Working with Decimals

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.


Working with Decimals Lessons
Revision Lessons


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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