CK-12 Interactive Middle School Math for CCSS

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Overall Summary

The materials reviewed for CK-12 Interactive Middle School Math 8 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 8 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 8 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 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 \pi = 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) Indicator {{'1b' | indicatorName}} Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials reviewed for CK-12 Interactive Middle School Math 8 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: 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) 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 8 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 8 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 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. 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 8 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 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. The problem states, “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 provided formula 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.”

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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 8 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 4.2 connects 8.EE.B with 8.F.B. In Activity 2, Proportional Relationships in Medicine Continued,  the problem reads, “The paramedics and EMTs arrive upon the scene of 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.”

• Lesson 4.8 connects 8.EE.B with 8.G.A as students identify similarity using geometry software and connect it to understanding slope. In Activity 1, Example states, “Natalie is starting her own bike rental business but is debating on whether or not to charge a flat cost for renting a bike. Below are her two potential business models. Without Flat Cost: Natalie will charge $3 per hour. With Flat Cost: Natalie will charge$5 to rent the bike and then $3 per hour. Use the Interactive below to make a table and graph for these two business plans.” • Lesson 7.8 connects 8.F.A with 8.F.B. Students define functions and model relationships as they complete the following Learning Objectives: “Understand a linear function as points on a graph that form a straight line; Understand why a vertical line is not a linear function; Identify if a table of values represents a linear or non-linear relationship; Interpret the rate of change of a linear function in terms of the situation it models; Interpret the initial value of a linear function in terms of the situation it models; Give examples of functions that are not linear; and compare properties of two functions represented differently.” • Lesson 8.6 connects 8.G.C with 8.NS.A. Students identify volume of spheres with the use of the irrational number approximated to 3.14. For example, Activity 3 Interactive states, “Recently, six scientists lived in a dome for an entire year in Hawaii to simulate the environment on a mission to Mars. Use the dimensions of the dome, in feet, shown below to find the volume of the oxygen that the dome could contain. Use 3.14 as the value for \pi.” Indicator {{'1f' | indicatorName}} Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. The materials reviewed for CK-12 Interactive Middle School Math 8 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: • Lesson 2.1 lists a focus standard of 8.G.5 and a pre-requisite standard of 7.G.5. Teacher Notes 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 Notes 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 Notes 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 Notes 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 Notes 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.” There are few instances that allude to content related to future grades, but the future grade-level content is not identified. For example, in Lesson 8.5, Volume of Pyramids (Deeper Learning), the Teacher’s Edition, the Teacher Notes references future learning: “This lesson is optional and goes beyond the standard for 8th grade. Students should understand that when a cone has a square for a base, it is called a square pyramid”, but there are no specifics given of how the lesson connects to future learning. Indicator {{'1g' | indicatorName}} In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification. The materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS can be completed within a regular school year with no modification. As described below, the lessons and assessments provided within the instructional materials can be completed in 152 days. An average lesson is 90 minutes with additional material available through Related Modalities and practice problems. In addition, lessons include a daily review problem session which is typically 15 minutes long that 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 Five Activities: Ranging between 5-35 minutes each • Review Questions: On average 15 minutes in length • Most lessons are 90 minutes long, but lessons range from 60 to 120 minutes. • There are 10 chapters. Each chapter ends with an assessment, and the chapters include from six to twelve lessons. • No lessons are marked as supplementary or optional. • The total number of minutes (7785) was divided by an average class period of 55 minutes. This computation resulted in approximately 142 days of instruction. There are 10 days for 10 chapter assessments, for a total of 152 days. Overview of Gateway 2 Rigor & the Mathematical Practices The materials reviewed for CK-12 Interactive Middle School Math 8 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 8 for CCSS meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and do not always treat the three aspects of rigor together or separately. The materials partially meet expectations for spending sufficient time working with engaging applications of mathematics, Indicator {{'2a' | indicatorName}} Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. The materials reviewed for CK-12 Interactive Middle School Math 8 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 have multiple opportunities for students to independently develop conceptual understanding of congruence and similarity using physical models, transparencies, or geometry software (8.G.A) through the use of Interactives. Examples include: • In Lesson 1.5, first Interactive, students explore rotations to find shapes that are congruent. The student directions state, “Using the Interactive below, match any shapes that are congruent. Then answer the questions below it.” (8.G.2) • In Lesson 2.3, Activity 2, students develop understanding of finding angle measurements based on the side lengths of the triangle. The Interactive has students manually adjust the triangle to find the angle measurements. The student directions state, “Use the Interactive below to find the angles of a triangle with the ratio 2:3:4.” (8.G.5) • In Lesson 2.5, Activity 1, students develop understanding of similarity by identifying relationships between pairs of shapes. The student directions state, “Use the Interactive