# Representing the Laws of Arithmetic

## Mathematical goals

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

- Perform arithmetic operations, including those involving whole-number exponents, recognizing and applying the conventional order of operations.
- Write and evaluate numerical expressions from diagrammatic representations and identify equivalent expressions.
- Apply the distributive and commutative properties appropriately.
- Use the method for finding areas of compound rectangles.

## 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 and difficulties. You then review their responses and create questions for students to consider when improving their work.
- After a whole-class introduction, students work collaboratively on a card matching activity. Towards the end of the lesson there is a whole-class discussion.
- In a follow-up lesson, students work alone on a similar task to the introductory assessment task.

## Materials required

- Each student will need a copy of the two assessment tasks:
*Expressions and Areas*and*Expressions and Areas (revisited),*a mini-whiteboard, a pen, and an eraser. - Each small group of students will need cut-up copies of
*Card Set: Expressions*and*Card Set: Area Diagrams*, a large sheet of paper for making a poster, and a glue stick. - 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 to support discussions.

## Time needed

15 minutes before the lesson, an 85-minute lesson (or two 50-minute lessons), and 15 minutes in a follow-up lesson. Timings are approximate. Exact timings 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
- 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:*

- 6.EE: Apply and extend previous understandings of arithmetic to algebraic expressions.
- 6.G: Solve real-world and mathematical problems involving area, surface area, and volume.