Problem solving

Problem-solving Investigations - Year 4

The problem-solving investigations below match Hamilton’s weekly maths plans. We now also provide Year 4 maths as short blocks. We will eventually be phasing out the plans, as we believe our short blocks offer you all of the same advantages and more, including the integration of the problem-solving investigations into each unit of study. Find out more about the advantages of Hamilton's short blocks.

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.