Problem solving

Problem-solving Investigations - Year 6 Spring

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.

Please note, we do not provide Investigations for Year 6 Summer Term in order to make space for SATs.

Supporting documents for set
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Noughts and negatives

Children play an adapted game of noughts and crosses, aiming to get negative number answers.  

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All at 6s and 7s

Children try to make every number to at least 10 using 6s, 7s and sometimes 2 and 3, and any operations. 

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Decimal pyramids

Children add numbers with three decimal places to give a number with two decimal places, then add numbers with two decimal places to give a number with one decimal before finally adding numbers with one decimal place to give a whole number.  

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Cycling co-ordinates

Children use a sequence of co-ordinates to create quadrilaterals.

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Riveting reversals

Children multiply three-digit numbers with consecutive digits by a two-digit number; reverse the three-digit number and repeat. They look at the difference between the two answers.

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Mean score

Children design a dice such that the mean score is 5.

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Stars and crosses

Children find totals of the numbers in shapes on a 1-100 grid, make generalisations and then write a formula to find the total of any similar shape on the grid.

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Mixed up fractions

Children add a pair of fractions, multiply the same pair, then find the difference between the two answers, looking for patterns.

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Queued cubes

Children apply a combination of knowledge of 3D shape, area and volume to solve a problem that introduces surface area.

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Geometry genius

Children use what they know about how to find the areas of triangles and parallelograms to find the areas of rhombi, kites and trapezia.

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Why is it so?

Children identify a pattern in the division of a total of six numbers created using the same three digits.  They use algebra to explain why it is so.