# Sampling and 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 improve 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 and comparing them with their own work.
- In a whole-class discussion, students compare and evaluate the methods they have seen and used.
- In a follow-up lesson, 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*How Did You Work?*questionnaire. - 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 the*Sample Responses to Discuss.*

## Time needed

15 minutes before the lesson, a 95-minute lesson (or two 50-minute lessons), and 10 minutes in a follow-up lesson. Exact timings will depend on the needs of your class.

## Lesson Type

## 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
- 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:*

- 7.G: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- 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.