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.
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?
This article for teachers suggests ideas for activities built around 10 and 2010.
Number problems at primary level that require careful consideration.
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
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
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
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
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?
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?
There are nasty versions of this dice game but we'll start with the nice ones...
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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.
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?
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.
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Can you substitute numbers for the letters in these sums?
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.
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?
Replace each letter with a digit to make this addition correct.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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
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?
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.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
If you have only four weights, where could you place them in order
to balance this equaliser?
Number problems at primary level to work on with others.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
This task combines spatial awareness with addition and multiplication.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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.
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?
Number problems at primary level that may require determination.
Who said that adding couldn't be fun?
Investigate what happens when you add house numbers along a street
in different ways.