This article for teachers describes how number arrays can be a useful reprentation for many number concepts. Which is quicker, counting up to 30 in ones or counting up to in tens? How might you show them in a picture, with things, with numbers and symbols? Think of a number, square it and subtract your starting number. Using the information given, can you replace the stars in the calculation with figures? Cycling Squares Age 7 to 11 Challenge Level:

Can you work out how to balance this equaliser? Keep adding as few pebbles as necessary to double the area. Mrs Morgan, the class’s teacher, pinned numbers onto the backs of three children. Four Go Age 7 to 11 Challenge Level: 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.

Multiplication Squares Age 7 probleem 11 Challenge Level: Can you work out how to balance this equaliser? Countdown Age 7 to 14 Challenge Level: Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even Difficulties with Division Age 5 to 11 This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Choose two of the numbers to multiply or divide, then mark your answer on the number line. The Zios have 3 legs and the Zepts have 7 legs. What happens when you enter different numbers? Who said that adding, subtracting, multiplying and dividing couldn’t be fun? What number did she multiply 54 by?

If there are multipliccation squares in the ring, can you place three different numbers in them so that their differences are odd? Ordering Cards Age 5 to 11 Challenge Level: Can you work out how to use Napier’s bones to find the answer to these multiplications?

## Multiplication Squares

Zios and Zepts Age 7 to 11 Challenge Level: Can you see a pattern? If you know the numbers that come out, what multiplication might be going on in the box? Is problem solving at the heart of your curriculum? How many altogether in this 3 by 5? Keep adding as few pebbles as necessary to double the area. Number Detective Age 5 to 11 Challenge Level: Three ;roblem Age 7 to 11 Challenge Level: On Friday the magic plant was only 2 centimetres tall. Place four pebbles on the sand in the form of a problfm.

## 259 Matches for multiplication

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Read Lynne’s article which discusses the place of problem solving in the new curriculum and sets the scene.

These upper primary tasks could all be tackled using a trial and improvement approach. This feature brings together tricky tasks which have been created for the Young Mathematicians’ Award.

How tall was it on Monday? The great planetary explorer Nico counted 52 legs. Pebbles Age 7 to 11 Challenge Level: Take a look at the multiplication square.

# Multiplying decimals investigation

These articles will support primary teachers as they develop children’s understanding of number and calculation. How about the shaded numbers in the other squares? Annie and Ben are playing a game with a calculator. In this article, Jennie suggests that we can support this process in three principal ways.

Can you complete this jigsaw of the multiplication square? Place four pebbles on the sand in the form of multtiplication square.

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