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!
If you have only four weights, where could you place them in order to balance this equaliser?
Can you complete this jigsaw of the multiplication square?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
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.
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?"
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you make square numbers by adding two prime numbers together?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. 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?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
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.
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?
Can you explain the strategy for winning this game with any target?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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 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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you work out what a ziffle is on the planet Zargon?
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
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?
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?
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
Number problems at primary level to work on with others.
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
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?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Number problems at primary level that may require resilience.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
A game that tests your understanding of remainders.
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?
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?