Problem solving

# Problem-solving Investigations - Year 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
• Week
• Title
1
+ Details
Dancing digits

Children use place value addition and subtraction to write chains which ‘swap’ the 10s and 1s digits.

2
+ Details

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
+ Details
Make it the same

Children use trial and improvement to find a way of arranging 4 coins on a square so that each row and each column add up to a constant total. They explore diagonal patterns.

4
+ Details
Star of change

Children use trial and improvement to arrange amounts of change from 20p along a star to give constant totals along each star line.

5
+ Details
Fanned fingers

Children work together to first estimate and then find an accurate measurement of the distance around their hand with the fingers ‘fanned out’ or splayed wide.

6
+ Details
Guess the starter

Children use their knowledge of inverse operations to work out the ‘starter’ numbers round multiplication grids.

7
+ Details
Digit sums (1), Best foot forward (2)

Digit sums (1): Children find the sum of the digits in a sequence of numbers and compare the pattern found to that identified in the digits sums of the doubles. Best foot forward (2): Children plot routes across the number grid by adding or subtracting 1 and 10 using arrow cards.

8
+ Details
Count down to zero

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

9
+ Details
Pyramids

Children explore addition patterns in pyramids. They arrange numbers in a pyramid to create the largest and smallest possible totals.

10
+ Details
Cut and paste

Children use Escher’s method of creating tessellations from rectangles and regular triangles or hexagons. Using the language of 2-D shape and symmetry they describe the patterns created.

11
+ Details
Sackful of 10s

Children play a game which requires that they add multiples of ten using their knowledge of number bonds. They then challenge themselves to work out the longest game possible.

12
+ Details
Nines to zero

Children repeatedly add 9 or 19 to numbers until they get a multiple of 10, and look for patterns. They make and test predictions based on the patterns.