Proportional reasoning is an important topic that middle school teachers need to address, but it is also foundational for later topics in high school algebra and calculus: slope, changing rates (quadratic functions), and instantaneous rates of changes (derivative). Pre-service teachers experience an inquiry-oriented mathematics unit on proportional reasoning, which provides them with opportunities to: (a) make explicit and deepen implicit conceptual underpinnings of their own proportional reasoning; (b) learn to create drawings, explanations and representations that will help their future students develop understanding of ratios and proportions; and (c) analyze secondary school students’ reasoning and conceptual challenges through the regular use of student work and Project MathTalk videos.
Lesson 1: What Is Proportional Reasoning?
- Lesson 1 PowerPoint: Click on link. Download as a PowerPoint presentation. Do NOT open/download in Google Slides, or formatting and some content may be lost.
- Lesson 1 Instructor Notes
- Activity 1 for Lesson 1
- Activity 2 for Lesson 1
- Homework 1
- Reading for Homework 1
Lesson 2: What Does NON-Proportional Reasoning Look Like?
- Lesson 2 PowerPoint: Click on link. Download as a PowerPoint presentation. Do NOT open/download in Google Slides, or formatting and some content may be lost.
- Lesson 2 Instructor Notes
- Activity 1 for Lesson 2
- Activity 2 for Lesson 2
- Activity 3 for Lesson 2
- Homework 2
- Reading for Homework 2
Lesson 3: Forming a Ratio as a Composed Unit
- Lesson 3 PowerPoint: Click on link. Download as a PowerPoint presentation. Do NOT open/download in Google Slides, or formatting and some content may be lost.
- Lesson 3 Instructor Notes
- Activity 1 for Lesson 3
- Activity 2 for Lesson 3
- Activity 3 for Lesson 3
- Homework 3
- Reading for Homework 3
Lesson 4: Forming a Ratio as Multiplicative Comparison
- Lesson 4 PowerPoint: Click on link. Download as a PowerPoint presentation. Do NOT open/download in Google Slides, or formatting and some content may be lost.
- Lesson 4 Instructor Notes
- Activity 1 for Lesson 4
- Activity 2 for Lesson 4
- Homework 4
- Reading for Homework 4
Lesson 5: Effective Explanations
- Lesson 5 PowerPoint: Click on link. Download as a PowerPoint presentation. Do NOT open/download in Google Slides, or formatting and some content may be lost.
- Lesson 5 Instructor Notes
- Activity 1 for Lesson 5
- Explanation 1 for Activity 1
- Explanation 2 for Activity 1
- Activity 2A for Lesson 5
- Activity 2B for Lesson 5
- Homework 5
- Reading for Homework 5
Lesson 6: Interpreting Ratios as Functions
- Lesson 6 PowerPoint: Click on link. Download as a PowerPoint presentation. Do NOT open/download in Google Slides, or formatting and some content may be lost.
- Lesson 6 Instructor Notes
- Activity for Lesson 6
- Homework 6
- Reading for Homework 6
- Optional Additional Reading