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So It's Times!

Age 7 to 14
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On the table in front of you is a grid like this:

 Six by six grid of the numbers 1 to 36

Imagine that you have another version of this grid (with the same numbers), but this one is made of plastic that you can see through. You place the plastic one over the other grid so that it covers it completely. You can flip it over and/or turn it around as you put it down. Now, each pair of numbers (one above the other) is multiplied together, and all of these products are added together.

Your challenge is to say which way of flipping over and/or turning the plastic grid will give you the highest total and which way will give you the lowest total, without calculating and adding together the 36 multiplications.

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This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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