Alejandro thinks of a number. "If I double my number and add 4 the answer is 20"


Alex thinks of a number. "If I multiply my number by 4 and add 5 the answer is 85"


Alexa thinks of a number. "If I add 5 to my number then divide the result by 2, the answer is 3.5"


Alexandra thinks of a number. "If I multiply my number by 2 and subtract 6 then multiply the result by 2, the answer is 4 less than 8"

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.

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.
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This starter has scored a mean of 3.3 out of 5 based on 735 votes.

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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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Texas Instruments Nspire Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a gift for a special occasion but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

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Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.

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

Student Activity



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