An investigation that gives you the opportunity to make and justify
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This challenge focuses on finding the sum and difference of pairs of two-digit 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?
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Find the sum of all three-digit numbers each of whose digits is
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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 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.
What happens when you round these three-digit numbers to the nearest 100?
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?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Find out what a "fault-free" rectangle is and try to make some of
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?
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.
How many centimetres of rope will I need to make another mat just
like the one I have here?
What happens when you round these numbers to the nearest whole number?
This activity involves rounding four-digit numbers to the nearest thousand.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Got It game for an adult and child. How can you play so that you know you will always win?
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.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
This challenge asks you to imagine a snake coiling on itself.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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. . . .
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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.