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Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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Follow the clues to find the mystery number.

Grouping Goodies

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Carroll Diagrams

Age 5 to 11
Challenge Level

We had a lot of answers to this activity sent in, but only a few children explained their thinking - we would love to hear your ideas about the way you answered these questions!

Lyra from Westridge in the USA explained her method for putting numbers into these Carroll diagrams:

I know the number 1 is odd and less than ten, so I know that I should put it in the box that says "odd, less than 10". I continued with this strategy with the rest of the numbers. So: All the numbers that are odd and less than 10 go in the "odd, less than 10" box. All the numbers that are not odd and less than 10 go in the "not odd, less than 10" box. The numbers that are not less than ten and are odd go in the "odd, not less than 10" box. And, all the numbers that are not odd and not less than 10 go in the "not odd, not less than 10" box. The same thing happens with the next diagram.

Well done for explaining how to put numbers into a Carroll diagram, Lyra. I wonder if anybody else approached this in a different way?

We had a lot of solutions sent in from pupils at the ABQ Education Group in Oman - thank you all for your ideas. Taqiya made a video explaining how to put the numbers from 1-20 into the first Carroll diagram:

Well done, Taqiya! Taqiya has made the diagram simpler by changing the label 'Not odd' to 'Even'. Do all numbers have to be either odd or even? Can you think of a number that isn't odd or even?