Term 3 Week 8

Apologies for the delay here - between year 8 and year 9 camps and some time off with the flu there has not been a lot of action on this blog.

The topic we are completing is Pythagoras.

Students will have covered this before, however it is very important to be able to use Pythagoras' theorem quickly and effectively.

As we all know Pythogoras was the first to prove the relationship between the lengths of the two short sides of a right angle triangle and the long side:

h² = a² + b²

Which literaly means that if you draw a square on each side of the triangle the two small squares add up to the size of the big square.

Very useful!

Using this formula we can calculate any side of the triangle if we know the other two sides. We only need to be careful to check whether we are finding the long side (hypotenuse) or a short side.

Pythagoras Assignment 1 is here

Term 2 Week 9

Due to Winter Festival commitments there is no Year 8 maths this week.

Congratulations to those who completed the Probability topic test last week, you have all done very well.

I will post next weeks assignment here shortly anyway...

Regards,

Josh

Term 2 Week 8

Due to the class play, and other delays the Probability Assignment 2 due date is extended to Thursday - at which time we will have an end of topic exam.

The next assignment will be set on Tuesday week 9 for the new topic and due Tuesday of Week 10.

Term 2 Week 7

We continue our study of probability by giving absolutely impossible and absolutely certain events a number value:

P(certain) = 1
P(impossible) = 0

We also note that probabilities are 'complementary', that is the probability of something happening added to the probability that it won't happen is always 1.

Eg The probability of rolling a '5' is 1/6 and the probability of not rolling a '5' is 5/6. Adding these together we get the probability of either rolling a '5' or not rolling a '5' is 1.

Knowing this we can calculate the probability of some events very simply:

Eg If we know the probability of winning a lottery is 1/1000000, then we can subract that number from 1 and work out that the probability of not winning the lottery is 999999/1000000.

The Probability Assignment 2 is here

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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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