Multiplying and Dividing Numbers by 0.1 and 0.001: A Guide for Key Stage 3 Teachers

Part 1: Starter – Recapping multiplying and dividing by 10, 100 and 1000

Students begin by revisiting multiplication and division by 10, 100, and 1000. Through matching exercises, they mentally connect numbers to their corresponding calculations.

Key Questions:

1. What happens to a digit when we multiply it by 100?
2. How does dividing by 10 affect the position of a number on the place value table?

Part 2: Main Teaching Phase – Multiplying and Dividing Numbers by 0.1 and 0.001

Students learn to multiply and divide using negative powers of ten. By appealing to their intuition, teachers can help students grasp that dividing by a negative power of ten shifts numbers to the left, while multiplying does the opposite.

Click here to watch the video tutorial

Key Questions:

1. When we multiply by 0.01, how many places does our number move, and in which direction?
2. How does the position of a digit change when dividing by 0.1 on the place value table?

Part 3: Independent Practice – Multiplying and Dividing Numbers by 0.1 and 0.001

In the independent practice section, students will be presented with a similar set of questions as the previous slide. They will need to work through these questions independently to consolidate their learning. The teacher can use this as an opportunity to check their progress and feedback. A differentiated independent learning worksheet is included for early finishers.

Key Questions:

1. Are there any patterns you notice when multiplying or dividing by 0.1, 0.01, or 0.001?
2. How does using the place value table help in ensuring your answers are accurate?

Plenary – Rising to the Challenge

The plenary will act to consolidate students’ learning by giving them a range of questions that includes an introduction to standard form. Students will complete this on mini-whiteboards and present their solutions, with working to the teacher, so the teacher can check progress and feedback.

1. How does the concept of multiplying and dividing by 0.1 and 0.01 relate to standard form?
2. Can you explain, using your mini-whiteboard, the process of multiplying a number by 0.001?