How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
There are nasty versions of this dice game but we'll start with the nice ones...
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Can you hang weights in the right place to make the equaliser
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?
Choose four of the numbers from 1 to 9 to put in the squares so
that the differences between joined squares are odd.
Use the number weights to find different ways of balancing the equaliser.
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Can you substitute numbers for the letters in these sums?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Find the sum of all three-digit numbers each of whose digits is
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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 a symbol to put into the number sentence.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Here is a chance to play a version of the classic Countdown Game.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
If you have ten counters numbered 1 to 10, how many can you put
into pairs that add to 10? Which ones do you have to leave out?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
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.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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?
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?
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!
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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?
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!
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?