8th Grade - Gateway 1

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for focus within assessment. Overall, the instructional material does not assess content from future grades within the assessment sections of each unit.

There are multiple Self-Assessments within each unit. Each assessment includes a scoring rubric that helps students articulate their understanding of key concepts being assessed. All assessments have answer keys provided in the Teacher Workbook.

On grade-level examples include:

• Chapter 4 Section 4.1- Students demonstrate their knowledge of 8.EE.8 by graphing or solving simultaneous, linear equations by substitution or elimination. Question 3 on the Self-Assessment states: “One equation in a system of linear equations is ???? = −2???? + 4. a. Write a second equation for the system so that the system has only one solution.”
• Chapter 5 Section 5.3- Students demonstrate their knowledge of 8.F.5 by analyzing and then describing a graph. Question 1 Concept 3 on the Self-Assessment states: “Below are two graphs that look the same. Note that the first graph shows the distance of a car from home as a function of time and the second graph shows the speed of a different car as a function of time. Describe what someone who observes the car’s movement would see in each case.”
• Chapter 8 Section 8.2- Students demonstrate their knowledge of 8.EE.4 by subtracting, adding, multiplying, and dividing numbers in scientific notation and then converting the answer to standard form. Question 2a on the Self-Assessment states: “Change the numbers below into scientific notation. 3,450,000,000.” Question 2c states: “Change the number given below into standard form. 6.03 x 108.”

The instructional materials reviewed for Grade 8 meet the expectation for focus by spending a majority of class time on the major clusters of the grade including all clusters in 8.EE, 8.F, 8.GA, and 8.G.b. To determine this, three perspectives were evaluated: 1) the number of chapters devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of weeks devoted to major work. Of the three perspectives, the number of lessons is most representative and was used to determine the score for this indicator.

Overall, the materials spend approximately 80 percent of instructional time on the major clusters of the grade. The Grade 8 materials have 10 chapters that contain 164 lessons, which accounts for a total 33 weeks of class time including Anchor Problems and Self-Assessments.

• Grade 8 instruction is divided into 10 chapters. Approximately 8 out of 10 chapters (80 percent) focus exclusively on the major clusters of Grade 8, while the other 2 chapters focus primarily on supporting work that does not often support major work.
• Grade 8 instruction consists of 139 lessons. Approximately 131 out of 164 lessons (80 percent) focus on the major clusters of the grade.
• Grade 8 instruction is divided into 33 weeks. Approximately 24.5 out of 33 weeks (74 percent) focus exclusively on the major work of the grade.

The Instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Overall, the lessons that focus on supporting content also engage students in major work where natural and appropriate.

The following examples demonstrate where the supporting work enhances understanding of the major work of Grade 8.

• Chapter 6: Section 6.1 focuses on fitting a straight line to the scatter plot. Students then write a prediction function for the line of best fit and explain the meaning of the slope and y-intercept of the function in context. This work uses 8.SP.A to support 8.F.A and 8.F.B.
• Chapter 6: Section 6.2a and 6.2b uses 8.SP.A to support 8.EE through the use of trend lines and finding the line of best fit.
• Chapter 7: In Activity 7.1a 8.NS.A supports 8.G.B. Through creating squares of different areas, the idea of the Pythagorean Theorem emerges as the sides of a right triangle form three squares and the two sides of a right triangle place together equals the longest side square.
• Chapter 7: Activity 7.2a uses 8.NS.A to support 8.EE through students creating and solving expressions and equations based on powers and roots.
• Chapter 7: Section 7.3 8.NS.A is used to support major work as it focuses on rational and irrational numbers. Under Concepts and Skills to be Mastered, it lists, “Know that the square root of a non-perfect square is an irrational number,” which is a part of 8.EE.2.
• Chapter 10: This chapter links geometry with both number system and expressions and equations, 7.EE.4, as students write and solve Pythagorean Theorem equations where solutions are approximated.

The instructional materials reviewed for Grade 8 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. The instructional materials are designed to take approximately 165 days. According to the publisher, completing the work would take a total of 33 weeks. (There is some discrepancy in the material regarding Chapter 3. The Chapter overview states that the Chapter is designed for 4 weeks, but the title of the Chapter folder indicates 3 weeks.) Completing the work includes days for Anchor Problems, Class Activities, and Homework. According to the Preface, “Each lesson covers classroom activity and homework for a 50-minute class. Sometimes the demands of the material exceed this limitation; when we recognize this, we say so; but some teachers may see different time constraints, and we defer to the teacher to decide how much time to devote to a lesson, how much of it is essential to the demands of the relevant standard. What is important are the proportions dedicated to the various divisions, so that it all fits into a year’s work. Within a lesson, the activities for the students are graduated, so that, in working the problems, students can arrive at an understanding of a concept or procedure. In most cases there is an abundance of problems, providing the teacher with an opportunity to adapt to specific needs.” The number of weeks was converted to days for this review. Each chapter has built-in days for Self Assessments. Overall, the amount of content that is designated for this grade level is viable for one school year.

