Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

• Articulate verbally the relationships between variables arising in everyday contexts.
• Translate between everyday situations and sketch graphs of relationships between variables.
• Interpret algebraic functions in terms of the contexts in which they arise.
• Reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.

Introduction

The lesson unit is structured in the following way:

• Before the lesson, students work alone on a task designed to reveal their current understanding. You review their solutions and create questions for them to consider to help improve their work.
• In the lesson, students work in small groups on a collaborative task, matching situations, sketch graphs, and algebraic functions. They refine the graphs and interpret the formulas to answer questions. Students then discuss as a whole-class what has been learned and the strategies used.
• In a follow-up lesson, students review their responses to the original task and the questions posed. They use what they have learned to complete a similar task; Another Four Situations.

Materials required

• Each student will need a copy of Four Situations and Another Four Situations and a mini-whiteboard, pen, and eraser.
• Each small group of students will need cut-up card sets: Everyday Situations 1, 2, and 3; Graphs 1 and 2; and Algebraic Functions, poster paper, glue, and a graphing calculator to check answers.
• There is a projector resource to support whole-class discussions. You may also want to copy the card sets onto transparencies to be used on an overhead projector.

Time needed

Approximately 20 minutes before the lesson, an 80-minute lesson (or two 45-minute lessons), and 20 minutes in a follow-up lesson.