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

## Estimating: Counting Trees

### Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

- Solve simple problems involving ratio and direct proportion.
- Choose an appropriate sampling method.
- Collect discrete data and record them using a frequency table.

### Introduction

The unit is structured in the following way:

- Before the lesson, students attempt the
*Counting Trees*task individually. You then assess their responses, and formulate questions that will prompt students to review their work. - At the start of the lesson, students think individually about their responses to the questions set.
- Next, students work in small groups to combine their thinking and work together to produce a collaborative solution to the
*Counting Trees*task, in the form of a poster. - Working in the same small groups, students evaluate and comment on sample responses, identifying the strengths and mistakes 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.
- Finally, students reflect on their work and their learning.

### Materials required

- Each individual student will need a copy of the task
*Counting Trees,*at least one copy of*The Tree Farm*, and a copy of the questionnaire*How Did You Work?* - Each small group of students will need at least one enlarged copy of
*The**Tree Farm*, a sheet of poster paper, a glue stick, felt tipped pens, and copies of*Sample Responses to Discuss.*

There are some projector resources to help introduce activities and support whole-class discussions.

### Time needed

15 minutes before the lesson, a 70-minute lesson and 10 minutes in a follow-up lesson (or for homework.) Timings given are only approximate. Exact timings will depend on the needs of your class.

### 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
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically

### Mathematical Content

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

- 7.RP: Analyze proportional relationships and use them to solve real-world and mathematical problems.
- 7.SP: Use random sampling to draw inferences about a population.
- 7.G: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

### Resources

#### Lesson (complete)

- estimating_counting_trees_complete.pdf ( 1662.5K PDF/Acrobat 15 Mar 2012)

#### Projector Resources

- counting_trees_slides.ppt ( 605.5K MS PowerPoint 15 Mar 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?*