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

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!

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?

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

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?

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

Can you complete this jigsaw of the multiplication square?

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

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

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 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?

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 the interactivities to complete these Venn diagrams.

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

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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.

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?

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?

An environment which simulates working with Cuisenaire rods.

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

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.

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

A game that tests your understanding of remainders.

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.

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

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

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?

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

A game in which players take it in turns to choose a number. Can you block your opponent?

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.

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?

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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?

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?

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

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?

Can you work out what a ziffle is on the planet Zargon?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Can you make square numbers by adding two prime numbers together?

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