below to determine whether the two shapes are congruent, similar or neither.” (8.G.4) Chapter 7 has multiple opportunities for students to work independently to build conceptual understanding of defining, evaluating, and comparing functions and using functions to model relationships between quantities (8.F.A,B) through the use of Interactives. Examples include: • In Lesson 7.1, Activity 2, students use an Interactive to explore different numbers and operations when creating functions, which helps students understand what a function is. The student directions state, “All functions need a rule for determining the outputs for corresponding inputs. This rule can be complicated or as simple as adding one to the input. Use the Interactive below to create your own function.” (8.F.1) • In Lesson 7.3, Activity 2, students work in the Interactive by moving points on a coordinate plane and identify if a function is created. This develops understanding of what a function is and what the graph of a function looks like. The way to identify a function is stated as, “To determine whether a relation is a function, you need to check whether one input value leads to two different output values. If one input value does lead to two different output values, you will be able to tell visually because the two points will line up vertically. You can often find this using what is called ‘The Vertical Line Test.’” (8.F.1) • In Lesson 7.6, Activity 2, students write a function for a given graph, which develops understanding of analyzing graphs for functions. This is introduced to the students as, “Construct a function to represent the following situation: An app developer is looking at a graph which shows active users as a function of time. This means that the input value is the time and the output value is the number of people using the app at that time. The time 0 hours represents 12:00 AM EST. The graph shows that from 0 hours to 7 hours, the number of users stays constant at 600. From 7 hours to 12 hours, the number of users increases to 2,000. The number of users stays constant at 2,000 until 20 hours at which point the number of users decreases to 800 at 24 hours. Construct this function below.” (8.F.5) Indicator {{'2b' | indicatorName}} Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency. The instructional materials reviewed for CK-12 Interactive Middle School Math 8 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 (8.EE.7,8b). In Chapter 3, the materials develop and students independently demonstrate procedural skill in solving linear equations in one variable (8.EE.7). Examples include: • In Lesson 3.5, Review Questions, students demonstrate procedural skill in solving linear equations with a single variable on each side of the equation. Some examples include, “1. Solve: 8(2k-1)=13(2k+4); 2. Solve for y: 3(4y-2)=2(2y+5); and 5. Solve for x: 10x-4=2x+60. • In Lesson 3.8, students determine the number of solutions for an equation. Activity 1: Accounting For All Possibilities Continued explains how an equation can have an infinite number of solutions. The materials state, “$$.75(x+23) = .75x + 17.25$$; .75x + 17.25 = .75x + 17.25; 17.25 = 17.25. Any value for x would work so there are an infinite number of solutions.” Activity 2 contains No Solutions: “$$x = x - 1$$; if x = 0 then 0 = 0 - 1; 0 = -1. Since no value for x makes the statement true, there is no solution.” The practice page in the teacher edition provides independent practice. Examples include, “1. Does the following equation have no solution, infinite solutions, or exactly one solution? \frac{1}{3}(6k + 12) = 2k - 2 and 4. Does the following equation have no solution, infinite solutions, or one solution? 8(t - 1) = 2(4t - 5).” In Chapter 5, the materials develop and students independently demonstrate procedural skill in solving systems of two linear equations in two variables algebraically and estimating solutions by graphing the equations (8.EE.8b). Examples include: • In Lesson 5.2, the Interactives provide opportunities to input equations, and the Inline Questions help to direct an analysis of the graphs. For example, in Activity 1: Changing the Game, students input the equations y = 1.08x + 1.07 and y = 1.05x + 12.6 to determine if a basketball player should take a 2 point or a 3 point shot. Activity 3: Number of Solutions uses the Interactive to determine the amount of solutions, one, none or infinite, a problem may have. For example, Inline Question 3 states, “Look at each of the following as a second equation in a system with an equation 8x + 6y = 14. Decide if each system has 1 solution, no solution or infinite solutions.” Students develop procedural skill through practice questions at the end of the lesson or from the teacher edition, including, “4. Solve the system by graphing: y^2 - x - 44 = 0 and x - 2y = 4. or 2. Find the point of intersection of the graphs of the equations y = -x and y = x - 2,” respectively. (8.EE.8) • In Lesson 5.3, Review Questions, students solve multiple systems of equations independently using substitution. Some examples include, “1. Solve the following system of equations by substitution: x+2y-1=0, 3x-y-17=0; 4. Solve the following system using the substitution method. 2x + 3y = 5, 5x + 7y = 8; and 5. Solve the following system using the substitution method. 2x-5y=21, x=-6y+2.” (8.EE.8b) • In Lesson 5.4, Review Questions, students solve multiple systems of equations independently using elimination. Some examples include, “3. Solve the following system of equations by elimination. Express the solution as an ordered pair (x, y). 4x=-14-6y; -5x-6y=22 and 4. Solve the system using elimination. 3y-4x=-33, -5x-3y=40.5.(8.EE.8b) Indicator {{'2c' | indicatorName}} Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. The materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics. The materials include multiple opportunities for students to independently engage in routine application throughout the grade level, but the materials include limited opportunities for all students to engage, collectively or independently, in non-routine application problems. Examples of students engaging in routine application of grade-level skills and knowledge, within instruction and independently, include: • In Lesson 3.7, Writing and Solving Linear Equations, students write and solve routine linear equations in real-world contexts . Review Question 8 states, “The rent for a Toyota car contains two parts, one of which is a fixed charge of 100 dollars, and the other is 50 dollars for each day. Which equation correctly models the total cost of renting a Toyota car for x number of days?” (8.EE.7) • In Lesson 5.6, Writing and Solving Systems of Linear Equations, students solve routine problems using systems of linear equations in two variables . For example, Review Question 3 states, “Five years from now, a man’s age will be three times his son’s age and five years ago, he was seven times as old as his son. Find the present ages of father and son respectively.”(8.EE.8) • In Lesson 7.4, Equations of Functions, students construct a function to model a routine linear relationship between two quantities. 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?” (8.F.4)

