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Students learn how to solve problems with long multiplication and division using written methods. They use this knowledge to add, subtract, multiply and divide with fractions and mixed numbers. Finally, students learn the difference between terminating and recurring decimals and how to convert a recurring decimal to a simplified fraction.

This unit takes place in Term 1 of Year 9 and is followed by algebraic fractions.

- 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.

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 […]