## Lesson Plan A.2: Proportional Relationships and Similarity

**Essential Questions: **

**Lesson Plans and Seeds**

**Lesson Plan A.2: Proportional Relationships and Similarity**

Lesson Seed A.2: Creating a Graph from a Table

Lesson Seed A.2: Calculator and Direct Variation

**Download Seeds, Plans, and Resources (zip)**

**Content Emphasis By Clusters in Grade 7**

**Progressions from Common Core State Standards in Mathematics**

Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery..

**Lesson Plan: 7.RP.A.2 **– Proportional Relationships and Similarity

**Unit/Cluster: **Analyze proportional relationships and use them to solve real-world and mathematical problems.

**Lesson Topic: **Proportional relationships that lead to the idea of similarity.

**Focus Standard(s)**

**7.RP.A.2: **Recognize and represent proportional relationships between quantities

- Decide whether two quantities are in a proportional relationship.
- Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships.
- Represent proportional relationships by equations.
- Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.

It is critical that the **Standards for Mathematical Practices** are incorporated in ALL lesson activities throughout the unit as appropriate. It is not the expectation that all eight Mathematical Practices will be evident in every lesson. The **Standards for Mathematical Practices** make an excellent framework on which to plan your instruction. Look for the infusion of the Mathematical Practices throughout this unit.

**Coherence of Standards**

__Across-Grade Coherence: Content Knowledge from Earlier Grades__

**6.RP.A.1 **Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

**6.RP.A.2 **Understand the concept of a unit rate associated with a ration a:b with b 0, and use rate language in the context of a ratio relationship.

**6.NS.C.6 **Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

__Within-Grade Coherence: Content from Other Standards in the Same Grade that Provide Reinforcement__

**7.NS.A.3 **Solve real-world and mathematical problems involving the four operations with rational numbers. Note: Computations with rational numbers extend the rules for manipulating fractions to complex Fractions

**7.G.A.1 **Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

**7.SP.C.6 **Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

**7.SP.C.8 **Find the probabilities of compound events using organized lists, tables, tree diagrams and simulation.

**7.RP.A.1 **Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

**7.RP.A.3 **Use proportional relationships to solve multistep ratio and percent problems.

**RIGOR**

__Procedural Skill__

Students apply the concept of unit rate to develop the concept of constant of proportionality. Students will apply their knowledge of fractions to solve a proportion, ratio tables, and/or apply their knowledge to solve a proportion.

__Conceptual Understanding__

Students develop the meaning of constant of proportionality by modeling and writing equations.

__Modeling/Application__

Students represent constant of proportionality through graphing and writing equations.

**Enduring Understandings:**

- Recognize that a given proportional situation can be represented in more than one way.
- Distinguish between additive and multiplicative situations.
- Recognize two equivalent ratios represent a proportion.
- Recognize and represent the connection between equivalent ratios, values in a table, and graphed ordered pairs.
- Proportional reasoning involves comparisons of the relationships among ratios.

**Student Outcomes**

- Explore multiple representations to recognize proportional relationships.
- Represent proportional relationships to solve multi-step ratio problems.

**Method for Determining Student Readiness for the Lesson**
Ask students to answer the following ratio and unit rate questions.

- There are 300 people at a school play; 90 of these people are adults and the rest are students. What is the ratio of adults to students? Write your answer in three different ways.
- Last week Bill earned $210 for a 30-hour week. What was his hourly pay rate? What would he have earned for a 40-hour week?