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?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
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.
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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. . . .
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
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?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
An investigation that gives you the opportunity to make and justify
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?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
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.
Find out what a "fault-free" rectangle is and try to make some of
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you find the values at the vertices when you know the values on
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?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
Pick a square within a multiplication square and add the numbers on
each diagonal. What do you notice?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This challenge asks you to imagine a snake coiling on itself.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
This activity involves rounding four-digit numbers to the nearest thousand.