7th Grade - Gateway 1

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 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 2 Section 2.3- Students demonstrate their knowledge of 7.NS.2 by applying and extending previous understandings of multiplication and division of fractions to multiply and divide rational numbers. Question 2c on the Self-Assessment states: “Estimate each product or quotient. Then find the actual product or quotient of -89(0.5).”
• Chapter 6 Section 6.3- Students solve word problems leading to linear inequalities demonstrating their knowledge of 7.EE.4b. Question 3b on the Self-Assessment states: “Write an inequality to represent each of the following word problems. Solve each problem. Explain your solution in context. 'Jeremy is two years older than Rachel. The sum of the ages of Jeremy and Rachel is less than 46. How old could Jeremy be?'”

The instructional materials reviewed for Grade 7 meet expectations for focus by spending a majority of class time on the major clusters of the grade including all clusters in 7.RP, 7.NS, and 7.EE. 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 82 percent of instructional time on the major clusters of the grade. The Grade 7 materials have 8 chapters that contain 139 lessons, which accounts for a total of 31 weeks of class time including Anchor Problems and Self-Assessments.

• Grade 7 instruction is divided into eight chapters. More than half of Chapter 1 addresses 7.NS. Chapter 2 addresses 7.NS. Chapter 3 addresses 7.EE. Chapter 4 addresses 7.RP. More than half of Chapter 6 addresses 7.EE. Therefore, approximately 4.5 out of 8 chapters (56 percent) focus exclusively on the major work of the grade.
• Grade 7 instruction consists of 139 lessons. Approximately 114 lessons out of 139 (82 percent) focus on the major work of the grade level, which includes supporting work that connects to the major work of the grade.
• Grade 7 instruction is divided into 31 weeks. Approximately nineteen out of 31 weeks (61 percent) focus exclusively on the major work of the grade.

The Instructional materials reviewed for The Utah Middle School Math Project Grade 7 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 7.

• Chapter 5: Sections 5.2b, 5.2c, and 5.4b work with 7.G.1, and 7.G.6 supports 7.RP.2 by having students create and solve ratios and proportions to find similar figures. For example, in the overview teachers are told that the central idea of Section 5.2 is scale and its relationship to ratio and proportion. The standard for ratio and proportion are not listed. Ratio language is used in the Activities and Homework problems.
• Chapter 6: Section 6.1 supports 7.EE.4 and 7.NS.1 by having students find angle pairs which involves working with rational numbers and creating/solving equations.
• Chapter 7: Activities 7.1a and 7.1b support 7.NS.1 by having students compare populations which involves working with rational numbers.
• Chapter 7: Sections 7.1 and 7.2 include problems that are related to ratio and proportions (7.RP.2) while working with statistics. For example, Chapter 7, Class Activity 7.2b, Teacher Workbook, page 7WB7 – 43, students use the ratio of colors of jellybeans for a statistical experiment.
• Chapter 8: Activity 8.1c supports 7.EE.4 by having students create and solve equations in real-life mathematical problems based on composite area.

The instructional materials reviewed for Grade 7 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 155 days. According to the publisher, completing the work would take a total of 31 weeks. That includes days for Anchor Problems, Class Activities, Homework, and Spiral Review. 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 7 meet expectations 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 a 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 explains that “throughout the chapter, students are provided with opportunities to review fractions, decimals and percents.” (page 7WB1 - 2)
• Chapter 2: “The development of rational numbers in 7th grade is a progression in the development of the real number system that continues through 8th grade. In high school students will move to extending their understanding of number into the complex number system.” (pages 7WB2 – 3)
• Chapter 4: “The chapter begins by reviewing ideas from 6th grade as well as 7th grade chapters 1-3 and transitioning students to algebraic representations. Student will rely on knowledge developed in previous chapters and grades in finding unit rates, proportional constants, comparing rates and situations in multiple forms, writing expressions and equations, and analyzing tables and graphs.“ (page 7WB4 – 2)
• Chapter 6: “Work on inequalities in this chapter builds on Grade 6 understandings where students were introduced to inequalities represented on a number line. The goal in Grade 7 is to move to solving simple one-step inequalities, representing ideas symbolically rather than with models.” (page 7WB6 - 2)
• Chapter 8: “In 8th grade, students will continue working with volume, formalizing algorithms for volume of cylinders and adding methods for finding the volume of cones and spheres.” (page 7WB8 – 3)

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 4, Class Activity 4.1a: “Equivalent Ratios, Fractions, and Percents (Review from 6th grade): They should know a ratio expresses a numerical relation between two quantities. Students studied ratios extensively in 6th grade.” (p. 7WB4 – 14)
• Chapter 8, Connections to Content: “Towards the end of this section students review the use of nets (a concept from 6th grade) to find surface area of prisms and cylinders and then to differentiate this measure from volume, which they will also find.” (page 7WB8 – 2)

The instructional materials reviewed for The Utah Middle School Math Project Grade 7 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 7 domain, with sections within the chapter focusing 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.

• “Investigate chance processes, develop/use probability models, as well as the work within the section,” a learning objective from Chapter 1 Section 1.1, reflects Cluster 7.SP.C (Investigate chance processes and develop, use, and evaluate probability models).
• In Chapter 3, students are engaged in activities aligned to Cluster 7.EE.A (Use properties of operations to generate equivalent expressions). In Section 3.1a (page 7WB3-7 - 12), the first Activity, “Naming Properties of Arithmetic,” has an objective to “recognize properties of arithmetic and use them in justifying work when manipulating expressions.” Students are engaged in using the identified properties and identifying pairs of equivalent expressions. In Anchor Problem 3.0 (page 7WB3 - 6), a teacher’s note reflects the cluster heading: “A big idea you’re after right now is that one can write equivalent expressions in a number of ways and that different ways shed light on different thinking.”

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

• The Chapter 3 Overview connects 6.EE.1 and 6.EE.2 through this statement: “By the end of this section (3.1) students should be proficient at simplifying expressions and justifying their work with properties of arithmetic. Section 3.2 uses the skills developed in the previous section to solve equations…Section 3.3 ends the chapter with application contexts.” (pages 7WB3 - 2 and 7WB3 - 3)

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

• Chapter 3 Section 3.1 and 3.2 connects 7.NS.A and 7.EE.A as students transfer integer properties to algebraic expressions. Students use the Distributive Property of Multiplication and Division over Addition and Subtraction to write equivalent algebraic expressions and to develop an understanding of combining coefficients of like terms and calculating the product of two numbers. (pages 7WB3 – 6 and 7WB3 - 93 through 7WB3 - 109)
• In Chapter 4, Class Activities 4.3d and 4.3e 7.RP.A, 7.NS.A and 7.EE.B are connected as students write equations and compute to solve percent problems. (pages 7WB4 - 173 through 7WB4 - 181)