7th Grade - Gateway 3

The instructional materials for Grade 7 meet the expectation that the underlying design of the materials distinguishes between problems and exercises.

The chapters begin with a non-routine problem that introduces new concepts and is labeled as an Anchor Problem. The chapters are subsequently sectioned into Class Activities, Homework, Spiral Reviews, and Assessments.

Generally, each Class Activity has problems to solve together as a class with instructor guidance. Occasionally, they are intended to review previous grades' concepts in order to connect them to seventh grade concepts. Most often, the Class Activities are for the students to apply what they have already learned.

The mathematics taught in each Class Activity is reinforced by an accompanying Homework component.

The instructional materials for Grade 7 meet the expectation that the design of assignments is not haphazard; exercises are given in intentional sequences.

Students are presented with an Anchor Problem at the beginning of each chapter to introduce new concepts. Anchor Problems are sometimes referenced throughout the chapter.

Within each chapter, concept development is sequential. During Class Activities, the teacher introduces new concepts or builds upon prior knowledge. Students work individually or as a whole class when engaged in the Class Activities. The Homework component reinforces the mathematical concepts taught during the previous Class Activity. Spiral Reviews are used to provide continued practice of newly learned mathematical concepts throughout the year.

The progression of lessons taught is intentional and assists students in building their mathematical understanding and skill. Students begin with activities to build conceptual understanding and procedural skill, and progress to applying the mathematics with more complex problems and procedures.

The instructional materials for Grade 7 meet the expectation for the variety in what students are asked to produce.

Throughout the Class Activities, students are asked to produce answers and solutions, discuss ideas, make conjectures, explain solutions and justify reasoning, make sketches and diagrams, and use appropriate models. These aspects are found individually within problems as well as in combination with others, such as provide an explanation of a solution and include a diagram.

• Chapter 3 Class Activity 3.1b: Models are used to represent the quantities and relationships stated in contextual problems. Students examine the models and write numeric expressions that represent the quantities and relationships represented by the models as well as explain why the various correct representations are equivalent. In subsequent tasks students determine and explain which expressions are equivalent, write contexts for expressions, and explain how they determined if various expressions adequately represent given contexts. The final problems provide opportunity for application.

• Chapter 3 Class Activity 3.1c: Students transition from writing numeric expressions to algebraic expressions using the same types of tasks and problem formats as those presented in 3.1b. The materials provide additional practice for students to draw models, define variables, and write expressions that model given situations.

The instructional materials for Grade 7 meet the expectation that manipulatives are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written models.

Colored tiles are used when students work with probability. In Class Activity 1.1a, students are learning the difference between experimental and theoretical probability with the activity, “How Many Green Tiles Are In Your Bag?” Students draw several tiles out of a bag and record the color each time. By using the tiles, students are able to make conjectures, as well as compare theoretical and experimental probability.

The Anchor Problem in chapter 7, “The Teacher Always Wins,” uses teacher-created colored number cubes to create data through a game between the students and the teacher. Students use the data collected from the game to analyze the probability of winning when using different colored cubes.

The instructional materials for Grade 7 meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

• Anchor Problem 4.0 focuses on making sense of quantities given and understanding their relationship to each other as students connect prior learning from 6th grade on determining the unit rate. The teacher notes guide the students’ mathematical development by prompting the teacher to, “Consider having students share out different strategies so that students can consider and respond to the strategies and arguments of others.”

• Class Activities are the guided lessons where a teacher facilitates students through conceptual, procedural, and application work. In Class Activity 4.2c, “Equations of Proportional Relationships,” the teacher notes state, “Students should see that in order to get the output, we multiply the input by the constant of proportionality. It will be more difficult for them to connect the unit rate to the equation, so you may wish to help them transform the equation to the one shown above.”

The materials for Grade 7 meet expectations for containing a Teacher Workbook that has ample and useful annotations and includes suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

• The Teacher Workbook offers suggestions and annotations, labeled in red, on how to present the content.
  • Chapter 8 Class Activity 8.1a: Suggestions are listed as to the ideas that should be discussed as students engage in the activity. The suggestions include, “Are all squares rectangles? Are all rectangles squares?” and “Relationship between perimeter and area: Discuss similarities and differences in how each is found.”
• There are suggestions occasionally placed as to common student mistakes and misconceptions that teachers could expect. In Chapter 3 Class Activity 3.2a, “Model and Solve Equations,” the teacher notes read, “It will be very helpful to change the problem to x + (−1) = 6 and continue this structure throughout. In this way we are always adding the additive identity. As problems become more complex, students often become confused with problems like 5x – 7 = −3; students will not know if they should add 7 or −7 or if they should subtract 7 or −7. Attend to precision.
• Scaffolding is provided as, "remind students that...” or “probe students to think..."
• A small number of links are embedded to assist in presenting the material. However, geometry software and graphing calculators are mentioned for students use.

