When is a Quadratic “factorisable”? | mhorley

There are 3 standard ways of solving quadratic equations once they are in the form:
ax² + bx + c = 0

They are:
Factorise
Complete the square
Use the formula

I think I generally teach them in that order probably without much thought as to why. I guess the formula needs to be derived by using completing the square and factorising seems to follow on from multiplying out double brackets, which comes before all of this.  The I question that I sometimes get from students is “what’s the point in learning factorising if the two other methods always work?”.  Well, it’s quicker and you can do…

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When is a Quadratic “factorisable”? | mhorley

There are 3 standard ways of solving quadratic equations once they are in the form:
ax² + bx + c = 0

They are:
Factorise
Complete the square
Use the formula

I think I generally teach them in that order probably without much thought as to why. I guess the formula needs to be derived by using completing the square and factorising seems to follow on from multiplying out double brackets, which comes before all of this.  The I question that I sometimes get from students is “what’s the point in learning factorising if the two other methods always work?”.  Well, it’s quicker and you can do…

Continue reading at:

http://ift.tt/2paSckf

Concentric Equilateral Triangles | mhorley

The red equilateral triangle side length 4cm sits inside the larger pink equilateral triangle such that the “border” is 1cm wide.

What is the ratio of the height of the red triangle to the height of the pink triangle?

Can you solve using trigonometry or only using Pythagoras?

The border is now 2cm, whilst the side length of the red triangle remains 4cm.  What is the ratio of heights now?

Explore what happens for other border widths.  Can you generalise for any border width w?

Geogebra file here.

Spoiler here. 

Continue reading at:

http://ift.tt/2pnpdpW

Concentric Equilateral Triangles | mhorley

The red equilateral triangle side length 4cm sits inside the larger pink equilateral triangle such that the “border” is 1cm wide.

What is the ratio of the height of the red triangle to the height of the pink triangle?

Can you solve using trigonometry or only using Pythagoras?

The border is now 2cm, whilst the side length of the red triangle remains 4cm.  What is the ratio of heights now?

Explore what happens for other border widths.  Can you generalise for any border width w?

Geogebra file here.

Spoiler here. 

Continue reading at:

http://ift.tt/2pCml87

Recurring Decimals | mhorley

First up, this post is NOT going to be about this:

This is what came to mind when joining Derek Ball’s session at the ATM conference this week, entitled “Recurring Decimals”.

In fact, we were going the other way: converting fractions to recurring decimals, specifically looking at fractions where the denominator is prime.  It was a fascinating session, great for deepening subject knowledge.  This blog post is my attempt to reflect on what I learned and my thoughts about how I might use this in the classroom, probably Year 10 or 11, but really any group that is confident with bus stop…

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