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?

What two-digit numbers can you make with these two dice? What can't you make?

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

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

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

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

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

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?

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

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?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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?

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

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

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

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

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

This challenge is about finding the difference between numbers which have the same tens digit.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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

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.

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

What could the half time scores have been in these Olympic hockey matches?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Can you use the information to find out which cards I have used?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

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

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?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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?