However, whilst children need to be fluent with the mathematical content demands of any problem they tackle, it may be more productive to choose a problem that builds on a specific element of problem solving that you are working on as a class, and uses content that they are very familiar, and more confident, with. Find the chain which contains the smallest possible numbers. Investigate the sum of the numbers on the top and bottom faces of a line of three dice. Mystery Matrix Age 7 to 11 Challenge Level: Getting started Stage 2:

How many different squares can you make altogether? This article, written for primary teachers, discusses what we mean by ‘problem-solving skills’ and draws attention to NRICH tasks which can help develop specific skills. Counting Cogs Age 7 to 14 Challenge Level: The tasks in this collection can be used to encourage children to convince others of their reasoning, using ‘because’ statements. Can you order the digits from to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on? Highest and Lowest Age 7 to 11 Challenge Level:

# Problem Solving :

Explore Alex’s number plumber. Can you work out the table and the shift each time?

Age 5 to 7 Trial solvin Improvement at KS1 These lower primary tasks could all be tackled eky a trial and improvement approach. Trebling Age 7 to 11 Challenge Level: This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

Can you make 15, 16 and 17 too? Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. If you know the numbers that come out, what multiplication might be going on in the box?

These problem-solving skills are in a random order, although the first two, trial and improvement and working systematically, are key skills that will support children to become competent as problem solvers.

Square Subtraction Age 7 to 11 Challenge Level: What could my number be? Can you get four in a row?

## Problem-solving Skills

The tasks in this collection can solvnig used to encourage children to convince others of their reasoning, by first convincing themselves, then a friend, then a ‘sceptic’.

Choose two of the numbers to multiply or divide, then mark your answer on the number line. Tea Cups Age 7 to 14 Challenge Level: The idea is to go round the track in as few moves as possible, keeping to the rules.

Inky Cube Age 7 to 14 Challenge Level: The atage of Vuvv has seven moons. Magic Vs Age 7 to 11 Challenge Level: Use 4 four times with simple operations so that you get the answer This game can replace standard practice exercises on finding ntich and multiples. This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

We trust you will find it useful and we are always interested in your feedback and experiences as you explore problem solving together with the children in your class.

Can you work out what is on each face and the route it has taken?

These upper primary tasks could all be tackled using a trial and solvijg approach. Guess the Dominoes Age 7 to 14 Challenge Level: We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Reach Age 7 to 14 Challenge Level: Can sklving order the digits from to make a number which is divisible by 3 so when the last digit proble removed it becomes a 2-figure number divisible by 2, and so on?

Half Time Age 5 to 11 Challenge Level: To become fluent at trial and improvement they need to be able to think about how to adapt their first guess so that it is more likely to become a solution rather than throwing the first one out and starting again.

The tasks in this collection encourage upper primary children to conjecture and generalise. Factor Track Age 7 to 14 Challenge Level: Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number.

What do we mean by ‘problem-solving skills’? In the aforementioned article, Jennie outlines four stages of the problem-solving process: