Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
An investigation that gives you the opportunity to make and justify predictions.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you find the chosen number from the grid using the clues?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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?
Follow the clues to find the mystery number.
Can you work out some different ways to balance this equation?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
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.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
Can you complete this jigsaw of the multiplication square?
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!
Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.
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.
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Can you place the numbers from 1 to 10 in the grid?
Can you make square numbers by adding two prime numbers together?
If you have only four weights, where could you place them in order to balance this equaliser?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Help share out the biscuits the children have made.
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.
Number problems at primary level that may require determination.
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?
An environment which simulates working with Cuisenaire rods.
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?
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?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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?
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.
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Are these domino games fair? Can you explain why or why not?
Number problems at primary level to work on with others.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?