Can you each work out the number on your card? What do you notice? How could you sort the cards?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

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

What do you see as you watch this video? Can you create a similar video for the number 12?

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

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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?

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

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

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

Make one big triangle so the numbers that touch on the small triangles add to 10.

Find all the numbers that can be made by adding the dots on two dice.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Try this version of Snap with a friend - do you know the order of the days of the week?

Can you split each of the shapes below in half so that the two parts are exactly the same?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

These pictures show some different activities that you may get up to during a day. What order would you do them in?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

These pictures show squares split into halves. Can you find other ways?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Can you put these shapes in order of size? Start with the smallest.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

Use the number weights to find different ways of balancing the equaliser.

For this activity which explores capacity, you will need to collect some bottles and jars.

Shapes are added to other shapes. Can you see what is happening? What is the rule?

In this activity focusing on capacity, you will need a collection of different jars and bottles.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

Try some throwing activities and see whether you can throw something as far as the Olympic hammer or discus throwers.

Dotty Six is a simple dice game that you can adapt in many ways.

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

This problem is intended to get children to look really hard at something they will see many times in the next few months.

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

Here are some short problems for you to try. Talk to your friends about how you work them out.

Here's a very elementary code that requires young children to read a table, and look for similarities and differences.

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.