Problem solving

Problem-solving Investigations - Year 3

Problem-solving investigations provide a fun, stimulating context in which children can develop and exercise their ability to reason mathematically and think creatively. They provide extra skills practice and also provide a real challenge if the skill itself is proving undemanding for some children.

These problems  are designed to help children identify patterns, explore lines of thinking and investigate properties of numbers, shapes and measures. They can be used alongside the Hamilton plan for the week or independently. The teacher instructions for the whole term are collated in the Overview. Ruth's Advice gives some background and tips for using these investigations with your pupils.

Supporting documents for set
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Counter place value

Children put counters on a place value grid to make three-digit numbers, and then use logic to ensure they have made all combinations.  

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Magic square differences

Children use the magic square to generate two-digit numbers and explore difference patterns. They use logic to ensure they have found all possible combinations. 

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Pattern subtractions

Children subtract two-digit from three-digit numbers, by counting up, and look out for patterns in the numbers.  

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Hands and fingers (1), Yukky food (2)

Hands and fingers (1): Children test a theory finding and using accurate measurements to the nearest half centimetre. Yukky food (2): Children use the skills of recording and analysing data to work out which food the class hate most! 

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Fraction bets!

Children look at fractions and make a hypothesis of which ones are closest. They then test this out by placing fractions on a line.

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Lost logic

Children use their knowledge of inverse operations to solve a logic problem.

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Magical subtractions

Children subtract the digital root of a three-digit number from that three-digit number. They think logically to try different options.

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Next door additions

Children add pairs of three-digit numbers and look for patterns in the digital roots of the answers.

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Mirror times

Children use mirrors and analogue clocks. They look at mirror images and record pairs of times using the digital format.

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Crack the code

Children work together to reason and think logically to crack a code.  They practise mental multiple and division strategies.

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Does it or not?

Children find numbers between 50 and 100 which they can divide by 4. They halve each number twice to find out.