Year 9-10 Maths Discussion & Resources (1 Viewer)

[davidgoes4wce]

What other Circle Geometry programs are there ? Or ones that the NSW curriculum encourage students to use?

Geogebra is one.

Efofex is one that is used in WA (but I never touched much on that subject in the past), so rarely touched it

Are there maybe other ones that are used?

 

[davidgoes4wce]

I came across this question in the Cambridge year 10 maths book and it got me thinking this early morning. This chapter was part of the Geometrical figures and circle geometry. (I haven't looked at the answer yet)

Q. Are these statements true or false?

" All circles are similar"



I think it's FALSE

When comparing different circles, they may the same shape and of a different size.

But there are no corresponding angles to compare against. However, the can very in proportion (or ratio)

 

[InteGrand]

I came across this question in the Cambridge year 10 maths book and it got me thinking this early morning. This chapter was part of the Geometrical figures and circle geometry. (I haven't looked at the answer yet)

Q. Are these statements true or false?

" All circles are similar"



I think it's FALSE

When comparing different circles, they may the same shape and of a different size.

But there are no corresponding angles to compare against. However, the can very in proportion (or ratio)

The answer is 'true'.

 

[InteGrand]

Don't need angles. You can see the definition of similarity here: https://en.wikipedia.org/wiki/Similarity_(geometry) .

 

[davidgoes4wce]

Now everybody on the forum can have a laugh at me now !

And the answer was True

 

[davidgoes4wce]

Interesting little fact from that wikipedia link:

"For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other."


I would have thought that would have applied to rectangles? Maybe it's too early in the morning and I can't get my head around that thought but what if we had a rectangle that was say 4 m v 5 m. A second rectangle that was 12 m v 15 m, that would be similar wouldn't it? (It has a scale factor of 3- which from my readings indicates it is similar)

 

[InteGrand]

Interesting little fact from that wikipedia link:

"For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other."


I would have thought that would have applied to rectangles? Maybe it's too early in the morning and I can't get my head around that thought but what if we had a rectangle that was say 4 m v 5 m. A second rectangle that was 12 m v 15 m, that would be similar wouldn't it? (It has a scale factor of 3- which from my readings indicates it is similar)

Two rectangles which have different aspect ratios (the ratio between longer and shorter sides) to each other will not be similar (they are different in shape). Two rectangles will be similar if and only if they have the same aspect ratio.

 

[InteGrand]

In your example, the two rectangles have the same aspect ratio, so yes, they're similar.

 

[davidgoes4wce]

In your example, the two rectangles have the same aspect ratio, so yes, they're similar.

Hence, why your correct when the question came

'All rectangles are similar'-----> FALSE (in the textbook)


Again, before today I would have said TRUE. I do understand now that you have to look at the aspect ratio (long sides v short sides of both shapes)

 

[davidgoes4wce]

'All rhombuses are similar'

I got this wrong admittedly. My only guess is even if they have the same (proportions ) for the sides, you can get instances where the corresponding angles are different. I've drawn a diagram below:

 

[Drongoski]

After all what is a rhombus? It is simply a quadrilateral will all 4 sides equal. A special case of a rhombus is a square. You can easily draw a few rhombuses and notice they have different shapes and therefore cannot be similar.

 

[davidgoes4wce]

Does doing Maths 5.2 in Year 10 at a high level allow a student to go on and do Maths Extension?

The 5.2 seems way easier compared to the 5.3

 

[Drongoski]

Students should be encouraged to do the highest level of maths they can manage. The creation of different pathways: 5.1, 5.2 and 5.3 is understandably to help those who are uninterested or are unable to handle 5.3 to fall back to 5.2 or 5.1 - thus catering for the spectrum of student abilities. But this also has the effect of providing escape routes for those who can but for a variety of reasons prefer the easy way out. Of course they are dead-ended into General Maths or no maths at all. Some of these people wake up a year or two later and decide they want to be engineers!

 

[davidgoes4wce]

That didn't quite answer my question, does doing Maths Stage 5.2 allow you to do Extension I and Extension II maths in Year 11 and 12?

I feel like a hard question in 5.2, is about a medium standard in 5.3.

 

[Drongoski]

That didn't quite answer my question, does doing Maths Stage 5.2 allow you to do Extension I and Extension II maths in Year 11 and 12?

I feel like a hard question in 5.2, is about a medium standard in 5.3.

I notice those who do 5.1 and 5.2 are destined for General Maths or no maths when they get to Yr 11. So if your teacher invites you to drop to 5.1 or 5.2 it is as good as being condemned to being unable to pursue 2U Maths, and therefore 3U. But this is not a hard and fast rule. Some schools allow those who do 5.2 to pursue 2U; don't know about the 3U. Of course no 3U means no 4U.

