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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Lost digit

Children explore patterns in six-digit numbers using a ‘trick’ based on reduced numbers (casting out nines).  

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Martian numbers

Children explore the facts that Arabic numbers use a base of 10, we can write numbers using a base of 3, and Roman numbers have no base.

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Percentage puzzles

Children work systematically to find equivalent percentages of different amounts. They look at patterns in percentage amounts.

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Billiard angles

Children use a knowledge of angles to draw lines of incidence and reflection on billiard tables of differing proportions. They identify patterns and make predictions.

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Durer's square magic

Children use Durer’s Magic Square and create two- or three-digit numbers and find the difference between different pairs. They identify patterns.

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What an odd thing!

Children create a triangle of odd numbers and identify the patterns when rows are summed or their end numbers are averaged.

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Reverse digits, same product

Children find the product of a pair of two-digit numbers then reverse the digits of both numbers and find an identical product.

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Annoying clock

Children apply their knowledge of time to solve a multi-step problem involving dates and organised reasoning. They explain their ideas and justify reasoning.

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Children work out the capacity of their classroom.  They also convert from cm3 to ml and then to litres.

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Fraction fireworks

Children find the answers to a sequence of fraction multiplications and look for patterns in the answers.

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Remainder runners

Children divide 1234, 2345, 3456 by 3, 4, 5 etc and look for patterns in the remainders.