Can you explain how this card trick works?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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.
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?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Find out about Magic Squares in this article written for students. Why are they magic?!
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Find the sum of all three-digit numbers each of whose digits is
Use the information to work out how many gifts there are in each
In the following sum the letters A, B, C, D, E and F stand for six
distinct digits. Find all the ways of replacing the letters with
digits so that the arithmetic is correct.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
What are the missing numbers in the pyramids?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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?
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?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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
Replace each letter with a digit to make this addition correct.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Here is a chance to play a version of the classic Countdown Game.
This is an adding game for two players.
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?
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.
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?
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 each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat. . . .
This challenge extends the Plants investigation so now four or more children are involved.
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.