The instructional materials for Grade 7 meet expectations for containing a Teacher Workbook that contains full, adult-level explanations and examples of the more advanced mathematical concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

• Mathematical Foundations, written for each chapter, is a resource for teachers to understand the mathematics of the chapter and for teachers to expand their understanding of the mathematical concepts.

• Each Mathematical Foundations includes problems, explanations of problems, examples, and connections to CCSSM.

• The Teacher Workbook provides clear, step-by-step solutions.

The instructional materials for Grade 7 meet expectations for containing a teacher edition (in print or clearly distinguished and accessible as such in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.

• Each chapter contains an overview section that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Knowledge required from prior chapters and/or grades is explicitly called out in this section. The Prior Knowledge section for Chapter 8 states, “During their study of geometry in 6th grade, students should have learned that the height and base of an object are always perpendicular to each other. They will build on this understanding as they apply their knowledge of area and volume to real life contexts and as they explore cross sections and plane sections.”

• The teacher edition connects the learning from previous grade levels and explains how standards build on one another throughout the program. The chapter overview for Chapter 4 states, “Students will use proportions as a basis for understanding scaling. In 8th grade, proportions form the basis for understanding the concept of constant rate of change (slope). Also in 8th grade students will finalize their understanding of linear relationships and linear functions; proportional relationships studied in this chapter are a subset of these relationships.”

The instructional materials for Grade 7 meet expectations for providing opportunities for ongoing review and practice for students in learning both concepts and skills.

Over the course of each chapter, responsibility for the learning process transfers from the teacher to the student. Students move from scaffolded support within the Class Activities to independent problem solving within the Homework. The Anchor Problems at the beginning of each chapter incorporate review and practice of previously taught standards.

• Chapter 1, Class Activity 1.3a, Teacher Note: “As you go through this lesson, repeatedly ask the students how much of the whole/original is left. This will help them transition to finding the percent change.”

• Anchor Problems engage students in both previously-taught standards as well as standards that are to be covered in the chapter. The Anchor Problems often guide the teacher to return to the problem while working through the concepts in the chapter. Anchor Problem 2.0: Operations on the Number Line, reads, “Ask students to justify their conjectures with viable arguments. Then give student groups the opportunity to communicate their reasoning. Return to this activity as you work through the chapter and ask students to reevaluate their conjectures.”

• Mathematical concepts are reinforced by an accompanying Homework component for each Class Activity that is designed for individual practice.

• The materials provide frequent opportunities for ongoing review and practice in the Spiral Review component located within the Homework. The Spiral Review consists of five questions from standards covered both from within the chapter and from previous chapters.

• Opportunities are provided for ongoing practice as extra lessons in a chapter. Chapter 6, Section 6.2e has a lesson labeled, “Extra Practice: Write and Solve Equations.” This lesson is treated separately as it does not contain the accompanying Homework lesson that do the Class Activities.

The instructional materials for Grade 7 meet expectations for frequently embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

Tasks allow students to use multiple entry points and to solve problems using a variety of strategies, paths, and/or models. For example, the Anchor Problem for Chapter 6 involves negative and positive numbers on a number line. Students determine what equations are positive or negative, given the information on the number line. This problem requires students to make their own assumptions and simplifications.

Teachers are asked to model various solution strategies and to lead students through finding a solution path.

The instructional materials for Grade 7 meet expectations for providing a balanced portrayal of various demographic and personal characteristics.

• No examples of bias was found.

• Pictures, names, and situations present a variety of ethnicities and interests. In Chapter 1, Class Activity 1.2e, a variety of ethnicities and interests are present throughout many multi-step problems. The examples include, “Juan earned money for creating a webpage for a local business. He used 1/2 of the money he earned for new shoes and 2/3 of the rest for music. He has $20 left. How much money did he earn for his work?” “Mila rode in a bike tour across Utah. On one particular day, 40% of her ride was uphill. Of the rest of her ride, 1/3 was downhill and 2/3 was flat. If the flat portion of her ride was 36 miles, how far did she ride that day?” and “Marco’s football team was 20 yards from the goal when they got possession of the football. At the end of one play, they got halfway to the goal. After the second play, they made half that distance closer to the goal. After the third play, they got half the remaining distance. How far were they from the goal line before the fourth play?”