Bob's Buttons Investigation Guide 1
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.
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- 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?:
- What if the task were changed to:
Groups of 4 with 3 remainder and groups of 5 also with 3 remainder?
- Investigate different remainders for each group.
Can you always find a pattern to predict the answers?
- 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,....
- What if there were three types of groups:
- in groups of 3 there were 2
- 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?