How many solutions can you find to this sum? Each of the different letters stands for a different number.
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Delight your friends with this cunning trick! Can you explain how
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you explain how this card trick works?
Find the sum of all three-digit numbers each of whose digits is
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
Replace each letter with a digit to make this addition correct.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Three dice are placed in a row. Find a way to turn each one so that
the three numbers on top of the dice total the same as the three
numbers on the front of the dice. Can you find all the ways to. . . .
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?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Can you substitute numbers for the letters in these sums?
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.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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
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.
What are the missing numbers in the pyramids?
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This is an adding game for two players.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This challenge extends the Plants investigation so now four or more children are involved.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Investigate the different distances of these car journeys and find out how long they take.
There are nasty versions of this dice game but we'll start with the nice ones...
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
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