Investigate what happens when you add house numbers along a street
in different ways.
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 15.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
There were 22 legs creeping across the web. How many flies? How many spiders?
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
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
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?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
If the answer's 2010, what could the question be?
Use these four dominoes to make a square that has the same number
of dots on each side.
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
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
How would you count the number of fingers in these pictures?
Can you hang weights in the right place to make the equaliser
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?