Got It game for an adult and child. How can you play so that you know you will always win?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
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?
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.
Can you explain the strategy for winning this game with any target?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Ben’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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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.
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
Are these statements always true, sometimes true or never true?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
An investigation that gives you the opportunity to make and justify predictions.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Here are two kinds of spirals for you to explore. What do you notice?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
This activity involves rounding four-digit numbers to the nearest thousand.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
This challenge asks you to imagine a snake coiling on itself.
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
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?
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .