Term 2 Week 6

After a whistle stop tour of percentages we are now moving to probablility. This is a very hands on subject where we can explore how chance works, and have fun tossing coins and rolling dice.

We have all heard expressions like 'you have a 50-50 chance' but what does this mean?

It simply means that the likelyhood of something working out is 1 chance out of 2 - ie a 50% or 1/2 chance.

Much study has been done on understanding chance and probability - particularly when there is money to be made (or lost!)

To formalise the maths of chance we write the chance that something will happen as a ratio of what we want to happen over number of possible ways things could happen.

So the probablility of winning the toss in a football match is 1 chance of heads over 2 (heads or tails) or again a 50% or 1/2 chance.

We call the range of possible out comes the 'sample space' and put curly braces around it to make it look flash:

What is the sample space for a 6 sided dice? {1, 2, 3, 4, 5, 6}

So we can work out the probablility of getting a '2':

P('2') = 1 / 6
(ie 1 desired outcome ('2') out of a sampe space with 6 things in it: {1,2,3,4,5,6})

By calculating and comparing probabilities for things it is possible to make more informed choices about taking risks.

It is said that mathemeticians never gamble - because they can calculate the exact probability that they are going to lose their money!

Probability Assignment 1 is here

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Term 2 Week 5

some people take their 50% very seriously

Percentages roll on this week.

By now we have reaffirmed that fractions, decimals and percentages are all interchangeable, and all indicate how much of something we have.

eg 1/2 is the same as 0.5 which is the same as 50%

We know how to change from one to another:

To convert 1/2 to a percentage we multiply by 100%

1/2 x 100% = 100/2 = 50%

To convert 0.5 we also multiply by 100%

0.5 x 100% = 0.5 x 100 = 50%

Converting from a percentage to a fraction or a decimal is just the reverse:
To convert 50% to a fraction just divide by 100 and then simplify

50% = 50/100 = 5/10 = 1/2

To convert 50% to a decimal just divide by 100 with a calculator (can also be done mentally if you are careful)

50% = 50/100 = 0.5

We also need to be able to recognise common fractions and so be able to quickly convert them:

1/2 = 0.5 = 50%
1/3 = 0.33 = 33.33%
1/4 = 0.25 = 25%
1/5 = 0.2 = 20%
1/10 = 0.1 = 10%

The Percentages Assignment 2 is here
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Term 2 Week 4

We finish Geometry this week with a topic test.

The next topic is Percentages. See pages 109 - 137 of the text.

Percentage Trivia: The symbol for percent (%) evolved from a symbol abbreviating the Italian per cento.

Being able to convert things to percentages allows us to compare 'apples' with 'apples'.

For example if one person scores 10 goals out of 20 attempts, whereas another scores 9 goals out of 15 attempts we can work out who is the higher scoring player by converting their score to a percentage. In this case player 1 has a 50% score rate, whereas player 2 has a 60% score rate and is probably a better goal shooter.

Fractions and decimal values also allow us to compare things.

The purpose of this unit is to increase students capability to convert things to and from percentages, and compare them. This is very applied mathematics as we know that percentages and proportions come up quite frequently in every day life.

The Hammer Percentages Assignment 1 is here.
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Term 2 Week 3

geometry in art

This week we continue with triangles, and then quadrilaterals.

We note that for any triangle at all if we measure the angles inside it they always add up to 180 degrees. Similarly for any shape with four sides (Quadrilateral) the angles always add up to 360 degrees.

Click here for Geometrical Figures Assignment 3
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