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What's My Weight?

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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Can you work out how many of each kind of pencil this student bought?

Squaring the Circle

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.

Counting Sweets

Age 7 to 14
Challenge Level

At a school fair there is a game where there is a jar full of sweets and whoever guesses  a number closest to the number of sweets in the jar wins. Can you think of some good ways to improve your chance of winning? Are there any tools or items that might be helpful? Would certain sorts of sweets be easier to estimate than others?

If you had the same sort of jar at home how could you use that to help you guess? Could a different sort of jar ever be helpful?
What about if you had to guess the combined weight of the sweets in the jar rather than how many there were?

To make this problem harder you could say that there were no more than 1000 sweets in the jar and you decide to make 10 guesses. What strategy might you use when distributing your guesses? How many guesses do you think you'd need to be confident that you had won? What factors would be important considerations in this previous question?