• In Lesson 8.8, Comparing Volumes, students use a volume formula to solve problems. 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{1}{4} as long. How does the volume of the second box compare to the volume of the shipping box?” (8.G.9)

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

• In Lesson 7.6 Interpreting Graphs of Functions, Activity 3, students are given a graph and asked to determine what it might represent. The activity states, “Look at the user activity function graph below. Independently, construct a story of an app which would have this user activity. Be sure to explain any increases, decreases, and constants.“ (8.F.5)

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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 8 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 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

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

The materials reviewed for CK-12 Interactive Middle School Math 8 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 8 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 1.5, Defining Congruence, Students develop and test a strategy for mapping lines through transformations.  This encourages them to make sense of the problems and persevere in finding a solution. In Activity 1: Mapping Shapes, the students are asked to generalize a strategy for mapping one shape onto another using a series of rigid transformations in as few moves as possible. The Teacher Notes state, “Rather than telling the students that they are correct or incorrect, encourage the students to come up with more creative ways to improve on their own strategies and the strategies of their classmates.”  This further encourages problem solving and perseverance. (8.G.2)

• In Lesson 5.3, Solving Systems of Equations Using Substitution, “Students solve puzzles that visually simulate systems of equations.” In Activity 1: Understanding Substitution, students work with five interactive puzzles “to develop strategies that allow them to substitute and solve for unknown variables.” The puzzles increase in difficulty after each stage, and students will have to persevere to solve all five. (8.EE.8)

• In Lesson 7.3, Identifying Functions, students intentionally develop MP 1 during the Warm Up as they explore solution pathways to determine how a function is broken. Warm Up: Drop Down Lists, “Explore the drop-down list below and determine the relationships between position and color.” The Discussion Question asks, “Explain the relationships between the input position and the output color. What do you notice?” Students will have to go through the drop-down list multiple times in order to answer the question. (8.F.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 6.2, Linear Patterns in Scatter Plots, MP2 is intentionally developed throughout the lesson using the Interactives, Inline Questions, and Discussion Questions as they contextualize linear trends. Activity 1: Positive Trends, looks at positive trends, while Activity 2: Negative Trends, looks at negative trends.  Inline Questions from Activities 1 and 2 include the following: “Which of the following data sets would have a positive trend? Which of the following data sets would have a negative trend? Which graph has a weaker relationship, and how do you know?”  The Discussion Question asks the following: “Which graph has a stronger relationship? How do you know? If there is a relationship between engine size and efficiency, what could cause larger engines to be less efficient?” (8.SP.1)

• In Lesson 7.6, Interpreting Graphs of Functions, “students are given app usage as a function of time and asked to construct a scenario which would fit this data.” In Activity 1: Understanding a Graph in the Context, students are asked to, “use the Interactive below to examine two sample velocity vs. time graphs and break down what happened over the course of the functions.” This analysis requires students to reason quantitatively and abstractly. (8.F.5)

• In Lesson 10.10, Finding Distance Using the Pythagorean Theorem, students reason abstractly and quantitatively as they use an Interactive to investigate finding the shortest distance between two points. Students are asked first, “1. Mark all true statements: (1) Routes A and C have equal distances. (2) Route B is shorter than route A.” And then, “2. The most optimal route would be a straight line from school to home.  How long is the optimal route? Round your answer to the nearest tenth.” (8.G.8)

