If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Find the next number in this pattern: 3, 7, 19, 55 ...
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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?
Use the information to work out how many gifts there are in each
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
This number has 903 digits. What is the sum of all 903 digits?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
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?
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?
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.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
What is happening at each box in these machines?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
Number problems at primary level that may require determination.
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.
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?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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 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?
This task combines spatial awareness with addition and multiplication.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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. . . .
There were 22 legs creeping across the web. How many flies? How many spiders?
If the answer's 2010, what could the question be?
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?
What is the sum of all the three digit whole numbers?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Number problems at primary level that require careful consideration.
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?
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?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
This activity focuses on doubling multiples of five.
This challenge combines addition, multiplication, perseverance and even proof.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
How would you count the number of fingers in these pictures?