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!
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
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?
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you hang weights in the right place to make the equaliser
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Here is a chance to play a version of the classic Countdown Game.
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.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
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.
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!
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Find all the numbers that can be made by adding the dots on two dice.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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 find all the ways to get 15 at the top of this triangle of numbers?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!