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.


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. There is a projector resource provided to support whole-class discussions.

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.