What happens when you round these three-digit numbers to the nearest 100?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Can you work out some different ways to balance this equation?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

What happens when you round these numbers to the nearest whole number?

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Can you replace the letters with numbers? Is there only one solution in each case?

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

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Try out the lottery that is played in a far-away land. What is the chance of winning?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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?

Investigate the different ways you could split up these rooms so that you have double the number.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?