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

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 order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

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

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

This challenge extends the Plants investigation so now four or more children are involved.

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

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

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

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

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?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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

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

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?

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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 find all the different ways of lining up these Cuisenaire rods?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How many different triangles can you make on a circular pegboard that has nine pegs?

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?