Number problems at primary level that require careful consideration.

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

Investigate what happens when you add house numbers along a street in different ways.

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

This number has 903 digits. What is the sum of all 903 digits?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Number problems at primary level to work on with others.

Are these statements always true, sometimes true or never true?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Use the information to work out how many gifts there are in each pile.

Number problems at primary level that may require determination.

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

There were 22 legs creeping across the web. How many flies? How many spiders?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

This task combines spatial awareness with addition and multiplication.

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

Can you score 100 by throwing rings on this board? Is there more than way to do it?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.