On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Number live Age 7 to 11 Challenge Level: How many possible necklaces can you find? Can you replace the letters with numbers? Sealed Solution Age 7 to 11 Challenge Level: Try with different steps and see if you can predict what will happen. Age 7 to 11 Reasoning and Convincing at KS2 The tasks in this collection can be used to encourage children to convince others of their reasoning, by first convincing themselves, then a friend, then a ‘sceptic’.

Can you work out the table and the shift each time? Can you work out the arrangement of the digits in the square so that the given products are correct? He could then pay any sum of money from 1p to 15p without opening any bag. Choose two of the numbers to multiply or divide, then mark your answer on the number line. How could you put these three beads into bags? This challenge combines addition, multiplication, perseverance and even proof.

My number is both a multiple of 5 and a multiple of 6. Multiply Multiples 3 Age 7 to 11 Challenge Level: Mystery Matrix Age 7 to 11 Challenge Level: Cover the Tray Age 7 to 11 Challenge Level: Highest and Lowest Age 7 to 11 Challenge Level: How could you put these three beads into bags?

This challenge is a game for two players. Make 37 Age 7 to 14 Challenge Level: These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

This feature draws together tasks which give learners opportunities to reason for different purposes. What numbers could be inside the envelopes? Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down? Abundant Numbers Age 7 to 11 Challenge Level: Can you replace the letters with solvng What questions would you like to ask? How many possible necklaces can you find? Can you prove it?

## Multiplication and Division KS2

Factor Lines Age 7 to 14 Challenge Level: The fourth article builds on the third by discussing what we mean by problem-solving skills and how NRICH can help children develop these skills. Working Systematically at KS2. Four bags contain a large number of 1s, 3s, 5s and 7s. Design an arrangement of display boards in the school soving which fits the requirements of different people.

How could you record what you’ve done? Choose two of os2 numbers to multiply or divide, then mark your answer on the number line. How many Zios and how many Zepts were there?

# Using NRICH Tasks to Develop Key Problem-solving Skills :

This feature is somewhat prlblem than our usual features, but that is because it is packed with resources to help you develop a problem-solving approach to the teaching and learning of mathematics.

Can you make square numbers by adding two prime numbers together?

Always, Sometimes or Never? How might you show them in a picture, with things, with numbers and symbols?

## Using NRICH Tasks to Develop Key Problem-solving Skills

The lower primary tasks in this collection could each be solved by working backwards. These eleven shapes each stand for a different number. Can you make square numbers by adding two prime numbers together? How many different shaped boxes can you design for 36 sweets in one solfing How Do You Do It?

Can you work out the arrangement of the digits in the square so that the given products are correct? Can you complete this calculation by filling in the missing numbers?