Bob's Buttons Investigation Guide 1

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Bob arranged the buttons in groups of 4 and had 2 left over, and in groups of 5 and had 1 left over. The smallest number of buttons he could have had was 6.

  1. Investigate what other numbers of buttons would also fit the pattern.
    Can you find a way of describing all the possibilities?
    Which of the following fit the pattern?:
    316 220 846 715 3,476
  2. What if the task were changed to:
    Groups of 4 with 3 remainder and groups of 5 also with 3 remainder?
  3. Investigate different remainders for each group.
    Can you always find a pattern to predict the answers?
  4. Investigate if the groups were other numbers apart from 4 and 5, say groups of 3 and 4, or groups of 3 and 5, or 2 and 7, or 5 and 7,....
  5. What if there were three types of groups:
    • in groups of 3 there were 2 remainder
    • in groups of 4 there was 1 left over
    • in groups of 5 there was 2 left over

    What is the smallest number of buttons?
    What other possibilities are there?
    1.  

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