In Key Stage 3 mathematics, students learn about multiplying and dividing numbers by 0.1 and 0.001. This can be a difficult concept for some students to grasp, but it is important for them to understand in order to be successful in later mathematics courses.
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.
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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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.
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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