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?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Investigate what happens when you add house numbers along a street
in different ways.
At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
If the answer's 2010, what could the question be?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the 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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Find the next number in this pattern: 3, 7, 19, 55 ...
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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 of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
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?
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?
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 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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Use these head, body and leg pieces to make Robot Monsters which are different heights.
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What is happening at each box in these machines?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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?
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?
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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?