Problem solving

Problem-solving Investigations - Year 1

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
  • Download
+ Details
Calculating caterpillars

Children make add and subtract 1 and 10 in order to reach targets.

+ Details
Cross sums

Children arrange numbers 1 to 5 on a cross to show that the row and column have the same total.  

+ Details
Coins in my pockets

Children use clues, and trial and improvement to find different combinations of coins with a total of 20p.

+ Details
My new watch

Children use analogue clocks to try out different o’clock and half past times. They find all the possible different times between midnight and midday! 

+ Details
Odds and evens

Children use number shapes to find totals of odd and even numbers, to see if they can find any rules. 

+ Details
Pairs in purses (1), Calculator capers (2)

Pairs in purses (1): Children use reasoning and logic to work out pairs of 2-digit amounts that can be made in the two purses given only ten coins. Calculator capers (2): Children create teens numbers using place value additions.

+ Details
Four towers

Children arrange four towers of cubes such that the difference between neighbouring towers is at least two.  

+ Details
Fill the bucket

Children estimate then measure the capacity of a bucket, and play a game filling it.

+ Details
Pyramid sums

Children place three numbers in the bottom row of an addition pyramid and see that it is possible to end up with different numbers at the top. 


+ Details
10 to 50 challenge

Children find which numbers from 5 to 7 they can add repeatedly to 10 to land exactly on 50.

+ Details
Mr Know It All!

Children find out which amounts of money from 10 to 20p can be made using 10p, 5p, 2p and 1p coins, using no more than one of each.