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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 8 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 1.11, Sequences of Transformation on the Coordinate Plane, Standards for Mathematical Practice: “MP3: In activity 1, the students are asked if order matters when performing a sequence of transformation on a coordinate plane. The students must cite evidence to support their argument.” Activity 1: Identifying Sequences of Rigid Motions, Discussion Question states, “Jessie wants to reflect and translate a point. She believes that the order in which she does so does not matter. Does it matter if she translates the point first and then reflects it compared to if she reflects it first and then translates it? As long as the translation and reflection are the same, will the point end up in the same place?” (8.G.2 & 8.G.3 )

• In Lesson 4.7, Investigating Horizontal and Vertical Lines, Standards for Mathematical Practice are as follows:  “MP3: In Activities 1 & 2, the students are asked to make conjectures about horizontal and vertical lines and their slopes through discussion with classmates.” Warm-up: What Do Horizontal and Vertical Lines Mean? Discussion Question #3: “Discuss with a classmate how we can use our knowledge that the x-axis and y-axis are perpendicular to each other to prove that horizontal and vertical lines are perpendicular to each other? Do you agree with your classmate, why or why not?” Activity 1: Horizontal Lines, Discussion Question #2 “Discuss with a classmate what would the slope of all horizontal line equations be 0? Why or why not?” Activity 2: Vertical Lines, Discussion Question #2 “Discuss with a class would the slope of all vertical line equations be undefined? Do you agree with your classmate? Why or why not?” (8,EE.B)

• In Lesson 6.4, Fitting a Line to Data, Standards for Mathematical Practice are as follows: “MP3: In Activity 1, the students form an argument over the factors that separate a good line of fit from the best line of fit and their necessity.” Activity 1: Line of Best Fit, Discussion Question: “Manny says, "It doesn't matter if a line of best fit is perfect because it's not going to match the data anyway. As long as you are close it's fine." Do you agree or disagree with Manny? Support your argument with evidence.” (8.SP.2 & 8.SP.1)

• In Lesson 7.1, Introduction to Functions, Standards for Mathematical Practice are as follows: “MP3: In Activity 1, the students form arguments about the pros and cons of each function representation.” Activity 1: Visualizations of Relations and Functions, Discussion Question: “Grace claims that since each method displays the same function, it doesn't matter which you choose. Do you agree or disagree with Grace? When might one method for displaying a function be better than another?” (8.F.4)

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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 8 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 3.7,Writing and Solving Linear Equations, the students model real-world scenarios in Activity 3. In Activity 3: Pick a Truck states: “Zoe De Leon owns a chain of grocery stores located in the Northeast United States. She needs to buy tractor trailer trucks to deliver the food from the warehouse to the stores. She is trying to choose between two different trucks. The first truck costs $145,000 and will cost$0.31 per mile traveled based on the current gas prices. The second truck will cost $160,000 but gets better gas mileage, costing$0.27 per mile. Which truck should she buy? Use an equation to find the number of miles (m) driven, such that the cost of the trucks will be equal. What equation can you write to help you determine when the total cost of the trucks is equal?” (8.EE.7)

