This article for teachers suggests ideas for activities built around 10 and 2010.
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?
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
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.
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?
Find the numbers in this sum
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
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?
Who said that adding couldn't be fun?
Find the sum of all three-digit numbers each of whose digits is
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 nasty versions of this dice game but we'll start with the nice ones...
This challenge is to make up YOUR OWN alphanumeric. Each letter
represents a digit and where the same letter appears more than once
it must represent the same digit each time.
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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?
What is the sum of all the three digit whole numbers?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
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
Can you substitute numbers for the letters in these sums?
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?
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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.
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?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
What is the sum of all the digits in all the integers from one to
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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?
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?
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?
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.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Find a great variety of ways of asking questions which make 8.
If the answer's 2010, what could the question be?
A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
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?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
This dice train has been made using specific rules. How many different trains can you make?