# Generating Polynomials from Patterns

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to manipulate and calculate with polynomials. In particular, it aims to identify and help students who have difficulties in:

- Switching between visual and algebraic representations of polynomial expressions.
- Performing arithmetic operations on algebraic representations of polynomials, factorizing and expanding appropriately when it helps to make the operations easier.

## Introduction

In this lesson students make connections between representations, clear parentheses, simplify, factorize, and use the arithmetic of polynomials in a purposive context.

- Before the lesson students work individually on the
*Sequences and Equations*task*.*You review their responses and create questions for students to consider, to help improve their work. - You introduce the lesson by showing students how the card matching activity works. Students then work collaboratively in small groups to match diagrammatic and algebraic representations of polynomials, displaying their work on posters. Students share their finished posters, comparing reasoning and checking that explanations are clear and complete.
- In a whole-class discussion, you reflect on the strategies students have used to complete the task.
- In a follow-up lesson students work individually to review their solutions to the initial assessment task before completing a second task,
*Sequences and Equations (revisited)*.

## Materials required

- Each student will need a copy of
*Sequences and Equations*and*Sequences and Equations (revisited)*, a mini-whiteboard, pen, and eraser. - Each small group of students will need the cut-up card sets
*Sequences of Dots*and*Adding Polynomials*, a large sheet of poster paper, a glue stick, and a pencil. - Students needing an extension should be given
*Card Set: Blank Cards*to create their own sequences of dots with algebraic expressions.

## Time needed

Approximately 15 minutes before the lesson, a 75-minute lesson (or two 40-minute lessons), and 15 minutes in a follow-up lesson. Exact timings with 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
- 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-APR: Perform arithmetic operations on polynomials
- H.A-SSE: Interpret the structure of expressions