# Using Positive and Negative Numbers in Context

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the structures:

Starting temperature + Change in temperature = Final temperature Final temperature – Change in temperature = Starting temperature Final temperature – Starting temperature = Change in temperature

## Introduction

The lesson unit is structured in the following way:

- Before the lesson students work individually on an assessment task designed to reveal their current understanding. You review their responses and write questions to help them improve their work.
- After a whole-class introduction, students work together in small groups on a card-matching task.
- In the same small groups, they then create directed number calculations to correspond to temperature changes or city temperatures. To end the lesson there is a whole-class discussion.
- In a follow-up lesson, students again work alone on a task similar to the assessment task.

## Materials required

- Each student will need a copy of the assessment task
*Temperature Changes*and*Temperature Changes (revisited),*a copy of the*Temperature Scale*, a mini-whiteboard, a pen, and an eraser. - Each small group of students will need a set of cut-up cards from the sheets
*City Temperatures*and*Changes in Temperature*, a glue stick, and a large sheet of paper for making a poster. - You will also need one copy of the cut-up cards
*Introduction to Negative Numbers*.

## Time needed

15 minutes before the lesson, a 100-minute lesson (or two 55-minute lessons), and 20 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of your class.

## 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
- 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:*

- 7.EE: Use properties of operations to generate equivalent expressions.
- 7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
- 7.NS: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.