Tuesday, September 4, 2012

New Gcse: Ratio

I've only marked my Year xi mocks in addition to noticed that ratio continues to survive an expanse of difficulty. This isn't a surprise - nosotros realised a few years agone that ratio questions on the novel GCSE are much harder than they used to be. Here's an instance of a straightforward ratio enquiry - this is what ratio used to hold back similar at GCSE:

The ratio of boys to girls at a schoolhouse is 5:7
There are 600 children at the school.
How many boys are at that spot at the school?

But GCSE questions are to a greater extent than challenging now. We're seeing a lot of 'ratio change' questions - this example, from blog post are a goodness house to start for the basics. Your local Maths Hub may run a bar modelling course. If you lot know the basics but combat amongst the harder questions, depository fiscal establishment check out this Twitter thread to run into a bar model inwards activity for a trickier ratio problem. It's also worth watching this fantabulous video on solving harder ratio problems using bar models from Colin Hegarty.

Bar modelling surely is a clear in addition to accessible approach for unproblematic ratio questions. I would tell though that for some trickier ratio questions it's non ever quite every bit intuitive in addition to obvious every bit proficient bar modellers advise it is.

Let's conduct maintain a hold back at methods for some other 'ratio change' enquiry - this i is from Don Steward:
The algebra method I described inwards a higher house plant real quickly. Using equivalent fractions in addition to setting upwards an equation gives us 8(5x + 2) = 7(6x). The whole solution takes exclusively a few lines of working.

Scaling plant too:
5:6 gives 7:6 when January gains 2 marbles ✗
10:12 gives 12:12 when January gains 2 marbles ✗
15:18 gives 17:18 when January gains 2 marbles ✗
20: 24 gives 22:24 when January gains 2 marbles ✗
25: xxx gives 27:30 when January gains 2 marbles ✗
30: 36 gives 32:36 when January gains 2 marbles ✗
35: 42 gives 37:42 when January gains 2 marbles ✗
40: 48 gives 42:48 when January gains 2 marbles - this simplifies to 7:8 ✓

Again, nosotros tin larn at that spot to a greater extent than rapidly if nosotros mean value most multiples. We start amongst a multiple of xi in addition to terminate amongst a multiple of 15, but nosotros gained ii marbles along the way. So nosotros tin listing all multiples of xi in addition to all multiples of xv in addition to discovery a duo which are ii apart.

11, 22, 33, 44, 55, 66, 77, 88
15, 30, 45, 60, 75, 90
So nosotros started amongst 88 marbles.

Not all tricky ratio questions are inwards the cast of these 'ratio change' problems. We also straight off larn GCSE questions similar this:


If the ratio a:b is 4:7, write a inwards price of b



Though this may seem obvious to many of us (a is the smaller of the two, thus a is 4 sevenths of b), writing the ratios every bit equivalent fractions tin attention students larn their numbers the correct means circular (providing they are confident inwards rearranging equations).

Another type of enquiry is this:

If the ratio a:b is 2:5 in addition to the ratio b:c is 3:10, what is the ratio a:c?



Again, fractions mightiness help.

Influenza A virus subtype H5N1 quicker option is scaling here. We tin write a:b:c every bit i ratio if nosotros larn the b parts to match.

a: b tin survive written every bit 6:15
b:c tin survive written every bit 15:50
So a:b:c is 6:15:50
This shows that the ratio a:c is 6:50, which simplifies to 3:25


And here's some other type of question:


Punch is made my mixing orangish juice in addition to cranberry juice inwards the ratio 7:2. Mark has xxx litres of orangish juice in addition to 8 litres of cranberry juice. What is the maximum amount of punch that Mark tin make?

Again, I mean value that scaling is likely the quickest approach here. Multiplying the punch ratio yesteryear 4 gives us 28:8. This is the most punch nosotros tin brand because we're using all the cranberry juice. So inwards full we're making 36 litres of punch.

In summary, at that spot are a diversity of approaches for solving trickier ratio problems - most tin survive solved efficiently using algebra, scaling or bar modelling. If you're educational activity this topic for the showtime fourth dimension at GCSE it's worth spending some fourth dimension looking at the diverse methods. I mean value our students volition demand a lot of practise of numerous dissimilar types of ratio enquiry to gear upwards for their GCSE.


Resources
I've created a lesson to accompany this postal service - download it from TES here.

