Problem solving

Problem-solving Investigations - Year 4

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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Roman numeral teaser

Children apply their knowledge of Place Value to a different number system.  

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Subtraction trios

Children look for patterns in answers when subtracting three-digit numbers from four-digit numbers with consecutive digits.

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Prime addition squares (1), Odds and evens mix up (2)

Prime addition squares (1): Children add sets of 3 three-digit numbers to find patterns in a magic square based on prime numbers. Odds and evens mix up (2): Children create two 4-digit numbers - 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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Pete's pond problem (1), Co-ordinate patterns (2)

Pete's pond problem (1): Children apply knowledge of perimeter and area to make a generalisation and help Pete to fence around his pond. Co-ordinate patterns (2): Children draw rectangles with a given area, and one fixed vertex. They label the other co-ordinates and begin to work them out.

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Target timings

Children add or subtract ones, tenths or hundredths to reach a target number. They use mathematical reasoning to choose the best strategies.

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Decimal detective

Children use clues to find a mystery number with two decimal places. 

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Race to 200

Children apply knowledge of factors within the 2, 3, 4, 5, 9 and 10x tables.

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Tremendous tiles

Children explore creating patterns of tiles with three asymmetrical blocks. They look for and identify lines of symmetry, creating patterns with at least two lines of reflective symmetry.

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Day I was born

Children calculate the day they were born on, and other birthdays of friends and family. They then investigate corresponding months.

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Fancy fraction answers

Children find non-unit fractions of multiples and look for patterns.

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Set square

Children use digits 1-9 once only to complete a calculation grid with given answers for each row and column.