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**Scheme of work: GCSE Higher: Year 9: Term 1: Fractions and Decimals**

- Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
- interpret fractions as operators
- estimate answers; check calculations using approximation and estimation, including answers obtained using technology
- order positive and negative decimals

- Apply the four operations, including formal written methods, simple fractions (proper and improper)
- express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
- apply the four operations, including formal written methods, to mixed numbers both positive and negative;
- calculate exactly with fractions

- All rational numbers are written using exact proper or improper fractions.
- When adding or subtracting fractions the denominators need to be equal.
- Dividing fractions is equivalent to multiplying by a reciprocal.
- When calculating with decimal numbers encourage students to estimate the solution as means to check their working.
- Students may need to recap multiplying and diving by powers of ten when calculating the product of decimal numbers.
- Use equivalent fractions when performing long division. Simplifying the fractions help to break down the calculation.

- A fraction with a smaller denominator has a lesser value.
- Fractions such as 3/5 can incorrectly assumed to have a decimal equivalence of 3.5.
- Students incorrectly consider multiplications to always increase a number and divisions to decrease.
- Students fail to spot incorrect calculations due to not estimating solutions.

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