In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
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?
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?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Can you make square numbers by adding two prime numbers together?
How many different sets of numbers with at least four members can you find in the numbers in this box?
Can you find a way to identify times tables after they have been shifted up or down?
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?"
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?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you complete this jigsaw of the multiplication square?
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.
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Can you find any perfect numbers? Read this article to find out more...
Number problems at primary level that may require resilience.
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
"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 ...?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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.
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 am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
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?
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.
Can you find different ways of creating paths using these paving slabs?