An excellent puzzle – alternate methods | srcav

Yesterday I wrote this post looking at a nice puzzle I’d seen and how I solved it.

The puzzle again:

Lovely, isn’t It?

After I published my previous post I wondered if I may have been better using a vector approach or a coordinate geometry approach. So I gave them a try.

Coordinate Geometry

I started by sketching the figure against an axis.

I place the origin at the centre of the circle, worked out the equation if the circle and the right leg of the triangle and solved simultaneously for x. Giving x =1 and x=1/3. These x values correspond to half the base of each triangle,…

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http://ift.tt/2vBZYTc

An excellent puzzle – alternate methods | srcav

Yesterday I wrote this post looking at a nice puzzle I’d seen and how I solved it.

The puzzle again:

Lovely, isn’t It?

After I published my previous post I wondered if I may have been better using a vector approach or a coordinate geometry approach. So I gave them a try.

Coordinate Geometry

I started by sketching the figure against an axis.

I place the origin at the centre of the circle, worked out the equation if the circle and the right leg of the triangle and solved simultaneously for x. Giving x =1 and x=1/3. These x values correspond to half the base of each triangle,…

Continue reading at:

http://ift.tt/2vBZYTc

An excellent puzzle | srcav

Today I saw this tweet:

The puzzle looked grand. Thanks to those people that tweeted at me to make sure if seen it, it’s much appreciated.

The puzzle itself is:

I drew it out and labelled a few things:

But soon realised that it’s impossible unless you make assumptions. 

With the assumption that the vertex of the triangle is at the midpoint if the line I was in a position to have a good crack at it. My first thought, as is often the case, was to run at it using right angled triangles:

My initial thought was to use right angled trigonometry, but I realised I’d…

Continue reading at:

http://ift.tt/2tCFxUN

An excellent puzzle | srcav

Today I saw this tweet:

The puzzle looked grand. Thanks to those people that tweeted at me to make sure if seen it, it’s much appreciated.

The puzzle itself is:

I drew it out and labelled a few things:

But soon realised that it’s impossible unless you make assumptions. 

With the assumption that the vertex of the triangle is at the midpoint if the line I was in a position to have a good crack at it. My first thought, as is often the case, was to run at it using right angled triangles:

My initial thought was to use right angled trigonometry, but I realised I’d…

Continue reading at:

http://ift.tt/2tCFxUN

Group Work Issues | srcav

Recently I wrote this post (2017) that highlights various ways that I can see group work being of benefit to students study in mathematics.  In the post I allude to there being many issues around group work that can have a detrimental effect on the learning of the students and I intend to explore them a little further here.

The benefits of group work can be vast, and are often tied to the discussion around the mathematics involved in a way consistent with the writings of Hodgen and Marshall (2005), Mortimer and Scott (2003), Piaget (1970), Simmons (1993), Skemp (1987) and Vygotsky (1962)…

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http://ift.tt/2uwuUYv

Thoughts on the understanding paradox and introducing trigonometry | srcav

Recently I read a blog entitled “The understanding paradox” (William, 2017) which discussed the idea of maths teaching and put forward the idea that actually, it is better to bypass understanding when first teaching a topic and then fill that understanding in later. This was then applied to the teaching of right angled triangle trigonometry in an example that I found confusing to say the least.

The author, Rufus William, suggested that when teaching trig for the first time we should be solely teaching procedurally using SOHCAHTOA as a mnemonic, but then went on to say we shouldn’t be…

Continue reading at:

http://ift.tt/2tQz8sk

Thoughts on the understanding paradox and introducing trigonometry | srcav

Recently I read a blog entitled “The understanding paradox” (William, 2017) which discussed the idea of maths teaching and put forward the idea that actually, it is better to bypass understanding when first teaching a topic and then fill that understanding in later. This was then applied to the teaching of right angled triangle trigonometry in an example that I found confusing to say the least.

The author, Rufus William, suggested that when teaching trig for the first time we should be solely teaching procedurally using SOHCAHTOA as a mnemonic, but then went on to say we shouldn’t be…

Continue reading at:

http://ift.tt/2tQz8sk