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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you complete this jigsaw of the multiplication square?
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.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
56 406 is the product of two consecutive numbers. What are these
Can you work out what a ziffle is on the planet Zargon?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Given the products of adjacent cells, can you complete this Sudoku?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Are these statements always true, sometimes true or never true?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
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?
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?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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.
Number problems at primary level that may require determination.
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?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.