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.


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.