# Optimizing Coverage: Security Cameras

## Mathematical goals

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

- Analyze a realistic situation mathematically.
- Construct sight lines to decide which areas of a room are visible or hidden from a camera.
- Find and compare areas of triangles and quadrilaterals.
- Calculate and compare percentages and/or fractions of areas.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students attempt the
*Security Cameras*task individually. You review their responses and formulate questions for students to consider in order to improve their work. - At the start of the lesson, students respond individually to the questions set. They then work in small groups to produce a joint solution to the
*Security Cameras*task, in the form of a poster. - In the same small groups, students evaluate and comment on sample responses, identifying the strengths and weaknesses in these responses and comparing them with their own work.
- In a whole-class discussion students compare and evaluate the methods they have seen and used.
- In a follow-up lesson, students reflect on their work and what they have learned.

## Materials required

- Each individual student will need a copy of the assessment task
*Security Cameras,*a mini-whiteboard, a pen, and an eraser. Provide rules if requested. - Each small group of students will need at least two copies of the
*Plan View,*a sheet of poster paper, felt tipped pens, a glue stick, and copies of*Sample Responses to Discuss*.

There is a projector resource to help to introduce activities and support whole-class discussions.

## Time needed

20 minutes before the lesson, a 90-minute lesson (or two 50-minute lessons) and 10 minutes in a follow-up lesson. Timings given are only approximate and 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:*

- 6.G: Solve real-world and mathematical problems involving area, surface area, and volume.
- 6.RP: Understand ratio concepts and use ratio reasoning to solve problems.