• In Lesson 5.6, Writing and Solving Systems of Linear Equations states, “ Throughout the lesson, the students use systems of equations to model real-world problems.” In Activity 1: Solar Energy Continued, students “Identify the Problem or Question; You are considering getting solar panels for the roof of your house. You want to know if solar panels are a better option than what you have now. Gather Data and Research; The solar panels and installation will cost you $17,000. The inspector tells you that your new monthly bill is estimated to be$55 per month. Your current bill is $124 per month on average. Analyze the Data: To determine how long it will take the solar panels to pay off you must write the system of equations which models this situation.” (8.EE.8) • In Lesson 10.8, The Converse of the Pythagorean Theorem, in Activity 3, “The students extend the Pythagorean Theorem to explain non-geometric relationships like voltage.” In Activity 3: The Pythagorean Theorem and Energy Continued; Discussion Question states, “Using some of the strategies that we have learned thus far to determine what produces more power: one 10-volt battery or a 6-volt and an 8-volt combined?” (8.G.6) MP 5 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 2.5, Defining Similarity, Warm-Up: Thales and the Pyramids, students are asked, “How is it possible to measure the height of something too tall to climb easily, or something with a height that just can't be measured directly, such as the Great Pyramids of Giza in Egypt? Clearly there is no way to drop a measuring tape from the peak down through the solid rock to the base directly beneath it! What tools might you use to make such tall measurements? Are there any?” However, in Activity 2, they are told one specific strategy for measuring a tall object. They are not given the opportunity to use appropriate tools strategically. (8.G.4) • In Lesson 2.6, Angle-Angle Similarity, Warm-Up: Thales Revisited, students are asked, “How could you measure the distance of a ship from the shore? Would you use any specific tools to accomplish this?” However, in Activity 1, they are told one specific strategy for measuring a distance using similar triangles. They are not given the opportunity to use appropriate tools strategically. (8.G.5) Indicator {{'2h' | indicatorName}} Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The materials reviews for CK-12 Interactive Middle School Math 8 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 2.4, Properties of Dilations, 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.” (8.G.3 & 8.G.4) • In Lesson 4.4, Defining Slope, 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.” ( 8.EE.5 & 8.EE.6) • In Lesson 7.1, Introduction to Functions, MP6 is intentionally developed as the students “explore the different ways to express a function,” such as ordered pairs, in a table, in a mapping, a graph, or an equation. 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.” (8.F.4) The materials use precise and accurate terminology and definitions when describing mathematics, and the materials also support students in using the terminology and definitions. There is no separate glossary in these materials, but definitions are found within the units in which the terms are used. The vocabulary words are in bold print. Examples include: • In Lesson 3.1, Writing Equations with Variables, students attend to precision as they answer Inline Questions with immediate feedback and accuracy. An example is in Activity 2: “In the Interactive, what is the coefficient for x and y in the given expression?” In addition, the Teacher Notes stress accurate language: “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.”. (8.EE.7) • In Lesson 6.1, Representing Data in Scatterplots, students are given exact definitions of bivariate and quantitative data in the Warm Up: “Bivariate data means that the data comes from two variables. For example, if the temperature of a room changes over time, the two variables are the temperature and the time at which the temperature was measured. Quantitative data is data that can be measured. Examples of quantitative data are the height of a person, the speed of a car, the mass of a baseball, etc.” In Activity 1, they answer precise Inline Questions about the bivariate quantitative data in a scatter plot., such as, “Find the coordinate (9, 63). What does this coordinate mean?” (8.EE.8) • In Lesson 10.11, Representing Rational Numbers with Decimals, Activity 1, MP6 is intentionally developed as students “label numbers to their corresponding number systems. Additionally explore the vocabulary associated with different types of decimal values.” In Activity 3 students answer Inline Questions that require precision of language and answers, such as Question 3: “A decimal that can never be fully written because it repeats forever is considered a rational number because it can be described as a _________. (8.NS.1) Indicator {{'2i' | indicatorName}} Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The materials reviewed for CK-12 Interactive Middle School Math 8 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 3.4, Linear Equations and the Distributive Property, Activity 1, the students explore how an expression representing profit can be equivalent to the difference between expressions representing revenue and cost. Using the same equation that was used in Warm-Up: Selling Shirts, students work to find out the answer to the following statement, “Patrick wants to know how many shirts he will have to sell to reach this goal ($400,000) without changing the sales price or costs.” Students manipulate the structure of the previous equation to answer this statement.Then students are asked questions about their results, “Discussion Questions, 1)”You  combined 15q and -6.5q to get 8q.  What does this 8q represent? 2) Does the answer "62,000 shirts" make sense within the context of the problem? How can you check your answer mathematically? Does it check out mathematically?” (8.EE.7)

• In Lesson 4.10, Linear Equations in Standard Form, students intentionally develop MP7 as they “explore how a linear equation in standard form can be written in slope-intercept form and vice-versa.” Throughout the lesson students are shown different ways to graph an equation, for example graph by plotting points or graph by plotting the intercepts. All the linear equations in all activities start off in standard form. In Activity 3: Graph by Converting to Slope-Intercept Form, students examine the structure of a linear equation in standard form and solve it for y using the same structure they would solve a two-step equation. (8.EE.5 & 8.EE.6)

• In Lesson 5.4, Solving Systems of Equations Using Elimination, Activity 3: Rearranging Equations, the students examine how the placement of the terms in an equation affects their ability to eliminate a variable. “Solve the system of equations using the elimination method:

2x + 4y = 40

x  = 4y - 22

”Students examine the structure of the system of equations as they follow the steps in solving it. Students also examine the structure of the system of equations when the Inline Questions asked them to consider two more system of equations, one which they have to add without structural manipulation to the equations, resulting in no variable being eliminated and one where they are asked to pick the operation that would eliminate a certain variable. (8.EE.8b)

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

• In Lesson 4.1, Graphing Proportional Relationships, students intentionally develop MP8 as they “use repeated reasoning to look for shortcuts in identifying the points of a proportional relationship on a graph.” In Activity 1: Proportional Relationships, students are tasked with using an interactive graph to show Emily’s earnings as the number of hours that she babysits increases. Students are tasked with graphing at least five points in order to use repeated reasoning to answer the Inline and Discussion Questions. For example, Discussion Question 3 asks, “Did you notice a pattern while you were plotting points? What was it and how might you be able to use this pattern when plotting in the future?” (8.EE.5)

