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Students learn how to calculate equivalent fractions and convert between mixed numbers as a top-heavy fractions. They use this knowledge to add, subtract, multiply and divide with fractions and mixed numbers.

This topic takes place in Term 4 of Year 9 and follows properties of number.

**Prerequisite Knowledge**

- Recognise, find and name a half as one of two equal parts of an object, shape or quantity
- Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

**Success Criteria**

- order positive fractions
- 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;
- interpret fractions as operators
- express a multiplicative relationship between two quantities as a fraction
- calculate exactly with fractions

**Key Concepts**

- Fractions represent a proportion of an amount hence the equivalence with decimals and percentages.
- A fraction is equivalent to a division
- 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.

**Common Misconceptions**

- A shape that is split in two is not necessarily split in half. A half must be two equal proportions of a shape.
- A fraction with a larger denominator has the greater value.
- A fraction with a smaller denominator has a lesser value.
- Fractions such as 3/5 incorrectly have a decimal equivalence of 3.5.

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson. Writing Equivalent Ratios A few students immediately go […]