Problem solving

Problem-solving Investigations - Year 4

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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No zero

Children investigate how many numbers between one and ten thousand have a zero. They use their understanding of place value in numbers with up to 4-digits.

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Make 100

Given a pattern of four one-digit numbers, children attempt to make a total of exactly 100.

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Cats and dogs

Children work to solve a puzzle involving adding two 3-digit numbers. They find several possible solutions, and then invent their own puzzle.

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Soma cube

Children create specified 3-D shapes using 2-D representations and then combine these to create other 3-D shapes including a cube.


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Doubling forever

Children double numbers up to 20 and look for duplicate sequences.

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Magic chains

Children use their knowledge of inverse operations to quickly work out a sequence of calculations.

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Total £10

Using only digits 1-9 without the ‘5’, children find all possible pairs of amounts to make £10.

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Hole-y subtractions

Children create 3-digit palindromic numbers with a ‘hole’ (i.e. a zero) in the middle. They subtract 3-digit numbers with equal numbers of 1s, 10s and 100s and identify patterns in their answers.

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Palindromic time intervals

Children systematically find palindromic digital times and list them in an ordered way.  They convert these to analogue times and calculate the intervals between them.

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Magical nines

Children look for patterns when multiplying ‘nearly numbers’ by 9 using mental multiplication strategies.

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Foodie fractions

Given fractions of amounts children use their knowledge of table facts to work out how many friends are at a picnic.