Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

This package will help introduce children to, and encourage a deep exploration of, multiples.

Can you complete this jigsaw of the multiplication square?

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?

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?

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?

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Can you find the chosen number from the grid using the clues?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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!

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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?

If you have only four weights, where could you place them in order to balance this equaliser?

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.

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

Use the interactivities to complete these Venn diagrams.

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?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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 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?

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.

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

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?

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?

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.

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.

56 406 is the product of two consecutive numbers. What are these two numbers?

How many different sets of numbers with at least four members can you find in the numbers in this box?

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?

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 am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Got It game for an adult and child. How can you play so that you know you will always win?