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Students learn about multiplying and dividing with fractions and mixed numbers using both visual and written methods. Learning progresses from finding the product of two fractions to using reciprocal value to divide one mixed number by another.

This unit takes place in Year 8 Term 2 and follows on from working with fractions in Year 7.

- Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥
- Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

- When multiplying and dividing with fractions students should cross-simplify the question to cancel out common terms.
- Being able to visualise division with fractions and mixed numbers helps students understand the written methods.
- To divide with fractions students need to understand reciprocals and how to multiply and divide with 0.1 and 0.01.
- Answers should be left in their simplest terms.

Develop fluency

- Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals and fractions.

Reason mathematically

- Extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations

Solve problems

- Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems

Number

- Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals.
- Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
- Use a calculator and other technologies to calculate results accurately and then interpret them appropriately

January 26, 2022

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