If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube? What do the numbers shaded in blue on this hundred square have in common? Half Time Age 5 to 11 Challenge Level: Look at three ‘next door neighbours’ amongst the counting numbers. A magician took a suit of thirteen cards and held them in his hand face down. Age 7 to 11 Challenge Level:

What is the largest ‘ribbon square’ you can make? Sweets in a Box Age 7 to 11 Challenge Level: Keep adding as few pebbles as necessary to double the area. Multiples Grid Age 7 to 11 Challenge Level: Andy’s Marbles Age 7 to 11 Challenge Level: Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. Working backwards can be a very useful problem-solving skill.

## Problem-solving Skills

Addition and Subtraction KS2. The numbers 1 – 9 may be used once and once only. One block is needed to make an up-and-down staircase, with one step up and one step down.

You could investigate your own starting shape. How many different triangles can you make on a circular pegboard that has nine pegs? Sealed Solution Age 7 to 11 Challenge Os2 Reach Age 7 to 14 Challenge Level: Which pairs do not let this happen?

# Working Systematically at KS2 :

These practical challenges are all about making a ‘tray’ and covering it with paper. Each light in this interactivity turns on according to a rule.

Age 5 to 7 Reasoning and Convincing at KS1 The tasks in this collection can be used to encourage children to convince others of their reasoning, using ‘because’ statements. Digging deeper Stage 4: Can you fill in this table square? Can you use the information to find out which cards I have used?

## Working Systematically at KS2

Mystery Matrix Age 7 to 11 Challenge Level: Can you see how these factor-multiple solvinv work? Which is quicker, counting up to 30 in ones or counting up to in tens? Find the chain which contains the smallest possible numbers. He could then pay any sum of money from 1p to 15p without opening any bag.

# Problem Solving :

What do you notice? Can you prove it? Becoming confident and competent as a problem solver is a complex process that requires a range of skills and experience. Tim had nine cards each with a different number from 1 to 9 on it. Nim-7 Age 5 to 14 Challenge Level: All the Digits Age 7 to 11 Challenge Level: The upper primary tasks in this collection could each be solved by working backwards.

Amy’s Dominoes Age 7 to 11 Challenge Level: Can you work out how long it is between each super-eclipse? How did he do it?

Can you sort out the clues and find the number? The sum of the numbers inside it is written on each envelope.

Explore Alex’s number plumber. Register for our mailing list. Flashing Lights Age 7 to silving Challenge Level: In how many different ways can you do it?

Can you sort out the clues and find the number? Factor Lines Age 7 to 14 Challenge Level: