Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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?

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.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Can you complete this jigsaw of the multiplication square?

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

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

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

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

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

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Play this game and see if you can figure out the computer's chosen number.

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?

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?

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

Can you sort numbers into sets? Can you give each set a name?

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.

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?

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.

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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?

How many different rectangles can you make using this set of rods?

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?

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.

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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.

Are these statements always true, sometimes true or never true?

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

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?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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

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

An investigation that gives you the opportunity to make and justify predictions.

Have a go at balancing this equation. Can you find different ways of doing it?

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?