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Two Cubes

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]

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Rationals Between...

What fractions can you find between the square roots of 65 and 67?

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Square Mean

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

Inside Outside

Stage: 4 Challenge Level: Challenge Level:1
Time playing with the balance is important.
It would be easy to just tell students about "moments" as a formula, but finding this relationship for themselves through practical investigation is of much higher value.