Teaching multiplying and dividing by 0.1, 0.01 and 0.001 can be surprisingly difficult for students. Many rely on memorised rules rather than understanding how digits move within the place value system.
In this lesson, I use the place value table to make that movement explicit, helping students build a secure method they can apply consistently.
One way to help students understand multiplying and dividing by a power of ten is to use the place value table. The place value table shows the value of each digit in a number, and it can be used to track the movement of the numbers when multiplying or dividing by a power of ten.
The following is a summary of the key teaching points for this lesson:
When students approach multiplying and dividing by 0.1, 0.01, and 0.001, common misconceptions often arise. Many believe that numbers “become smaller” when multiplied by these decimals, which can result in incorrect solutions. Others may add zeros rather than shift digits in the appropriate direction on the place value table. Addressing these misconceptions early is crucial for building a robust foundation in the subject.
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:
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.
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Key Questions:
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:
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.
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Students learn to use the place-value table and written methods to multiply and divide numbers by 0.1 and 0.01.
As learning progresses, more able students multiply and divide by powers of ten expressed in index form.
Related Blog: Multiplying and Dividing Numbers by 0.1 and 0.001: A Guide for Key Stage 3 Teachers
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