Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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?
There are nasty versions of this dice game but we'll start with the nice ones...
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!
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Here is a chance to play a version of the classic Countdown Game.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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
An environment which simulates working with Cuisenaire rods.
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?
Use the number weights to find different ways of balancing the equaliser.
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?
Can you hang weights in the right place to make the equaliser
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!
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?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
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
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
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.
Find all the numbers that can be made by adding the dots on two dice.
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?
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?
Choose a symbol to put into the number sentence.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
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.
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 is an adding game for two players.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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!
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?