Deducting Relationships: Floodlight Shadows
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.
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.
- 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. There is a projector resource provided to support whole-class discussions.
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.
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: