Read more about the purpose of the MAP *Classroom Challenges*…

## Solving Geometry Problems: Floodlights

### 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.

### 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.

### 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
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP7: Look for and make use of structure

### Mathematical Content

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

### Resources

#### Lesson (complete)

- solving_geometry_problems_complete.pdf ( 3958.8K PDF/Acrobat 17 Apr 2012)

#### Projector Resources

- solving_geometry_problems_slides.ppt ( 3413.5K MS PowerPoint 17 Apr 2012)

A draft Brief Guide for teachers and administrators (PDF) is now available, and is recommended for anybody using the MAP *Classroom Challenges* for the first time.

We have assigned lessons to grades based on the Common Core State Standards for Mathematical Content. During this transition period, you should use your judgement as to where they fit in your current course.

The Beta versions of the MAP Lesson Units may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved. Please send any enquiries about commercial use or derived works to map.info@mathshell.org.

Can you help us by sending samples of students' work on the *Classroom Challenges?*