The materials reviewed for The Utah Middle School Math Project Grade 8 meet the criteria for consistency with the progressions in the Standards. In general, materials develop according to the grade-by-grade progressions in the Standards and provide extensive work with grade-level problems. Materials consistently relate grade-level concepts explicitly to prior knowledge from earlier grades.

Content from prior and future grade levels is identified in Connections to Content at the beginning of each student and teacher workbook chapter. Chapter overviews/summaries, as well as section overviews, include written explanations of what students will be doing throughout the chapter. Summaries explain what students will learn and how they will use this knowledge in future learning.

• Chapter 1: The Section 1.1 Overview explains that Section 1.1 “involves a review of algebraic expressions.” The teacher notes emphasize this further, telling teachers that the first section is 7th grade material and to work through it faster with an honors class or assign it as homework. (page 8WB1 - 8)
• Chapter 2: “Students begin this chapter by reviewing proportional relationships from 6th and 7th grade, recognizing, representing, and comparing proportional relationships. In 8th grade, a shift takes place as students move from proportional linear relationships, a special case of linear relationships, to the study of linear relationships in general.” (page 8WB2 – 2)
• Chapter 3: “In Chapter 5 students will solidify the concept of function, construct functions to model linear relationships between two quantities, and interpret key features of a linear function. This work will provide students with the foundational understanding and skills needed to work with other types of functions in future courses.” (page 8WB3 - 2)
• Chapter 5: “This chapter builds an understanding of what a function is and gives students the opportunity to interpret functions represented in different ways, identify the key features of functions, and construct functions for quantities that are linearly related. This work is fundamental to future coursework where students will apply these concepts, skills, and understandings to additional families of functions.” (page 8WB5 – 2)

Materials consistently relate grade-level concepts explicitly to prior knowledge from earlier grades. Connections between concepts are addressed in the Connections to Content, chapter overviews/summaries, and Math Textbook. Examples of these explicit connections include:

• Chapter 1, Math Textbook: “The first three chapters of grade 8 form a unit that completes the discussion of linear equations started in 6th grade and their solution by graphical and algebraic techniques.” (page 8MF1 - 1)
• Chapter 6, Class Activity 6.1a: “Problems 1 and 2 provide students with an opportunity to connect what they have learned in 6th/7th grade with what they will learn in 8th grade. Problem 1 is a review of 6th and 7th grade content where students learned to display and analyze univariate data. Students have learned…In 8th grade, students connect this learning with bivariate data.” (page 8WB6 - 10)

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

In the teacher's workbook, the CCSSM are identified on the introduction page of each chapter. Each chapter correlates to a Grade 8 domain, with sections within the chapter focused on standards within the domain. There is a section titled “Concepts and Skills to Master" which identifies specific learning objectives for each section in the teacher, parent, and student workbooks.

• The Chapter 4 Overview reflects 8.EE.C (Analyze and solve linear equations and pairs of simultaneous linear equations) as students work with and “discuss intuitive, graphical, and algebraic methods of solving simultaneous linear equations; that is, finding all pairs (if any) of numbers (x, y) that are solutions of both equations.” (page 8WB4 - 2)
• In Chapter 5 Cluster 8.F.A students work with functions (define, evaluate, and compare functions). In Section 5.2 Explore Linear and Nonlinear Functions, students distinguish between linear and nonlinear functions given a context, table, graph, or equation. In Section 5.3 Model and Analyze Functional Relationships, the objective is to analyze functional relationships between two quantities given different representations.

The materials include problems and activities that serve to connect two or more clusters in a domain where connections are natural and important.

• Chapter 3 Section 3.1 Classroom Activity 3.1f problems 1-6 include content from both 8.F.A and 8.F.B as students review the slope-intercept form of a linear equation and then use their understanding to model relationships between quantities. (page 8WB3 – 49)
• Chapter 5 Section 5.3 Classroom Activity 5.3a connects 8.F.A and 8.F.B. Students construct functions to model linear relationships while they are comparing properties of functions that are represented in different ways. (page 8WB5 - 76)

The materials include problems and activities that serve to connect two more domains in a grade where connections are natural and important.

• Chapter 2 Section 2.3d-g connects 8.EE.5 and 8.F.A as students determine the rate of change from graphs. Students compare the rates of graphs, compare the steepness of several lines on the same graph, and relate the steepness of the lines to their rates of change. (pages 8WB2 - 84, 8WB2 - 85 & 8WB2 - 126)
• Chapter 8 Section 8.3 connects 8.EE.A and 8.G.C as students use square root and cube root symbols and evaluate square roots and cube roots while solving problems involving the volume of cylinders, cones, and spheres. (page 8WB8 - 72)