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?
Are these statements always true, sometimes true or never true?
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?
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?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
Number problems at primary level that may require determination.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Benâ€™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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
Number problems at primary level to work on with others.
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
Follow the clues to find the mystery number.
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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?
An investigation that gives you the opportunity to make and justify
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?
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Can you find any perfect numbers? Read this article to find out more...
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.
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
If you have only four weights, where could you place them in order
to balance this equaliser?
What is the smallest number with exactly 14 divisors?
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.
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!
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?