linear relationships to construct an argument about a real-world example of a nonlinear relationship. The question states, “Think of a real-world example for a nonlinear relationship. Explain how you know the relationship is not linear using a table and graph.” There are no opportunities for students to analyze the arguments of others, and examples include, but are not limited to: • In Lesson 5.5, Warm Up, the materials include, “There are three methods for solving systems of equations: graphing, substitution, and elimination. Take a break from solving and discuss when each method is most efficient.” Students are not prompted to provide feedback or analyze the arguments of their classmates during the discussion. • In Lesson 8.2, Activity 3, students discuss their design of an energy drink with the class. However, the materials do not state for students to provide feedback or analyze the arguments of others. The question states, “Discuss your design with your classmates or post in the cafe! How did you decide on your final dimensions?” • In Lesson 10.12, Activity 1, Challenge Question, students construct an argument to answer, “Mathematically, $$0.\bar{9}=1.0$$. How could you prove this? Join the discussion in the Math Cafe!” The materials do not state for students to provide feedback or analyze the arguments of others. ##### Indicator {{'2g.ii' | indicatorName}} Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. The materials include some examples of assisting teachers in engaging students to construct viable arguments and analyze the arguments of others, but there are also multiple instances where the materials do not assist teachers. Examples of the materials assisting teachers to engage students in constructing and/or analyzing the arguments of others include: • In Lesson, 1.10, Activity 1, the Teacher Notes state, “Allow students time to explore the interactive. Ask them to make a table to catalog 90°, 180°, or 270° both clockwise and counterclockwise. They should list the starting coordinate, the rotated coordinate, and what they believe the rule is. Have students share their ideas on what the rules are. The rules can be found in the next section. Why do you think a 90° clockwise rotation and a 270° counterclockwise rotation have the same rule? They both take the point to the same location going in different directions. They are equivalent rotations. What other rotations are equivalent rotations? A 90° counterclockwise rotation and a 270° clockwise rotation. Also a 180° clockwise rotation and a 180° counterclockwise rotation.” • In Lesson 3.5, Activity 2, Discussion Question, the Teacher Notes state, “Be sure to stress the connection to combining variables on both sides. Students could simply add revenue,$15, and cost, $6.25, in this case; they would need to subtract, make the expense negative or something along these lines. How much revenue will Jared earn if he sells 216 posters? What will his profit be? His revenue will be 216⋅15 =$3,240 and his profit will be $0. He will need to sell more than 216 to make a profit. He will make$8.75 profit for each poster he sells after the 216th poster. Do you think Jared should raise the sales price, lower the sales price, or that he won’t be able to make a profit at any sales price? Answers may vary. There is no right answer. The goal is to encourage students to discuss and understand the effect of a change in sales price on the solution to the equation and its general context.”
• In Lesson 5.1, Activity 3, Take Action, the Teacher Notes state, “Now you can answer the question "What are the financial benefits of going to college?" Answers may vary. Allow students to discuss their findings (MP3, MP4). The equations are $$y = 34,700x + 138,800$$ for the high school student and $$y = 62,000x - 128,000$$ for the college student.”

Examples where the materials do not assist teachers to engage students in constructing and/or analyzing the arguments of others include:

• In Lesson 2.2, Activity 3, Discussion Question, the Teacher Notes state, “Have students discuss their observations from the interactive. Emphasize that the exterior angles of any triangle appear to form a circle. Remind students that there are 360 degrees in a circle, which means the exterior angles of the triangle always sum to 360 degrees.” The materials encourage discussion among students, but they do not assist teachers in having students analyze the arguments of others.
• In Lesson 4.9, Activity 1, Supplemental Question, the Teacher Notes indicate that the question has multiple possible answers about situations with negative slopes, but there is no assistance as to how students construct an argument. The Teacher Notes state, “What are some situations that a negative slope could represent? Answers may vary: it could represent a falling rate like the amount of water in a water tank that is being drained. Any situation where a quantity is decreasing at a constant rate should be acceptable.”
• In Lesson 8.7, Activity 3, Supplemental Questions, the Teacher Notes provide questions to ask the students with specific answers given. The Teacher Notes state, “How do you think cutting the radius in half will affect the volume of the sphere? Why? Cutting the radius in half decreased the volume by a factor of $$2^3$$ or 8. The reasoning is the same as the above questions.” The materials do not assist teachers in having students analyze the arguments of others.
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for explicitly attending to the specialized language of mathematics. The materials provide instruction on communicating mathematical thinking using words, diagrams, and symbols. Examples include:

