Problem solving

Problem-solving Investigations - Year 3/4

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.

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Puzzling squares

Use numbers 0 to 7 (or multiples of 10 from 0 to 70) to make a total of 10 (or 100) on each side of a square.

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Twisted subtractions

Subtract a number which is the reverse of another, e.g. 62 - 26, or 462 - 264.

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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 10 (Y3) or 20 (Y4) and look for duplicate sequences.

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Magic chains

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

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Magic 147

Children arrange the 'nearly numbers' in a square so that each row and column adds to Magic 147.

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Hole-y subtractions

Year 3: Children subtract numbers with identical digits from 101, 102, 103...and look for patterns in the answers.  Year 4: 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.

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Dodgy digital clock

Children work out which times won't show correctly because of a faulty segment in the digital display.

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Mystery age

Year 3: Children use their knowledge of the 3, 4, and 5 times tables to work out mystery numbers.  Year 4: Children use their knowledge of the 5, 6, and 8 times tables to work out mystery numbers.

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Fraction clues

Children use their knowledge of fractions and tables to find mystery numbers.