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?
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 ...?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
This challenge asks you to imagine a snake coiling on itself.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
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?
This activity involves rounding four-digit numbers to the nearest thousand.
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?
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?
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.
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Got It game for an adult and child. How can you play so that you know you will always win?
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.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Delight your friends with this cunning trick! Can you explain how
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Can you explain how this card trick works?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
An investigation that gives you the opportunity to make and justify
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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.
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
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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. . . .
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.
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?
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?
Find the sum of all three-digit numbers each of whose digits is
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Pick a square within a multiplication square and add the numbers on
each diagonal. What do you notice?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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 three-digit numbers to the nearest 100?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Find out what a "fault-free" rectangle is and try to make some of
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
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?