Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
If you have only four weights, where could you place them in order
to balance this equaliser?
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.
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!
Got It game for an adult and child. How can you play so that you know you will always win?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Can you work out what a ziffle is on the planet Zargon?
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over 2 coins, then one third show heads. How many coins are there altogether?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Number problems at primary level to work on with others.
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
Given the products of adjacent cells, can you complete this Sudoku?
Can you complete this jigsaw of the multiplication square?
56 406 is the product of two consecutive numbers. What are these
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
A game that tests your understanding of remainders.
Number problems at primary level that may require determination.
Can you explain the strategy for winning this game with any target?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?