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

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?

Got It game for an adult and child. How can you play so that you know you will always win?

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

Are these statements always true, sometimes true or never true?

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?

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.

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

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

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?

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

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

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 any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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

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

Can you explain the strategy for winning this game with any target?

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

This task follows on from Build it Up and takes the ideas into three dimensions!

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

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?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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?

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

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

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

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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

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.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

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

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

Are these statements relating to odd and even numbers always true, sometimes true or never true?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?