Module 3 Calculating
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Can I solve multi-step problems that involve using inverse operations and explain my methods?

Example review questions

  • Sam thinks of a number. She divides it by 5 and gets the answer 20. What number did Sam think of?
  • Find the missing numbers:
    empty box + 15 = 25 × 5
    empty box × 4 − 19 = 5
  • If you double Joe's age and add 8, you get his mum's age. Joe's mum is 32. How old is Joe?
  • I buy some packets of chewing gum. Each packet costs 25p. I pay with a £2 coin and receive 25p change. How many packets of chewing gum did I buy?
  • When a number is divided by 9, it gives an answer of 13 with a remainder of 7. What is the number?

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 solve multi-step problems that involve using inverse operations and explain my method? | 73KB 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 function blocks ITP | 93KB new window

SWF file Function blocks ITP | 52KB new window

EXE file Empty box program | 874KB new window

XLS file Flash cards spreadsheet | 35KB new window

XLS file Multiplication and division facts mixed
spreadsheet | 39KB new window

PDF file Inverse operations teaching activity | 103KB new window

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

Function blocks

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This interactive teaching program (ITP) is an ICT-based tool to support the exploration of calculation and inverses. Function blocks ITP allows the child or teacher to display and explore the effect of up to three operations on a starting or finishing number. The keypad can be used to input decimal numbers, and two rows of function machines can be displayed to compare the effect of using different input values, order or type of operations.

Empty box program

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This ICT-based tool can be used by children to practise and consolidate multiplication, division, addition and subtraction, and to develop understanding of inverse operations and when not to use a calculator. Different activities, numbers of questions and operations can be selected to vary the level of challenge.

Opportunities to use and apply

Possible contexts include:

  • Missing number calculations, e.g. (empty box ÷ 5) + 19 = 25; 25 × empty box = 3 × 50
  • Word problems, e.g. Robert saves his pocket money for 7 weeks. He uses his savings to buy his mum a present that costs £9.99. He has 51p left over. How much pocket money does he get each week?
  • 'I think of a number' problems, e.g. I think of a number, add 99 and then double. I get the number 288. What number did I think of?

PDF file Mathematical Challenges Year 5 and 6: Slick Jim; Shape Puzzle new window

 

Confirming learning

Ask probing questions such as:

  • I think of a number, divide it by 3 and add 11. I get the answer 21. What number did I think of?
  • Becky buys 3 milkshakes. She pays with a £5 note and gets 35p change. How much does each milkshake cost? Draw a function machine to represent the process you went through to find your answer.
  • What number when multiplied by 4 gives itself plus 60?
  • Ricky is at school from 8:40 am to 3:15 pm. He has 20 minutes registration, 25 minutes break and 50 minutes for lunch. The rest of the school day is organised into 6 equal lessons. How long is each lesson?