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?

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

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

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

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

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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?

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

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?

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

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.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

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

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 numbers to the nearest whole number?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Nim-7 game for an adult and child. Who will be the one to take the last counter?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Can you work out how to win this game of Nim? Does it matter if you go first or second?

This activity involves rounding four-digit numbers to the nearest thousand.

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?