Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
How many different shapes can you make by putting four right-
angled isosceles triangles together?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
Explore the different snakes that can be made using 5 cubes.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
My coat has three buttons. How many ways can you find to do up all
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
Can you find out in which order the children are standing in this
How many triangles can you make on the 3 by 3 pegboard?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
Try this matching game which will help you recognise different ways of saying the same time interval.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
This challenge is about finding the difference between numbers which have the same tens digit.
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
Can you find all the ways to get 15 at the top of this triangle of numbers?
The brown frog and green frog want to swap places without getting
wet. They can hop onto a lily pad next to them, or hop over each
other. How could they do it?
What two-digit numbers can you make with these two dice? What can't you make?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
This task follows on from Build it Up and takes the ideas into three dimensions!
This train line has two tracks which cross at different points. Can
you find all the routes that end at Cheston?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?