Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Ben has five coins in his pocket. How much money might he have?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
The pages of my calendar have got mixed up. Can you sort them out?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
A challenging activity focusing on finding all possible ways of stacking rods.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
In how many ways can you stack these rods, following the rules?
In this matching game, you have to decide how long different events take.
On a digital 24 hour clock, at certain times, all the digits are
consecutive. How many times like this are there between midnight
and 7 a.m.?
Use the clues about the symmetrical properties of these letters to
place them on the grid.
Try this matching game which will help you recognise different ways of saying the same time interval.
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
An activity making various patterns with 2 x 1 rectangular tiles.
This article for primary teachers suggests ways in which to help children become better at working systematically.
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
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?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Can you find the chosen number from the grid using the clues?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
How many triangles can you make on the 3 by 3 pegboard?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
If you put three beads onto a tens/ones abacus you could make the
numbers 3, 30, 12 or 21. What numbers can be made with six beads?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?