Use these four dominoes to make a square that has the same number of dots on each side.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
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
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?
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?
Try grouping the dominoes in the ways described. Are there any left
over each time? Can you explain why?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
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 these head, body and leg pieces to make Robot Monsters which
are different heights.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you find 2 butterflies to go on each flower so that the numbers
on each pair of butterflies adds to the same number as the one on
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Are these domino games fair? Can you explain why or why not?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Who said that adding couldn't be fun?
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.
Find all the numbers that can be made by adding the dots on two dice.
This challenge is about finding the difference between numbers which have the same tens digit.
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?
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 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?
Investigate the different distances of these car journeys and find
out how long they take.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
This is an adding game for two players.
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!
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
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.
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?