# Increasing and Decreasing Quantities by a Percent

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to interpret percent increase and decrease and in particular, to identify and help students who have the following difficulties:

- Translating between percents, decimals, and fractions.
- Representing percent increase and decrease as multiplication.
- Recognizing the relationship between increases and decreases.

## Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on an assessment task that is designed to reveal their current understanding and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
- Students work in small groups on collaborative discussion tasks, to organize percent, decimal and fraction cards. As they do this, they interpret the cards’ meanings and begin to link them together. They also try to find relationships between percent changes. Throughout their work, students justify and explain their decisions to their peers.
- Students return to their original assessment task and try to improve their own response.

## Materials required

- Each student will need two copies of the assessment task
*Percent Changes*, a calculator, a mini-whiteboard, a pen, and an eraser. - Each small group of students will need copies of
*Card Sets: A, B, C, D,*and*E*. All cards should be cut up before the lesson. Optional materials are a large sheet of card on which to make a poster and some glue sticks and/or the poster template*Percents, Decimals, and Fractions (1)*. - You will also need copies of the extension material:
*Percents, Decimals, and Fractions (2)*.

## Time needed

15 minutes before the lesson, a 90-minute lesson (or two shorter lessons), and 10 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of the 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.NS: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
- 7.RP: Analyze proportional relationships and use them to solve real-world and mathematical problems.