8th Grade - Gateway 1

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for assessing grade-level content. Overall, assessments are aligned to grade-level standards, and the instructional materials do not assess content from future grades. Each chapter has an End of Chapter Assessment in both Word and PDF formats.

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

• In Chapter 3, Item 1 states, “Diana and Bruce work at different car dealerships. Diana earns a base salary of $20,000 plus a commission of $200 per car sold. Bruce has no base salary but earns a commission of $1,000 per car sold. Set up an equation to represent the number of cars sold for which Diana's total salary will equal Bruce’s. Solve the equation.” (8.EE.7)
• In Chapter 4, Item 3 states, “A police department imposes a fine of $15 for every mph (miles per hour) over the speed limit. d. A bill passes to add a base fine of $25 to the $15 for every mph over the speed limit. Graph the new total fine, y, for driving x miles per hour over the speed limit including the $25 base fine.” (8.EE.5)
• In Chapter 7, Item 1 states, “While walking through the zoo, you keep track of the number of animals and the number of people at different exhibits. Let the number of animals be the input and the number of people be the output. Each coordinate point represents a different animal exhibit in the form (input, output): (2, 8) (4, 3), (1, 10) (0, 2) (4, 7) a. How many people were at the exhibit with no animals? b. How many animals were in the exhibit being visited by 7 people? c. Graph the coordinate points. Determine whether the relation is a function or not. Explain.” (8.F.1)
• In Chapter 8, Item 3 states, “A company wants to transport grain in cylindrical barrels. The barrels have a radius of 11 inches. If each barrel needs to hold 12,705 cubic inches of grain, what must the height of the barrel be? Use ???? = 3.14. Round your answer to the hundredths place if necessary.” (8.G.9)
• In Chapter 9, Item 3 states, “There are about 3.2 million public school teachers in the US. The average teacher has 15.9 students. Estimate the total number of students in the US. Express your answer in scientific notation.” (8.EE.3)

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for spending a majority of class time on the major clusters of the grade. 

• The approximate number of chapters devoted to major clusters of the grade is ten out of ten, which is 100%.
• The number of lessons devoted to major clusters of the grade (including assessments and supporting clusters connected to the major clusters) is 81 out of 87, which is approximately 93%.
• The number of days devoted to major clusters (including assessments and supporting clusters connected to the major clusters) is 91 out of 97, which is approximately 94%. 

A day-level analysis is most representative of the instructional materials because this calculation includes assessment days that represent major clusters. As a result, approximately 94% of the instructional materials focus on major clusters of the grade.

The instructional materials reviewed for CK-12 Interactive Middle School Math 8 for CCSS meet expectations for supporting work enhancing focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major standards/clusters of the grade. Lessons in Grade 8 incorporate supporting standards in ways that support and/or maintain the focus on major work standards. Examples of the connections between supporting and major work include the following:

• Lesson 6.2 connects 8.EE.5 and 8.SP.2. Students identify trends in scatter plots that compare two sets of proportional data. For example, in Activity 1, Inline Questions 1 and 2, students use data from two graphs to answer questions on comparing and identifying trends, “1. Which of the following data sets would have a positive trend? Multiple Choice: The amount of money you make vs the hours you work at a job paying $15 per hour. 2. Imagine drawing a line through the center of the data for MLB Homeruns from 1871 to 2017. Which of the following is true? Multiple Choice: As the x values get larger (increase), the y values get larger (increase).”
• Lesson 8.2 connects 8.G.9 and 8.EE.A. In the warm-up, an energy drink design introduces how the dimensions of a soda can have a significant impact on sales and profit. In the next two activities, students use the formula, which is provided, to find the volume of a cylinder and how cylinders of different height and radius can have the same volume. Activity 3 states, “Imagine that you have been tasked with creating a new energy drink. You are responsible for naming the drink and designing the can. The can needs to be able to hold 12 ounces of liquid which is equivalent to approximately 354.88 cubic centimeters. To add extra space for air in the can, the volume needs to be 360 cubic centimeters. You are responsible for designing the dimensions of the can. Choose the radius first and then solve for the accompanying height. Use 3.14 as a value for pi.”
• Lesson 10.4 connects 8.NS.1 and 8.EE.2. Students use rational and irrational numbers when evaluating square roots. For example, in Activity 2, Inline Question 3 states, “You know that the square root of 9 is 3 and the square root of 16 is 4. You also know that the numbers 10 - 15 lie between 9 and 16, so their square roots will lie between 3 and 4. Knowing this, match the following numbers with their approximate square roots.”

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

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

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

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All lessons contain a Warm-Up, two or more activities, Extension Activities, Inline Questions, and Review Questions that are at grade level. Inline Questions range in number, and lessons generally contain around 10, which are used throughout the lesson to check for understanding. Also, there are Supplemental Questions and Extension Activities. These questions and activities are only seen in the Teacher’s Edition. The Review Questions are mostly multiple choice, and there are approximately 10 per lesson. Examples include:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• Lesson 4.2 connects 8.EE.B with 8.F.B. In Activity 2, Proportional Relationships in Medicine Continued, “The paramedics and EMTs arrive upon the scene at an emergency, they need to be able to make smart decisions quickly. If they arrive on the scene and a patient has chest pain they might give the patient Diltiazem to relax the muscles and increase blood flow in the patient’s chest. The amount of the medicine they give would depend on the patient’s weight. A graph of this relationship is shown in the interactive below. Use the interactive to populate the table, determine the relationship between weight and medicine dosage and express that relationship as an equation.”
• 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 .”