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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.

July 3, 2020

Students are challenged to apply their understanding of the mean, mode, median and range to calculate datasets by setting up and solving equations.

June 30, 2020

Five, real-life and functional problem solving questions on compound percentage changes.