# Generalizing Patterns: Table Tiles

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to identify linear and quadratic relationships in a realistic context: the number of tiles of different types needed for a range of square tabletops. In particular, this unit aims to identify and help students who have difficulties:

• Choosing an appropriate, systematic way to collect and organize data.
• Examining the data and looking for patterns; finding invariance and covariance in the numbers of different types of tile.
• Generalizing using numerical, geometrical or algebraic structure.
• Describing and explaining findings clearly and effectively.

## Introduction

The unit is structured in the following way:

• Before the lesson, students attempt the task individually. You then review their work and formulate questions for students to answer in order for them to improve their work.
• At the start of the lesson, students work individually to answer your questions.
• Next, they work collaboratively, in small groups, to produce a better joint solution than those they produced alone. In the same small groups, students critique examples of other students’ work.
• In a whole-class discussion, students explain and compare the approaches seen and used.
• Finally, students reflect on their work and their learning.

## Materials required

• Each student will need the Table Tiles task, a copy of the Grid Paper and a copy of the How Did You Work? questionnaire.
• Each small group of students will need a copy of the Grid Paper and the Sample Responses to Discuss.
• There is a projector resource to help you with the whole-class discussions.

Time needed:

15 minutes before the lesson, a 1-hour lesson, and 10 minutes in a follow-up lesson. All timings are approximate. Exact timings 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 Standards

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