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.
This article for teachers suggests ideas for activities built around 10 and 2010.
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?
Number problems at primary level that require careful consideration.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Investigate what happens when you add house numbers along a street
in different ways.
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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
There are nasty versions of this dice game but we'll start with the nice ones...
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?
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
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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?
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Can you substitute numbers for the letters in these sums?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
If the answer's 2010, what could the question be?
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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Who said that adding couldn't be fun?
Number problems at primary level that may require determination.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Number problems at primary level to work on with others.
If you have only four weights, where could you place them in order
to balance this equaliser?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Find the next number in this pattern: 3, 7, 19, 55 ...
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