• In Lesson 2.4, students are introduced to scale factor and dilations. In the Warm Up, students are reminded, “Transformations change the location or orientation of an image but not the shape. Rigid motions are transformations that move an image, but do not change the size. The only transformation that is not a rigid motion is a dilation. A dilation is a transformation that changes the size of a figure.” In Activity 1, students read directions for the interactive and are also given important vocabulary. “To perform a dilation, you need to specify a scale factor and a center of dilation. The scale factor is the number which is used to multiply the size of the image. The center of dilation is the point from which the image is being dilated.”
• In Lesson 4.4, Activity 2, students connect the definition of linear relationships to the example from the Warm-up. “A linear relationship is a relationship that traces a line when plotted. As you may be able to tell by the first four letters in LINEar, the word linear means arranged in a straight line. Proportional relationships are a specific type of linear relationship where the starting amount is 0. All proportional relationships are linear because they form a straight line when graphed. However, not all linear relationships are proportional because they do not have to start at 0. In the example of the firefighter, you were dealing with a linear relationship between pressure and floor number. The pressure started at a given non-zero number and then increased by 5 psi for every floor.”
• In Lesson 7.1, the Teacher Notes include how the language relating to functions will connect with students prior knowledge. “In this lesson, the language about input/output/functions is connected to prior learning in 6th grade relating to independent and dependent variables.”

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

• In Lesson 3.1, the Teacher Notes include, “Be sure to consistently use the words ‘constant, coefficient, term, expression and equations’ with students throughout the lesson so that they can identify the different parts of the equations.” Activity 1 defines the terms for the students. Activity 2 uses the interactive to help the students identify the parts of an expression, and Activity 3 uses the interactive to help students identify the parts of an equation. There are Supplemental Questions that can be used, such as “ How can 5 be a constant, term and expression at the same time?” This allows the students to use the proper terminology in discussion.
• In Lesson 5.1, Activity 1, students read the definition of system of equations and an example related to an Interactive to help support them in the proper use of the mathematical language. The definition states, “A system of equations is two or more equations with the same set of variables. This means that the equations relate to each other. You can compare the values for the variables of both equations to determine information about the situation. The first situation relates to examining flow rates. Plumbers and engineers commonly face this problem rather than analysts, but it is a great tangible example to help one understand the concept. Engineers and plumbers need to have a strong understanding of flow rates when designing drainage systems. Fluids need to be able to leave the system faster than they enter to prevent back-up and overflow. The ability to measure the rate at which a fluid enters and leaves a system is vital to the performance of the system. Example There are two water bottles that each hold 16.9 fluid ounces. Bottle A is slowly being filled with water at an average rate of 0.8 fluid ounces per second. Bottle B is full and has a small hole poked in it and is leaking water at an average rate of 0.5 fluid ounces per second. If bottle B starts to drain at the same time that bottle A begins to be filled, at what time will bottle A and bottle B have the same amount of water?”
• In Lesson 10.6, Activity 1, students read the definition of the Pythagorean Theorem and have the opportunity to identify the sides through an interactive to help support the use of the mathematical language. The definition states, “The Pythagorean Theorem is stated as follows: The square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.” The Interactive is introduced to students as, “Use the interactive below to label the sides of a right triangle as either being the hypotenuse or the leg.”

### Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Not Rated

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
##### Indicator {{'3a' | indicatorName}}
The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.
##### Indicator {{'3c' | indicatorName}}
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
##### Indicator {{'3g' | indicatorName}}
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.
##### Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
##### Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
##### Indicator {{'3aa' | indicatorName}}
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

## Report Overview

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

#### Math 6-8

The instructional materials reviewed for CK-12 Interactive Middle School Math for CCSS partially meet expectations for Alignment to the CCSSM. In Gateway 1, the materials for Grades 6 and 7 meet expectations for focus and coherence by meeting expectations for focus and partially meeting expectations for coherence. In Gateway 1, the materials for Grade 8 meet expectations for focus and coherence by meeting expectations for focus and meeting expectations for coherence. In Gateway 2, the materials for Grades 6-8 partially meet expectations for rigor and practice-content connections by meeting expectations for rigor and partially meeting expectations for practice-content connections. Since the materials did not meet expectations for Alignment, Gateways 1 and 2, they were not reviewed for Usability in Gateway 3.

###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated
###### Alignment
Partially Meets Expectations
Not Rated

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

### Overall Summary

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