Current students please correct me if I have misconstrued the whole thing.

 

[davidgoes4wce]

I have 2 students that I tutor in Year 10, one is in 5.2 and the other girl is a 5.3 she had a splendid 2016. (Got 141/150 in her exams-ranked 5th or 6th in her school for that subject). The difference between the 2? The girl is super motivated (also seems less well off) at a mid 60's ranked school in NSW. The boy seems pampered and dare I say it spoilt. (at a school ranked in the 100's)

It's really hard to motivate the 5.2 boy. I give homework, make up diagnostic tests, I do occasion mix up a 5.3 question (Which he can hardly get right. Maths is all about challenges right?). Then you give him 5.2 work, from the year prior (Yr 9) and he gets about 60-65% of the questions right. (and some of these questions were from the lesson prior). Any ideas how I could motivate him? I want him to do Extension Level maths, not General. (no disrespect to those kids). Yes her mum has hit the panic button! She has hired me for extra hours in a week and I think she demands results. (As you can tell I am only slowly getting more familiar with the NSW curriculum on a day by day basis)

 

[davidgoes4wce]

Is it possible to say move to a lower ranked school to fulfill your goal of doing higher ranked subjects? I am acutely aware that all schools want to protect their rankings.

Has anyone been a position or know of any , whereby you could take a subject against the schools discretion?

In my high school days, I actually was restricted from doing a couple of science based subjects. I had to get the permission of my parents and go speak to the principal to allow me to enrol into a particular subject. We said to the school we would get a tutor and the school accepted it.

Not sure if that same process happens in NSW.

 

[He-Mann]

I have 2 students that I tutor in Year 10, one is in 5.2 and the other girl is a 5.3 she had a splendid 2016. (Got 141/150 in her exams-ranked 5th or 6th in her school for that subject). The difference between the 2? The girl is super motivated (also seems less well off) at a mid 60's ranked school in NSW. The boy seems pampered and dare I say it spoilt. (at a school ranked in the 100's)

It's really hard to motivate the 5.2 boy. I give homework, make up diagnostic tests, I do occasion mix up a 5.3 question (Which he can hardly get right. Maths is all about challenges right?). Then you give him 5.2 work, from the year prior (Yr 9) and he gets about 60-65% of the questions right. (and some of these questions were from the lesson prior). Any ideas how I could motivate him? I want him to do Extension Level maths, not General. (no disrespect to those kids). Yes her mum has hit the panic button! She has hired me for extra hours in a week and I think she demands results. (As you can tell I am only slowly getting more familiar with the NSW curriculum on a day by day basis)

Although irrelevant, you haven't made it clear on the gender of the 5.2 person.

The problem I see is laziness, lack of motivation. Why? It seems that he/she does not care about their education. He/she must identify their goals and you must convince them to add education and education performance as a goal. It's important that you incorporate the mother's reasoning for tutoring. It's hard to force someone to do something that they don't want to.

Try to associate studying as a duty as a secondary solution. Most students don't study much because they don't want to; they'd rather play and have fun. So to fix this, make them study because they need to, somehow.

You could spark interest in maths for them but that'll require something special...

 

[davidgoes4wce]

I'm reading it a bit differently at the moment

I looked at this website:

http://www.karabarhigh.com.au/img.ashx?f=f&p=curriculum/maths/CourseInformationStage5.pdf

If you are in 5.3-----------> You can go on to do Prelim Mathematics/Maths Extension 1 in Year 11----> Maths Extension I and/or Maths Extension 2 In year 12
If you are in 5.2 (Highest)---> You can go on to do Prelim Maths in Year 11---> Mathematics (2 Unit) in Year 12
If you are in 5.2 (Standard)---> your more likely to do General Maths in Year 11 (im going to guess 80% chance) and if you do outstanding in Year 10 you will do Prelim Maths (20% chance)
If you are in 5.1 ---> You will do General Maths or No maths in Year 11

He is in the highest 5.2 maths class...........so I personally don't think it would be impossible for him to do 2 Unit. I'm aware in Year 10 they have different levels of 5.2 maths classes: Highest rank, 2nd highest rank, 3rd highest rank etc

(And yes He-Mann- I think its a fantastic idea that I should sit down and discuss with him about the future direction. To me the boy doesn't seem hungry enough but if I give him a bit of a pathway he may be more motivated to study hard this year)

 

[davidgoes4wce]

I should have listed down Mathscape as well