Paige thinks of a number. "If I double my number and add 4 the answer is 40"


Rachel thinks of a number. "If I multiply my number by 4 and add 2 the answer is 78"


Rebecca thinks of a number. "If I add 4 to my number then divide the result by 2, the answer is 6"


Richard thinks of a number. "If I multiply my number by 3 and subtract 5 then multiply the result by 4, the answer is 2 less than 186"

What numbers are they thinking about?

Think Of A Number

Topics: Starter | Algebra | Functions | Puzzles

  • C Fleming, Lancashire
  • Unfortunately the faces on these starters are an excuse to be distracted for some of my pupils.
  • It was quite a challenge but we achieved it!
  • Transum,
  • While it is certainly possible to solve these problems by trial and improvement, older children could use the 'working backwards' method using inverse operations. Secondary students may decide to use algebra to produce a linear equation to be solved.
    Each time you refresh the page a new set of problems appear.
  • Year 7 St Michaels, St Michaels
  • We found it hard but did it. We are amazing!
  • Noah, Charnwood Primary Lichfield, Year 6
  • Not too tricky but you needed to read things carefully or it could catch you out. A good maths starter.
  • Transum,
  • Here's a different type of THOAN mystery. Think of a three digit number that has all three digits the same. Divide the number by the sum of the digits. I know what your answer is! Is it 37?
  • Mrs Royde, Manchester
  • The weakest girl in Year 9 bottom managed to work out one of these, much to my surprise. I asked her how she did it, she said 'I worked it out backwards'. I said, 'but you told me you can't do algebra!' She said 'this isn't algebra.' I told her it is, and then showed her how to write it using an x and how to figure it out. She was so chuffed that she had done it that she concentrated and worked brilliantly for the rest of the lesson.
  • Mrs Amin, Francis Holland School
  • I gave my girls in year five 2 minutes to do these and they all completed it and said it was very fun!
  • St Michaels,
  • We loved this starter, it was awesome.
  • Hanna Giha, Bruntsfield Primary, Edinburgh
  • This was a challenging, especially the angel one but I managed to do it.

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

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Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.

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Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to a related student activity.

Student Activity


Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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