# Deducting Relationships: Floodlight Shadows

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, it aims to identify and help students who have difficulty in:

- Making a mathematical model of a geometrical situation.
- Drawing diagrams to help with solving a problem.
- Identifying similar triangles and using their properties to solve problems.
- Tracking and reviewing strategic decisions when problem-solving.

## Introduction

The lesson is structured in the following way:

- Before the lesson, students attempt an assessment task individually. You review their solutions and formulate questions to help them improve their work.
- At the start of the lesson students work individually answering your questions. They then work collaboratively in pairs or threes to produce a joint solution to the same task. They justify and explain their chosen method. Working in the same small groups, they critique examples of other students’ work on the task.
- In a whole-class discussion, students explain and compare the alternative approaches they have seen and used.
- In a follow-up lesson, students work individually to reflect on what they have learned.

## Materials required

- Each student will need a copy of the
*Floodlights*task, the*How Did You Work?*questionnaire*,*and a sheet of squared paper. - Each small group of students will need a large sheet of paper and copies of the
*Sample Responses to Discuss.* - Provide squared and plain paper, rules, pencils, protractors, and calculators for students to choose from.

## Time needed

30 minutes before the lesson, an 80-minute lesson (or two 45-minute lessons), and 15 minutes in a follow-up lesson. Timings are approximate. Exact timings 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
- 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:*