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?
Can you follow the rule to decode the messages?
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Find the next number in this pattern: 3, 7, 19, 55 ...
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 design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Dotty Six is a simple dice game that you can adapt in many ways.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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? Why?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
How would you count the number of fingers in these pictures?
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. . . .
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?
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?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
If the answer's 2010, what could the question be?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
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?
Investigate what happens when you add house numbers along a street
in different ways.
Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Use these head, body and leg pieces to make Robot Monsters which are different heights.
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
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
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?