How many solutions can you find to this sum? Each of the different letters stands for a different number.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
There are nasty versions of this dice game but we'll start with the nice ones...
Find the sum of all three-digit numbers each of whose digits is
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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.
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.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
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?
Here is a chance to play a version of the classic Countdown Game.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
This is an adding game for two players.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
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
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Can you explain how this card trick works?
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
This challenge extends the Plants investigation so now four or more children are involved.
Replace each letter with a digit to make this addition correct.
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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Delight your friends with this cunning trick! Can you explain how
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
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?
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
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
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.
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.
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
What is happening at each box in these machines?