• In Lesson 7.3, Identifying Functions, students intentionally develop MP8 as they “use repeated reasoning...to derive the vertical line test.” In Activity 1: Functions vs. Relations, functions are defined, students are shown several different representations of relations that are not functions, and then they graph four functions on different graphs.  Discussion Question #3 asks, “What similarities do you notice between graphs that form functions and graphs that do not form functions?” The Teacher Notes states, “This question encourages students to use repeated reasoning to derive a version of the vertical line test. By repeatedly graphing relations that are functions and relations that are not functions, the students begin to see that a relation that is not a function can be identified by overlapping points.”(8,F.1)

• In Lesson 8.7, Finding Dimensions of Spheres: In Activity 3, the students use repeated reasoning to see how changing the radius changes the size of the sphere proportionally. “The lesson Volume of Pyramids discussed how the dimensions affected the volume of a pyramid. A sphere has only one variable in the formula, the radius.  Use the interactive below to see (how) the radius affects the volume of a sphere.” The following Inline Questions reinforce the relationship. For example, Question 2, “In the interactive, scaling the sphere by half (or 0.5) means…”  and Question 3: “In the interactive the original sphere has a radius of 2 and volume of 33.51. Scaling the original sphere by 3 will result in a sphere with a radius of 6. What will its volume be? Use the interactive to see!”  (8.G.9)

Usability

The materials reviewed for CK-12 Interactive Middle School Math 8 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 8 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.

Indicator {{'3a' | indicatorName}}

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

The materials reviewed  for CK-12 Interactive Middle School Math 8 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 1.1, Introduction to Rigid Motions, the Introductory Teacher Notes state, “In this initial lesson, students should understand why we move stuff around in the first place. They should get introduced to the language of image, preimage, rigid motion, and the different types of motion that can be done to a figure. By this point, students should be familiar with the idea of a degree, angles, and length. They will use these to translate, rotate, and reflect images, as well as understand their definitions. (8.G.1)

• Answers to all Inline Questions

• Instructions for help with the Interactives. For example, in Lesson 4.2, Constant of Proportionality in Different Representations, Activity 1, it directs students, “Use the Interactive below to create a table and make a graph which expresses the proportional relationship between pounds and kilograms.” The Teacher Notes state, “Before allowing students to use the Interactive ask what the variables x and y should represent. The variable x should represent the weight in pounds, and the variable y should represent the weight in kilograms. We need to multiply the weight in pounds by 2.2 to get the weight in kilograms.” (8.EE.5)

• Possible answers, further questions, and discussion ideas for the Discussion Questions are in the following examples. In Lesson 3.6, Linear Equations Written with Ratios, Activity 3, the Discussion Question Teacher Notes state, “Students should use what they know about ratios to answer this question. They should note that the equation they are working with is a ratio, which is used to compare values. In this case, they are comparing the number of red shoes sold out of the total to the percentage of red shoes sold. Since we are working with percentages the total for the right side of the equation (in the denominator) will be 100. So, the right side of the equation is the percentage of red sneakers. All in all, students should understand that they are comparing the number of red shoes sold to the percentage of red shoes sold.” (8.EE.7)

• 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.

• Learning Objectives -goals for each lesson.

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

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

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

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

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

Indicator {{'3b' | indicatorName}}

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

The materials reviewed for CK-12 Middle School Interactive Math 8 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 8 for CCSS partially meet expectations for including standards and correlation information that explains the role of the standards in the context of the overall series. Correlation information is present for the mathematics standards addressed throughout the grade level. However, there are few, if any, explanations of the role of the specific grade-level mathematics in the context of the series and no connection to future learning.

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

• Lesson 2.3, Solving For Missing Angles in Parallel Lines and Triangles, lists the following as Previous Learning Objectives: Solve problems using the triangle sum theorem (8th); Solve problems involving exterior angles (8th); Identify special angle pairs created when parallel lines are cut by a transversal (8th); Use informal arguments to establish facts about angles created when parallel lines are cut by a transversal (8.G.5); and Use properties of special angle pairs to identify equal angles when parallel lines are cut by a transversal (8th). The Introductory Teacher Notes state,  “Additionally students should use facts about angles that they learned about in Grade 7 such as vertical, complementary, and supplementary angles.” Pre-requisite Standards listed for the lesson are 7.G.5 and 7.EE.4a

• Lesson 3.1, Writing Equations with Variables, lists the following as Previous Learning Objectives: Write equations to solve real-world problems by reasoning about the quantities (7.EE.4) and Interpret an equation and its value in a real-world context (7th). Pre-requisite standards listed for the lesson are 6.EE.2 and 7.EE.4a.

