There are 78 prisoners in a square cell block of twelve cells. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether! Can you work out what is on each face and the route it has taken? Can you see how these factor-multiple chains work? Can you compare these bars with each other and express their lengths as fractions of the black bar? How many shapes can you build from three red and two green cubes? Strike it Out Age 5 to 11 Challenge Level:

How could you record what you’ve done? Find the product of the numbers on the routes from A to B. What numbers could be inside the envelopes? Amy’s Dominoes Age 7 to 11 Challenge Level: The numbers 2 were used to generate it with just one number used twice. Which pairs do not let this happen?

Can you predict what will happen?

How many different squares can you make altogether? To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

What do the numbers shaded in blue on this hundred square have in common?

Sweets in a Box Age 7 to 11 Challenge Level: What happens if you join every second point on this circle? Multiply Multiples 1 Age 7 to 11 Challenge Level: Can you get four in a row?

The ,aths is the first to make the total The upper primary tasks in this collection could each be solved by working backwards.

## Patterns and Sequences KS2

Tumbling Down Age 7 to 11 Challenge Level: These sixteen children are standing in four lines of four, one behind the other. Age 7 to 11 Visualising at KS2 These upper primary tasks all specifically draw on the use of visualising.

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?

How many pennies did Ram put in each bag?

Is it the same number for a 12 hour clock over a whole day? Domino Square Age 7 to 11 Challenge Level: A task which depends on members of the group noticing the needs of others and responding. Can you find ke2 where all the numbers have got to from these ten statements?

# Patterns and Sequences KS2 :

This task depends solvinf learners sharing reasoning, listening to opinions, reflecting and pulling ideas together. Can you see how these factor-multiple chains work? What do you think is solvjng to the numbers? If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance? This feature draws together tasks which give learners opportunities to reason for different purposes. Counting Cogs Age 7 to 14 Challenge Level: This task offers opportunities to subtract nrifh using A4 paper.

I’m thinking of a number. Domino Sets Age 7 to 11 Challenge Level: Four bags contain a large number of 1s, 3s, 5s and 7s. Build it Up Age 7 to 11 Challenge Level: What numbers could be inside the envelopes?

# Problem-solving Skills :

These activities focus on finding all possible solutions so working in a systematic way will nruch none are left out. This challenge invites you to explore the difference in the number of small cubes I’ve used. Factor Lines Age 7 to 14 Challenge Level: Can you replace the letters with numbers? Is there only one solution in each case? Ordered Ways of Working Upper Primary Prohlem activities lend themselves to systematic working in the sense that it helps to have an ordered approach.