8th Grade - Gateway 1

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)

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)

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.

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.”

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.”