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?
Investigate the different distances of these car journeys and find
out how long they take.
Investigate what happens when you add house numbers along a street
in different ways.
This article for teachers suggests ideas for activities built around 10 and 2010.
Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Can you find six numbers to go in the Daisy from which you can make
all the numbers from 1 to a number bigger than 25?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
If the answer's 2010, what could the question be?
Complete these two jigsaws then put one on top of the other. What
happens when you add the 'touching' numbers? What happens when you
change the position of the jigsaws?
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
There are nasty versions of this dice game but we'll start with the nice ones...
If you have only four weights, where could you place them in order
to balance this equaliser?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Investigate this balance which is marked in halves. If you had a
weight on the left-hand 7, where could you hang two weights on the
right to make it balance?
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
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.
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
How is it possible to predict the card?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
These alphabet bricks are painted in a special way. A is on one
brick, B on two bricks, and so on. How many bricks will be painted
by the time they have got to other letters of the alphabet?