From nrich.maths.org/6227
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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Example: 5 - 2 = 3 |
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Not only does the NRICH website have intriguing problems and puzzles, but the site also offers teachers. notes, hints, pdf worksheets, and solutions, e.g.,
Teachers’ Notes (from nrich.maths.org/6227&part=note):
Why do this problem?
This problem is a challenging way of practicing subtraction at the same time as being logical about arranging the numbers. The idea of “difference” can be hard for children to grasp and this problem is an ideal way of coming to terms with it. You could also use this problem to focus on how children record their workings.
Possible approach
You could start by putting the numbers in any places in the pyramid and asking children to describe what they see. They may notice some accidental number patterns, but also which numbers are used. Then put two numbers into the pyramid, for example 4 and 5 in the bottom row, next to each other. Introduce the idea of the problem and invite pupils to suggest what number should go above the 4 and 5.
Hint: “Where can the largest number go?” (from nrich.maths.org/content/id/6227/FindDifa.pdf)
Worksheet: A sheet of blank pyramids. (nrich.maths.org/content/id/6227/FindDifa.pdf)
For children who want more of a challenge, add another row (nrich.maths.org/927)
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