# Representing Functions of Everyday Situations

## 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 - 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.

## 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.

## Lesson Type

## Mathematical Practices

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
- MP4: Model with mathematics
- 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:*

- H.A-SSE: Interpret the structure of expressions
- H.F-IF: Interpret functions that arise in applications in terms of the context
- H.F-IF: Analyze functions using different representations
- H.F-LE: Construct and compare linear and exponential models and solve problems
- H.F-LE: Interpret expressions for functions in terms of the situation they model