Read more about the purpose of the MAP *Classroom Challenges*…

## 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 understandings 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 tasks, and try to improve their own responses.

### 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)*.

There is also a projector resource to help with whole-class discussions.

### Time needed

15 minutes before the lesson, one 90-minute lesson (or two 45-minute lessons), and 10 minutes in a follow-up lesson (or for homework). Timings are approximate and will depend on the needs of the class.

### Mathematical Practices

This lesson involves a range of *mathematical practices* from the standards, with emphasis on:

### Mathematical Content

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

- 7.RP: Analyze proportional relationships and use them to solve real-world and mathematical problems.
- 7.NS: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

### Resources

#### Lesson (complete)

- percents_complete.pdf ( 3079.7K PDF/Acrobat 05 Jun 2014)

#### Projector Resources

- percents_slides.ppt ( 206K MS PowerPoint 14 Mar 2014)

A draft Brief Guide for teachers and administrators (PDF) is now available, and is recommended for anybody using the MAP *Classroom Challenges* for the first time.

We have assigned lessons to grades based on the Common Core State Standards for Mathematical Content. During this transition period, you should use your judgement as to where they fit in your current course.

The Beta versions of the MAP Lesson Units may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved. Please send any enquiries about commercial use or derived works to map.info@mathshell.org.

Can you help us by sending samples of students' work on the *Classroom Challenges?*