Choose your number to start and shade it on the grid.

To go to another number you can either MULTIPLY BY 2  or  SUBTRACT 5.

So if you start on 12,  you can either shade 12 x 2 = 24  or 12 – 5 = 7

Choose any shaded number and carry on until you can’t get to any numbers except numbers already shaded.

Record your results.

  1. Choose another number to start. Which numbers can you visit?
  2. Can you find a starting number that takes you to all the numbers in the grid?
  3. What happens if you use a grid for 1 to 100? You can download a grid here.
  4. Describe at least one pattern that you notice.
  5. This puzzle starts with a 5×5 square of numbers and you can either x2 or -5. Invent a new puzzle by slightly changing something in the rules of this puzzle. Tell us about your puzzle.

Click here to download the WHERE CAN WE VISIT worksheet.

Click here to download the Notes for Teachers.

This problem is adapted from the NRICH task with the same name with permission of the University of Cambridge. All rights reserved.

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6 Responses to Where can we visit?

  1. Cup Xalabile says:

    I try this with my learners, in grade 6, they struggled a lot. but at the end they master. They even come up with their examples

    • toni says:

      Thank you for your comment. It would be interesting for other teachers to know how you helped your learners to overcome their difficulties. Could you perhaps tell us more about the examples that your learners came up with?

  2. Fezzy Gxothiwe says:

    I did it with my chidre at home.They are doing grades 4 and 7.They enjoyed it.With my grade 4’s it was difficult at first,but when they masterd they did not want to stop.I showed it to my neighbor who is teaching maths in another school and she sai that she is going to do it with her learners.

    • toni says:

      Fezzy it is interesting that both Grade 4 and Grade 7 learners were able to tackle this problem. Did the older one help the younger one?

      Please ask your neighbour to tell you about what happened when she used the problem in her school and then report back.

      Will you use it in your teaching?

  3. Khosie Ntlantsana says:

    Idid this problem with my grade 07learners some enjoyed it but some have some prolem.

    • toni says:

      Khosie this comment is very brief. Try to explain the nature of the difficulties that your learners experienced and how you helped them to overcome their difficulties and to succeed eventually.

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