Classifying Proportion and Non-Proportion Situations
This lesson unit is intended to help you assess whether students are able to:
- Identify when two quantities vary in direct proportion to each other.
- Distinguish between direct proportion and other functional relationships.
- Solve proportionality problems using efficient methods.
This lesson unit is structured in the following way:
- Before the lesson, students work individually on a task designed to reveal their current levels of understanding. You review their solutions and write questions to help them improve their work.
- At the beginning of the lesson, there is a whole-class discussion about key features of direct proportionality.
- Students then work in small groups on a task related to the assessment task. They write and solve their own questions on direct proportion, exchange questions with another group, assess each other’s work, and write suggestions for improvement.
- In a whole-class discussion, students share their questions and solution methods, generalizing to identify criteria for identifying direct proportion.
- In a follow-up lesson, students use their learning and your questions to review their work.
- Each individual student will need a calculator, a mini-whiteboard, a pen, an eraser, a copy of the assessment task, Getting Things in Proportion, and a copy of the review task, Getting Things in Proportion (revisited).
- Each small group of students will need a copy of the lesson tasks, Direct Proportion or Not? and Swapping Questions.
15 minutes before the lesson, a 60-minute lesson, and 15 minutes in a follow-up lesson. These timings are approximate: exact timings will depend on the needs of your class.
This lesson involves a range of mathematical practices from the standards, with emphasis on:
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning
Mathematical Content Standards
This lesson asks students to select and apply mathematical content from across the grades, including the content standards: