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Students learn how to use a range of written methods to calculate and order decimal numbers. As learning progresses they use equivalent fractions to solve problems involving long division.

This unit takes place in Term 5 of Year 9 and is followed by working with fractions and mixed numbers.

**Prerequisite Knowledge**

- read and write decimal numbers as fractions [for example, 0.71 = 71/100 ]
- recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
- round decimals with two decimal places to the nearest whole number and to one decimal place
- read, write, order and compare numbers with up to three decimal places

**Success Criteria**

- order positive and negative decimals
- use the symbols =, ≠, <, >, ≤, ≥
- apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative;
- understand and use place value
- recognise and use relationships between operations
- estimate answers; check calculations using approximation and estimation, including answers obtained using technology

**Key Concepts**

- Use the place value table to teach the column method of addition and subtraction of decimal numbers. This helps students to align the digits to the decimal place.
- 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.

**Common Misconceptions**

- 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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