Here are some other resources that you lot mightiness discovery helpful:
  • Mel from JustMaths collated ratio Higher GCSE questions from sample in addition to specimen papers here, in addition to has written upwards her solutions here. 
  • If you lot subscribe to MathsPad thus you'll survive pleased to take away heed that they conduct maintain lovely resources for ratio including a laid of questions for Higher GCSE with loads of examples similar the problems I've featured inwards this post.  
  • Don Steward has enough of ratio tasks including his laid of 'Harder Ratio Questions' in addition to a actually helpful collection of blog post are a goodness house to start for the basics. Your local Maths Hub may run a bar modelling course. If you lot know the basics but combat amongst the harder questions, depository fiscal establishment check out this Twitter thread to run into a bar model inwards activity for a trickier ratio problem. It's also worth watching this fantabulous video on solving harder ratio problems using bar models from Colin Hegarty.

    Bar modelling surely is a clear in addition to accessible approach for unproblematic ratio questions. I would tell though that for some trickier ratio questions it's non ever quite every bit intuitive in addition to obvious every bit proficient bar modellers advise it is.

    Let's conduct maintain a hold back at methods for some other 'ratio change' enquiry - this i is from Don Steward:
    The algebra method I described inwards a higher house plant real quickly. Using equivalent fractions in addition to setting upwards an equation gives us 8(5x + 2) = 7(6x). The whole solution takes exclusively a few lines of working.

    Scaling plant too:
    5:6 gives 7:6 when January gains 2 marbles ✗
    10:12 gives 12:12 when January gains 2 marbles ✗
    15:18 gives 17:18 when January gains 2 marbles ✗
    20: 24 gives 22:24 when January gains 2 marbles ✗
    25: xxx gives 27:30 when January gains 2 marbles ✗
    30: 36 gives 32:36 when January gains 2 marbles ✗
    35: 42 gives 37:42 when January gains 2 marbles ✗
    40: 48 gives 42:48 when January gains 2 marbles - this simplifies to 7:8 ✓

    Again, nosotros tin larn at that spot to a greater extent than rapidly if nosotros mean value most multiples. We start amongst a multiple of xi in addition to terminate amongst a multiple of 15, but nosotros gained ii marbles along the way. So nosotros tin listing all multiples of xi in addition to all multiples of xv in addition to discovery a duo which are ii apart.

    11, 22, 33, 44, 55, 66, 77, 88
    15, 30, 45, 60, 75, 90
    So nosotros started amongst 88 marbles.

    Not all tricky ratio questions are inwards the cast of these 'ratio change' problems. We also straight off larn GCSE questions similar this:


    If the ratio a:b is 4:7, write a inwards price of b



    Though this may seem obvious to many of us (a is the smaller of the two, thus a is 4 sevenths of b), writing the ratios every bit equivalent fractions tin attention students larn their numbers the correct means circular (providing they are confident inwards rearranging equations).

    Another type of enquiry is this:

    If the ratio a:b is 2:5 in addition to the ratio b:c is 3:10, what is the ratio a:c?



    Again, fractions mightiness help.

    Influenza A virus subtype H5N1 quicker option is scaling here. We tin write a:b:c every bit i ratio if nosotros larn the b parts to match.

    a: b tin survive written every bit 6:15
    b:c tin survive written every bit 15:50
    So a:b:c is 6:15:50
    This shows that the ratio a:c is 6:50, which simplifies to 3:25


    And here's some other type of question:


    Punch is made my mixing orangish juice in addition to cranberry juice inwards the ratio 7:2. Mark has xxx litres of orangish juice in addition to 8 litres of cranberry juice. What is the maximum amount of punch that Mark tin make?

    Again, I mean value that scaling is likely the quickest approach here. Multiplying the punch ratio yesteryear 4 gives us 28:8. This is the most punch nosotros tin brand because we're using all the cranberry juice. So inwards full we're making 36 litres of punch.

    In summary, at that spot are a diversity of approaches for solving trickier ratio problems - most tin survive solved efficiently using algebra, scaling or bar modelling. If you're educational activity this topic for the showtime fourth dimension at GCSE it's worth spending some fourth dimension looking at the diverse methods. I mean value our students volition demand a lot of practise of numerous dissimilar types of ratio enquiry to gear upwards for their GCSE.


    Resources
    I've created a lesson to accompany this postal service - download it from TES here.

    Here are some other resources that you lot mightiness discovery helpful:
    There are loads to a greater extent than ratio resources inwards my number resources library.

    I promise this postal service volition survive helpful when you lot instruct ratio at GCSE. Do tweet me to permit me know what methods you lot purpose if I haven't mentioned them here.




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