How can we help students make sense of addition and subtraction of negative numbers?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
How would you count the number of fingers in these pictures?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
There are nasty versions of this dice game but we'll start with the nice ones...
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What is the sum of all the three digit whole numbers?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
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
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
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?
Find a great variety of ways of asking questions which make 8.
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 are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
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.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Find the next number in this pattern: 3, 7, 19, 55 ...
Here is a chance to play a version of the classic Countdown Game.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
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 a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
If the answer's 2010, what could the question be?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
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
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you substitute numbers for the letters in these sums?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
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?
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?