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
• Week
• Title
1
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Alternating chains

Children create chains of alternating positive and negative numbers and explore the patterns in their totals.

2
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Pence and pounds reversed

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

3
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Four of the best

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

4
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Triangle co-ordinates

Children draw different types of triangle on co-ordinate grids and reflect these in the y-axis.

5
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LCM squares (1), Get to the root (2)

LMC squares (1): Children use trial and improvement to find the smallest possible total on a square of Lowest Common Multiples. Get to the root (2): Children use their fluency in mental multiplication to explore the patterns of digital roots in multiplication.

6
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Big triangle of fractions

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

7
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Dozen divisions (1), Fraction frenzy (2)

Dozen divisions (1): Children use short division to divide three-digit numbers with consecutive digits by 12. They reverse the digits in the three-digit number and repeat. They then find the difference between the two answers. Fraction frenzy (2): Children multiply proper fractions by whole numbers in a mulitplication grid and look for patterns.

8
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Mobile differences

Children use trial and improvement to find the largest and smallest possible differences using numbers selected to given criteria.

9
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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 1cm3 cubes.

10
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Decimal differences

Children subtract pairs of numbers with consecutive digits and different numbers of decimal places, and explore patterns in their answers.

11
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Division remainder patterns

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