## Turn up the volume!

Welcome to Enrichment Mathematics for 2011 – this year will be intense, but fun. The purpose of this class is to challenge you, and prepare you for advanced studies of mathematics next year as part of your VCE.

We will be using the VCE General Mathematics (Advanced) textbook, but we will also be using other resources as appropriate. Just in case you were worried, this is a year 10 course, and you won’t be expected to do everything a year 11 student of advanced general would be. This doesn’t mean you should try – all of you are capable of mastering the content if you have enough commitment.

Our first topic of study is “Mensuration” – the study of areas and volumes, including calculation of compound formulas, pythagoras in three dimensions, and circular geometry. Each of these topics will be covered in one week, and our first test will be in the third week.

It is time to get started – you should begin by checking your notes from last year; Measurment was part of last year’s curriculum. You need to review your bound reference (a summary book that you write yourself; you may take this into all tests), and get it ready for this year. That means that if you have one, bring it to class. If you don’t, buy one and then bring it to class.

I’ve included a few videos below the fold to help you get started with the content. You need to make a point of visiting this blog, watching the videos and commenting. Part of your assessment this year will be throught your participation and contribution to this blog.

The rest of the playlist is here

See you in class.

**Explore posts in the same categories:**Mathematics

February 14, 2011 at 4:03 PM

Hey Mr G,

I found out that when dividing a fraction by a fraction a complex fraction is formed. When working with complex fractions the first thing you want to do is get rid of the denominator. Because multiplying any fraction by it’s reciprocal number equals 1, you flip the second number which becomes the denominators reciprocal and multiply them. Because you have to do the same for the top and bottom of a fraction, you then multiply the top number by the inverted second fraction, which is the only step we see as we don’t notice or set out the complex fraction. That’s how and why we get our answer by flipping the second fraction (:

February 14, 2011 at 8:14 PM

Hayley, that is very good. I like the way you have explained it, but I think you need to use an example to fully explain what is going on.

Perhaps you could start with the problem Prathamesh used, and then use a general type of problem, such as (a/b) / (c/d).

February 14, 2011 at 8:58 PM

using the equation (2/4)/(3/4) set out as a complex fraction would look like

(2/4)

_____

(3/4)

then the next thing you should do is get rid of the denominator by making it equal one. As I previously mentioned this is done by multiplying the fraction by its reciprocal which is the fraction inverted.

Eg:

(2/4)

_____

(3/4) x (4/3)

then of course whatever you do to the bottom of the fraction you have to do to the top as well so your workings will then be:

(2/4) x (4/3)

_____

(3/4) x (4/3)

which then will equal

(8/12)

______ or just (8/12) which equals (2/3)

1

When we do these workings out though we don’t look at the complicated fraction or aknowledge that it is even there, meaning we do the simple way by multiplying the first fraction by the inverted second fraction (the seconds reciprocal.)

So instead of seeing

(2/4) x (4/3)

_____ we see (2/4) x (4/3)

(3/4) x (4/3)

February 14, 2011 at 4:50 PM

The reason why you flip one of the fractions is just the make a complicated process simpler…

heres an example:

(2/4)/(3/4)=?

normally we would do this

(2/4)x(4/3)=?

and then the answer is simple it is 8/12, which equals to 2/3

NOW this is wat i think actually happens in the complicated version

(2/4)/(3/4)=?

= ((1/2)x1)x((1/4)x3)…right? i know its complicated.

and then..we solve it WITHOUT HAVING TO FLIP ANY OF THE FRACTIONS 😀

the final answer in this scenario is 2/3 which is correct

February 14, 2011 at 8:12 PM

You need to think a little harder about this. Remember that division is asking “How many of the divisor are in the dividend”. So, when you ask

what two quarters divided by three quarters is, you want to know how many three quarters it is possible to fit in two quarters.

Remember that fractions are equivalent to divisions, so what you have is (two divided by three) divided by (three divided by four)…

Can you go further?

February 14, 2011 at 6:30 PM

Why flipping a fraction will result in changing the discussion?

(Weird question)

Umm…. I think because, if you do for example 2/4 / 2/3. You should end up with an answer x.

When you do 2/4 x 3/2 the answer should also be x.

Because / and x are the opposite of each other, like + and –

The fraction operation allows you to flip the 2nd fraction to make it easier for you?

I think…

February 14, 2011 at 8:08 PM

Hi Hao,

It’s a good try, but it doesn’t quite make it. You need to start thinking about what happens when you divide 1 by a fraction, and why this result is important…

February 14, 2011 at 9:29 PM

what we are basically doing is inverse-ing one of the fractions by fliping it over and then making it even by changing the division sign into multiplication <—-(does that make sense) :S

Its something like this…heres one very good example…

3/ (2/1)=?

Now we know the answer is 1.5 or 1(1/2)

Now lets see wat happens when we flip the *2/1*

3 X (1/2)= and woah!!! The answer is still 1.5 or 1(1/2) 😀

So basically wat we are doing is.. Just rearrangeing the numbers so its easier for us to solve it… Just like..say if i tell u to add:

18+7+2+3= then we rearrange this equation into this:

18+2+7+3=

20+10=30

we just made it easier for us to solve it like this am i right?

February 15, 2011 at 2:53 PM

Hi Sir,

I was just wondering, if I have already figured out how I’m going to use my bound references, can I write in what we have done in the last two classes? Or should I wait until we start doing workbook exercises?

February 15, 2011 at 8:15 PM

Hi Lauren,

You can start whenever you are ready.

February 16, 2011 at 2:51 PM

hello sir,

another question.. do we ONLY write stuff which was taught by you..or are we allowed to write anything we know

February 15, 2011 at 8:55 PM

You certainly have a good bunch of year 10’s this year sir 🙂 Hope you torture them well with Year 11 maths 😛

February 16, 2011 at 2:39 PM

no, we will be his favourites and he’ll be forever nice to us. End of story.

February 16, 2011 at 4:45 PM

Favourites? Get ready to get enriched 🙂

March 1, 2011 at 9:14 PM

ahh that’s right you’re in 10H :O

that means you’re doing advanced general XD

haha good luck with that 😀

you seem smart so you’ll do fine 😀

February 16, 2011 at 6:31 AM

:paranoid:

February 16, 2011 at 3:55 PM

Haha is that Jack Huynh?

Also sir, are we actually learning year 11 maths or is it just year 10 maths advanced with certain elements of year 11?

February 17, 2011 at 7:11 AM

Hi Jana,

Definitely the second option. We are studying the year 10 Mathematics curriculum (you will be assessed by VELS), but we will be pitching at ~5.75 level and going up from there. We are definitely going to be including segments of year 11 for those that are interested.

March 1, 2011 at 9:13 PM

Wow, you’re doing advanced general :O

i wish last years advanced class did bits of advanced general :O

i feel so cheated :O