Problem solving

Problem-solving Investigations - Year 5

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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Exasperating 80 grand

Children use all of the digits 0 to 9 once only to create pairs of five-digit numbers, with a total as close to 80,000 as possible.

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Adding even and odd amounts

Children create two amounts of money – one with even digits, one with odd digits – and add these. They look for patterns of even/odd in the totals.

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Persistent answers

Children subtract numbers with consecutive digits from numbers with identical digits and record the different possible answers.

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Shapes in perspective

Children experiment with parallel and angular perspective when drawing 3D shapes.

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Long as you like (1), Fraction pictures (2)

Long as you like (1): Children create chains of numbers by finding factors and multiples.  Their aim is to create the longest chain possible. Fraction pictures (2): Children use knowledge of equivalent fractions to work out what fraction each shape is as part of the whole picture, and which shapes are the same size.

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Excellent eights

Children explore patterns when multiplying numbers with consecutive digits by 8.

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Prime differences

Children find out if prime numbers become less frequent as we consider sets of larger numbers.

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Talisman squares

Children explore patterns in a Talisman Square. They find differences between adjacent numbers on a 4 x 4 grid and then explore arrangements on a 3 x 3 grid.

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Digits of time

Children find out how many times the digit 9 is used on the 24 hour digital clock between noon and midnight.

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Oddly friendly fractions

Children explore patterns when adding fractions. They create fractions with related denominators and then add these, turning improper fractions into mixed numbers.

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Magic star additions

Children explore addition patterns on a star derived from a simple magic star.  They use mental or written addition to add 4-digit numbers.