Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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!
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
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?
If you have only four weights, where could you place them in order to balance this equaliser?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Here is a chance to play a version of the classic Countdown Game.
There are nasty versions of this dice game but we'll start with the nice ones...
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?
An environment which simulates working with Cuisenaire rods.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
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?
Use the number weights to find different ways of balancing the equaliser.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
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.
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!
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?
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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
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.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
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?
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 cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Can you hang weights in the right place to make the equaliser balance?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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.
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?
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?
Choose a symbol to put into the number sentence.
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.
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.