• Lesson 10.2, Introduction to Square Roots and Cube Roots, lists the following as Previous Learning Objectives: Understand that exponents represent repeated multiplication (6th) and Understand and identify perfect squares and perfect cubes (8th). In the introductory Teacher Notes: “This lesson starts with the prerequisite knowledge from earlier grades in a discussion of how to find 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. Remind students to pay careful attention to units and notation. Students should notice that the square root of perfect squares are integers (the same applies to cubes).” Prerequisite Standard listed for the lesson is 6.EE.1

Future learning objectives are seldom present and almost always refer to later in the grade level and not to a concept in future grade levels or courses. For example, in Lesson 8.5, Volume of Pyramids (Deeper Learning); the materials state that it is Building Towards G-GMD.A.3. The Introductory Teacher Notes state, “This lesson is optional and goes beyond the standards for 8th grade. Students should understand that when a cone has a square for a base, it is called a square pyramid. In this lesson, students extend their learnings from lessons on cones to understand the volume formula for square pyramids. The different terminologies and measurements for pyramids are introduced and explained.”

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

• In Lesson 1.8, Translation on the Coordinate Plane, the Focus Standard is 8.G.3, the Prerequisite Standards are 7.G.2 and 7.G.5, and the standards for mathematical practice listed with the lesson are MP6 and MP8. The Learning Objectives are the following: Translate a point on the coordinate plane, describe the effect of translations on two-dimensional figures using coordinates, and predict the coordinates of an image after a transformation.

• In Lesson 6.6, Representing and Analyzing Categorical Data, the Focus Standard is 8.SP.4, the Prerequisite Standard is 6.SP.4, and the standard for mathematical practice listed with the lesson is MP2. The Learning Objectives are the following: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies in a two-way table, use a two-way table of frequencies to make observations about a data set, construct a two-way table of frequencies to organize bivariate categorical data, and interpret two-way table of frequencies within the context of the data set.

• In Lesson 9.3 ,The Power of 0 and Negative Exponents, the Focus Standard is 8.EE.1, the Prerequisite Standards are 5.NBT.2 and 6.EE.1, and the standards for mathematical practice listed with the lesson are MP7and MP8. The Learning Objectives are the following: Understand the zero exponent property, apply the zero exponent property to write equivalent expressions, understand the negative exponent property, and apply the negative exponent property to write equivalent expressions.

Indicator {{'3d' | indicatorName}}

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

The materials reviewed for CK-12 Interactive Middle School Math 8 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 8 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.”

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

The materials reviewed for CK-12 Interactive Middle School Math 8 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 1.1, Introduction to Rigid Motion, Activity 1, Transportation Translations: Sheet of blank paper and Pencil, or other mediums for drawing.

• In Lesson 6.4, Fitting a Line to Data, Activity 2, Baseball Analytics Revisited: Printed out graph from activity 3, 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 8 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.

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

The materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS partially meet expectations for having assessment information included in the materials to indicate which standards are assessed. The materials sometimes identify the standards and mathematical practices addressed by formal assessments.

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

• In Lesson 7.8, Linear Functions, Review Question 1,“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.”

• Chapter 2, Similarity, Question 2: “(8.G.A.4) Determine whether or not the following parallelograms are similar. If they are similar, explain how you know by describing the transformations. If not, explain why.”

• Chapter 7, Functions, Question 4: “As your family is leaving the zoo, you pass by a gift shop. The shop is having a promotion on saltwater taffy! If you donate a certain amount of money to the zoo, you can get a discount on the price per pound of taffy. a. (8.F.A.4) Write equations to represent the total cost (y) as a function of pounds of taffy (x) with and without the promotion:”

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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 8 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.

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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 8 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.

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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 8 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 8 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.

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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 8 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.

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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 8 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 doing more assignments than their classmates. Examples include, but are not limited to:

• In Lesson 7.2, Domain and Range,  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 52, Identify the domain and range of [(-1,2),(-6,3),(10,7),(8,11)].” (8.F.1)

• In Lesson 10.5,  Approximating Irrational Numbers, Review Questions, the Teacher Notes state, “To customize the questions click here:” Under Assign to Class, Customize, Add question set, various “hard” questions may be assigned. For example, in “Set 1 Question 14 Evaluate the square root \sqrt{100} short-answer  “ (8.NS.2)

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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 8 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 7.6, Interpreting Graphs of Functions, Activity 3, the Interactive directions state, “Look at the user activity function graph below. Independently, construct a story of an app which would have this user activity be sure to explain any increases, decreases, and constants.” The Teacher Notes state, “This activity is designed to be completed independently before being discussed as a group.” (8.F.5)

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

• In Lesson 2.7, Fundamental Theorem of Similarity, Warm-up Activity, the Discussion Question asks, “How could you measure the height of a tree? What tools might be helpful?” The  Teacher Notes suggest that teachers, “allow students to discuss and offer solutions to the problem. There are many possible answers. Feel free to ask for clarification on a method presented by the student or ask if there is a situation where the method would not work. The students might recall using similar triangles created by the shadow of the sun. If this question is asked, ask students what would happen if the shadow couldn’t be measured because the sun wasn’t out or the tree was in a forest. Encourage out of the box solutions but discuss the challenges that they might present.” (8.G.4)

