Abigail thinks of a number. "If I double my number and add 2 the answer is 36"


Adam thinks of a number. "If I multiply my number by 3 and add 3 the answer is 54"


Adrian thinks of a number. "If I add 3 to my number then divide the result by 2, the answer is 3.5"


Aidan thinks of a number. "If I multiply my number by 5 and subtract 2 then multiply the result by 3, the answer is 6 less than 240"

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 740 votes.

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Apple iPad Pro

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

Math with Bad Drawings

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone.

A Compendium Of 	Mathematical Methods

A Compendium Of Mathematical Methods

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence?

A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more...

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

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Student Activity


Curriculum Reference

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


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