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?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you hang weights in the right place to make the equaliser
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
If you have only four weights, where could you place them in order
to balance this equaliser?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Choose a symbol to put into the number sentence.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
This is an adding game for two players.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
This challenge extends the Plants investigation so now four or more children are involved.
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?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Here is a chance to play a version of the classic Countdown Game.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Use the number weights to find different ways of balancing the equaliser.
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.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
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.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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.
Can you substitute numbers for the letters in these sums?
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Ben has five coins in his pocket. How much money might he have?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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!
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?