Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Use the information to work out how many gifts there are in each
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
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.
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
What is happening at each box in these machines?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
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.
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?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
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?
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
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
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.
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Investigate what happens when you add house numbers along a street
in different ways.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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.
How would you count the number of fingers in these pictures?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
Can you follow the rule to decode the messages?