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?
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?
Can you find the chosen number from the grid using the clues?
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 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?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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.
You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Follow the clues to find the mystery number.
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?
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.
Can you work out some different ways to balance this equation?
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?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
How many trains can you make which are the same length as Matt's, using rods that are identical?
An investigation that gives you the opportunity to make and justify predictions.
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?
Can you place the numbers from 1 to 10 in the grid?
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
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?
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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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.
This activity focuses on doubling multiples of five.
Have a go at balancing this equation. Can you find different ways of doing it?
If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?
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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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 are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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?
Are these domino games fair? Can you explain why or why not?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
Got It game for an adult and child. How can you play so that you know you will always win?
Number problems at primary level that may require resilience.
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.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you make square numbers by adding two prime numbers together?
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?
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?
How many different sets of numbers with at least four members can you find in the numbers in this box?