Problem solving

Problem-solving Investigations - Year 5/6

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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Nought and negatives

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

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Pence and pounds reversed

Children find patterns in the differences when pounds and pence are reversed.

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Four of the best

Children use an incomplete magic square to explore patterns in the addition of four numbers.

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Cycling co-ordinates

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

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Riveting reversals

Year 5: Multiply four-digit numbers with consecutive digits by a single-digit number; reverse the four-digit number and repeat. Find the difference between the two answers.  Year 6: Multiply three-digit numbers with consecutive digits by a two-digit number; reverse the three-digit number and repeat. Find the difference between the two answers.

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Big triangle of fractions

Children add fractions with related denominators and find equivalent fractions to identify patterns.

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Dozen divisions

Year 5: Children use short division to divide 3-digit numbers with consecutive digits by 12. They reverse the digits in the 3-digit number and repeat, then find the difference between the two answers.  Year 6: As year 5: but children use long division to divide 3-digit numbers by 2-digit numbers less than 30.

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Roomy boxes

Children cut squares from a square piece of paper, fold up the sides to form an open cuboid and find out which size will hold the most cm³ cubes.

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Mobile differences (Y5), Geometry genius (Y6)

Mobile differences (Y5): Children use trial and improvement to find the largest and smallest possible differences using numbers selected to given criteria.  Geometry genius (Y6): 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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Decimal differences (Y5), Stars and crosses (Y6)

Decimal difference (Y5): Children subtract pairs of numbers with consecutive digits and different numbers of decimal places, and look for patterns in their answers. Stars and crosses (Y6): 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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Division remainder patterns

Children look at patterns of remainders in four-digit numbers when dividing by numbers 3 to 6. The can establish a rule.