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"Lesson Activities"
You can weigh all integer masses from 1 to 60 with 6 weights putting the weights in one pan and the object in the other pan. Which weights are used?
What about weighing all integer masses from 1 to 1000?
What about from 1 to n?
What could this have to do with the […]
Bilbo decides to leave his hobbit-hole and go on an adventure. He walks 100 km South, then 100 km East, then finally 100 km North, at which point he is surprised to find that he has arrived back home!
Many people would think that because of this Bilbo must live at the North Pole. […]
What is the largest number that, when divided into each of 1905, 2587, 3951, 7020 and 8725, leaves the same remainder each time?
When a problem seems difficult a good strategy is to try a simple case.
The diagram should help you to find the answer to the same question […]
(a) You must mark four red squares and five blue squares in a 3 by 3 grid .
How many ways can you do this so that all the rows columns and diagonals have an even number of red squares?
Two solutions are considered the same if one can be transformed to […]
Suppose you had the never ending task of writing out all the natural numbers: 1, 2, 3, 4, 5…. and so on.
What would be the 1000th digit you would write down?
In what number would it occur?
What number would contain the millionth digit?
When would you have written six for […]
Think of a whole number. Square it. Subtract the number you first thought of. Is the answer odd or even?
Try this with other numbers. What do you notice? Can you explain why? Can you find different ways to explain (and prove) the result that you noticed. You might use what you […]
My car has number plate – S208VBJ.
Using my special code S208VBJ adds to 65.
Using the code every character, a digit or a letter, is separate.
Numbers are simply added together so that, in the first number plate 208 is 2 + 0 + 8 = 10.
Letters are translated into […]
If you change the order of these digits you can get 24 different numbers, for example 2547, 2574, 2745, … Can you find all 24 different numbers made by using each of the digits 2, 4, 5, 7 just once?
How many of these numbers have 2 in the thousands place? How many have 2 […]
Using the numbers 1, 2, 3, 4 and 5 once and only once and the symbols × and ÷ once and only once, what is the smallest whole number you can make?
Now suppose you have to use the symbol + once and the symbol ÷ twice what is the smallest fraction […]
A hundred square has been printed on both sides of a piece of paper.
One square is directly behind the other.
What is on the back of 100? 58? 23? 19?
Can you see a pattern?
Click here for the HUNDRED SQUARE Notes for Teachers.
Click here for the HUNDRED […]
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