• In Lesson 4.2, Constant of Proportionality in Different Representations, Activity 3, the Discussion Question, Teacher Notes suggest that teachers, “allow the students to discuss the following questions in small groups to help form arguments before transitioning to a full class discussion, allowing them to analyze the arguments of their classmates.” The Discussion Questions that follow are as follows: “1. What should represent x and y in the equation? How do you know? 2. Based on the table and graph, what is the relationship between time and final velocity? How did you get it and what does it mean? 3. What is the constant of proportionality and how did you determine it? 4. What is the equation for this relationship? “ (8.G.4)

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.

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

The materials reviewed for CK-12 Interactive Middle School Math 8 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 how to form the group based on the different needs of the students. Examples include, but are not limited to:

• In Lesson 1.6, Using Equations to Represent Proportional Relationships Double Number Lines & Equivalent Ratios, Activity 3, Discussion Question gives a recommendation in the Teacher Edition.  It states, “Group students in pairs.” (8.F.4) There is no information provided on how to group dependent on the needs of the student.

• In Lesson 4.2, Constant of Proportionality in Different Representations, Activity 2, Proportional Relationships in Medicine Continued, the Teacher Notes just prior to the Discussion Question state, “Allow the students to discuss the following questions in small groups to help form arguments before transitioning to a full class discussion, allowing them to analyze the arguments of their classmates.” (8.EE.5) There is no discussion on how to form the group dependent on the needs of the student.

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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 8 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.

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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 8 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 3.3, Linear Equations with Rational Numbers, Warm-up, it states,  “Jenny Chang is the owner of a small shop, Empire Fudge, that sells one product: fudge.” (8.EE.7)

• In Lesson 5.6, Writing and Solving Systems of Linear Equations, Activity 2, the directions state, “Cecelia is planning a community garden.” Then Activity 3 states, “Brandon is taking a trip from Boston to San Diego.” (8.EE.8)

• In Lesson 9.6, Comparing Numbers in Scientific Notation & Choosing Reasonable Units, Activity 2, it begins, “Mikaela is a doctor who was checking the red blood cells of a patient.” (8.EE.4)

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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 8 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.

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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 8 for CCSS do not provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning. While there is some culture implied by names or problem contexts, specific guidance on how to connect students' cultural and/or social background to facilitate learning or motivate students is not found.

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

The materials reviewed for CK-12  Interactive Middle School Math 8 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.

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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 8 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 1.3, Properties of Reflections, Activity 2, students are verifying and understanding corresponding angles. It states, “Use the Interactive below to examine whether the corresponding side lengths and angles of both shapes are equal. Then answer the questions following the Interactive.” (8.G.1)

• In Lesson 8.3, Volume of Cones, Activity 1, students want to know how many cubes fit inside a cone.  Using an Interactive,  students explore the relationship between the volume of a cone and the volume of a cylinder. (8.G.9)

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 8 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.

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

The materials reviewed for CK-12 Interactive Middle School Math 8 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.

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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 8 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.”

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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 8 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.

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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 8 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 1.8, Translations on the Coordinate Plane, Activity 1, the Teacher Notes on the Interactive state, “Before the students attempt the Inline Questions, ask the students to translate the point 9 times. For three of the translations the student should only translate the point vertically, for another three of the translations, the student should only translate the point horizontally, and the student should translate the point both vertically and horizontally for the final three translations. The students should write down the location of the points before and after translation. This activity is designed to encourage repeated reasoning to assist the students in looking for the patterns which define the rules for translating points on a coordinate plane.” (8.G.3)

• In Lesson 2.7, Fundamental Theorem of Similarity, Activity 4, the Teacher Notes on the Interactive state, “By transforming one shape into another, the students are able to prove that the shapes are congruent. Allow the students to compare answers and their experiences for Activity 4. The students should look for patterns and strategies. Point out that equivalence does not equal efficiency. Getting the same answer is good but a great mathematician seeks out the most efficient way to solve the problem. The students should come up with a general strategy to solve the problem in as few moves as possible.” (8.G.4)

Report Overview

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

Math 6-8

The materials reviewed for CK-12 Interactive Middle School Math 6-8 for CCSS meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials partially meet expectations for Usability. Within Gateway 3, the materials partially meet expectations for Teacher Supports (Criterion 1), meet expectations for Assessment (Criterion 2), and do not meet expectations for Student Supports (Criterion 3).

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

Overall Summary

Alignment
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Usability
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