Module 3 Calculating
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Can I make use of my understanding of place value to explain how to mentally multiply or divide a decimal number by an integer?

Example review questions

  • How many hundredths are equivalent to 0.35? Use this to work out 0.35 ÷ 5.
  • Explain how you can use the fact 24 ÷ 6 = 4 to answer 2.4 ÷ 6.
  • Find the answers to these calculations and explain your methods:
    • 0.15 × 8
    • 1.2 ÷ 4
    • 0.2 ÷ 5
    • 0.005 × 6
  • Find the missing numbers and explain how you know:
    • empty box × 6 = 3
    • 4.8 ÷ empty box = 0.6
  • Exercise books are 0.8cm thick. A pile of 9 exercise books is on the table. How thick is the pile?
  • A half metre piece of string is cut into 5 equal pieces. How long is each piece in m? How many cm is this?

Teaching guidance

This teaching guidance document suggests some of the key vocabulary, models, images and practical equipment that children should experience and be able to use. It also includes some teaching tips to provide a few starting points for ways of supporting children with this area of mathematics.

PDF file Teaching guidance: Can I make use of my understanding of place value to explain how to mentally multiply or divide a decimal number by an integer? | 52KB new window

Consolidation and practice

These resources are to support children in guided or independent work. Roll over the highlighted resources for a description.

PDF file How to use number dials ITP | 128KB new window

SWF file Number dials ITP | 38KB new window

XLS file Counting stick with further options spreadsheet | 246KB new window

PDF file How to use moving digits ITP | 160KB new window

SWF file Moving digits ITP | 160KB new window

XLS file Multiplying numbers spreadsheet | 40KB new window

PDF file Starter activities | 166KB new window

Visit the nrich website new window for further activities to support practice and application.

Number dials

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This interactive teaching program (ITP) is an ICT-based tool to support the exploration and recall of multiplication and division facts. Number dials ITP allows the child or teacher to generate sets of products of a central number and numbers from 1 to 10. The ITP can be used to practise multiplying and dividing by one- and two-digit whole numbers and decimals.

Moving digits

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This interactive teaching program (ITP) is an ICT-based tool to support the exploration of place value. Moving digits ITP allows the child or teacher to place and move digits on a place value board, investigating the effects of multiplying and dividing by 10 or 100.

Opportunities to use and apply

Possible contexts include:

  • Word problems involving decimal measures, e.g. A carton of juice contains 0.4 litres of juice. How many cartons are needed to have 2 litres of juice altogether?
  • Measure problems, e.g. Gym mats are 1.6 metres long. If 5 mats are placed end to end, what total length will they make?
  • Currency conversion, e.g. £1 is equal to about $1.4. What is the approximate value of £5 in US dollars?
  • Division giving a decimal answer, e.g. Divide 9 by 5 giving your answer as a decimal.
  • Missing number calculations, e.g. empty box ÷ 8 = 0.04; 0.6 × empty box = 4.2

Confirming learning

Ask probing questions such as:

  • Find half of 4.7. Explain how you worked out the answer.
  • Ryan says that 0.18 ÷ 9 = 0.2. Where do you think he went wrong? Explain his mistake and what he needs to do instead.
  • A chocolate bar weighs 0.125 kg. I eat 1/5 of it. How much chocolate is this? How do you know?
  • How does your knowledge of 56 ÷ 7 help you to calculate 0.56 ÷ 7?
  • Divide 0.9 by 6. Explain each step of your working.
  • 0.05 × 8 = empty box ÷ 6