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?
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
How many different rectangles can you make using this set of rods?
An investigation that gives you the opportunity to make and justify predictions.
Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.
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?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
Number problems at primary level that may require resilience.
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
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.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
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.
Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
How will you work out which numbers have been used to create this multiplication square?
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
"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 ...?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Can you find the chosen number from the grid using the clues?
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.
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?
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
How many different sets of numbers with at least four members can you find in the numbers in this box?
Can you make square numbers by adding two prime numbers together?
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?
Follow the clues to find the mystery number.
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
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 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?
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.
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Are these statements always true, sometimes true or never true?
Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?
Are these domino games fair? Can you explain why or why not?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Number problems at primary level to work on with others.