Problem solving

Problem-solving Investigations - Year 1/2

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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1
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Fill the box (Y1), Dancing digits (Y2)

Fill the box (Y1): Children fill a matchbox with items and count them accurately.  Dancing digits (Y2): Children use place value addition and subtraction to write chains which 'swap' the 10s and 1s digits.

2
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Addition towers

Children find the total number of spots on two dice in a game context, and consider why some totals come up more frequently than others.

3
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Make 20

Children use coins and number shapes to make a total of 20.

4
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Make a stick

Children find a collection of items which in total measure exactly one metre in length.

5
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Spot the difference

Year 1: Children find dominoes where one side has one more spot than the other, and then where one side has two more spots than the other.  Year 2 Children make 2-digit numbers using dominoes and find which complements to the next 10 are possible.

6
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Tricky tracks (Y1), Guess the starter (Y2)

Tricky tracks (Y1): Children use reasoning and logic to play ahead in playing a game on a 1-20 track.  Guess the starter (Y2): Children use their knowledge of inverse operations to work out the 'starter' numbers round multiplication grids.

7
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Sock doubles (Y1), Digit sums (Y2)

Sock doubles (Y1): Children double numbers 1 to 5 as part of a game, and find which answers from 1 to 10 are possible.  Digit sums (Y2): Children find the sum of the digits in a sequence of numbers and compare the pattern found to that identified in the digit sums of the doubles.

8
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Shape wheels

Children make a sequence of coloured shapes, changing one attribute at a time so that the sequence can end where it started, forming a circular sequence.

9
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Count down to zero

Year 1: Children take turns to subtract 1 or 2 from numbers up to 10.  Year 2: Children take turns to subtract 1, 2 or 3 from a two-digit number greater than 20. They use strategies to help them win the game by reaching zero first.

10
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Domino loop

Children make loops of dominoes such that meeting ends have a given total number of spots.

11
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Square tens

Children find pairs of dominoes such that the total number of spots is 10, 12 or 20.