Optimizing Coverage: Security Cameras
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.
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.
- 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.
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.
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.