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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Magical square decimals

Children use the arrangement of digits on a magic square to create one-place decimals. They use logic to demonstrate that they have found all the possibilities.

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Present prices

Children use logic and addition, along with some trial and improvement to solve a problem involving money.

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Wonderful 1089!

Children add two 3-digit numbers and subtract a pair of 3-digit numbers to find patterns. They use mathematical reasoning to begin to explain what they find.

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Timeline (1), Pencil power (2)

Timeline (1): Children use their knowledge about millimetres, centimetres and metres to create a scale timeline from 0 to the current year, and gain some sense of the order of historical events. Pencil power (2): Children use larger weights and numbers to find an accurate weight of one pencil by collecting data on a bar graph.

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Best score for me!

Children find equivalent fractions to cross numbers on a 6 x 6 square. They use reasoning strategies and knowledge of factors to find their highest score.

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Mystery multipliers

Using their knowledge of multiplication facts and place value children work out which single-digit numbers and multiples of 10 have given products in order to solve a puzzle.

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Tell the teacher

Children consider whether given calculations are harder or easier and work out a scoring system.

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Mobile subtractions

Children create subtractions using three contiguous numbers selected from a mobile phone display.

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Time to reflect

Children apply their knowledge of 24 hour digital clocks and look at their reflections in a mirror.

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Table digital roots

Children find the digital roots of multiples of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. They identify patterns and relate those to the properties of numbers.

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Rocking remainders

Children divide 11, 22, 33 up to 99 by 3, 4, 5 and so on up to 12 and look for patterns in the remainders.