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, this unit 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 work, and formulate questions to help them improve their solution.
• During the lesson, students first work individually, using your questions, to improve their solutions.
• They then work collaboratively in pairs or threes on the same task. They justify and explain their decisions to peers. 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. Finally, they again work individually to reflect on their solutions to the task.

Materials required

• Each student will need a copy of the task sheet Floodlights, a copy of the questionnaire How did you work?, 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.
• Throughout the lesson provide squared and plain paper, rulers, pencils, protractors, and calculators for students to choose from. There are some projector resources provided to support whole-class discussions.

Time needed

30 minutes before the lesson, a 60-minute lesson, and 10-15 minutes in a follow-up lesson. All timings are approximate. Exact timings will depend on the needs of the students.