ratio n proportion final pupils f3

7/16/2019 Ratio n Proportion FINAL PUPILS F3

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Bridging the Gap

Problem-Solving

Pupils’ Version



What Will You Learn ?

Never heard of ratio before?

How exactly do you keep numbers in proportion?

What’s the difference between ratio, proportion and fractions?

If you work through this slideshow,

you will find out that:

• Ratio and proportion are EASY!

• Fractions will make more sense too

• You can work out most of the maths in your head!



How to use this resource

You can control how fast or slow you go using:

FORWARD: OR OR Enter OR Left-hand mouse

BACK: OR OR Back Space

TO START POWERPOINT: F5 OR Slide Show > View Show

TO RETURN TO MENU: Escape



Contents

Slides 5 – 16: Part 1: Ratio, Proportion & Fractions

What is ratio? What is proportion? What’s the connection? Where do fractions fit in?

Slides 17 – 26 Part 2: Simplest Ratios and Proportions

Equivalent ratios. Simplest ratios. Equivalent proportion. Simplest proportions.

Slides 27 – 44 Part 3: Recipes & Proportion

How to scale a recipe for 10 people down to 4 people without disaster.

(TO GO TO LINK, HOLD DOWN CONTROL AND CL ICK ON YOUR CHOICE)



DO’s and DON’Ts

Working ThroughDO go as fast or as slow as you like!

You can use the mouse or arrow keys

to control the speed of the slideshow.

DON’T try to do it all in one go – there’s loads of stuff.

Working Out

You can work a lot of the questions out in your head,

-but keep a pen and paper handy.!

To START, press F5

To STOP, press ESC



First Thoughts …

There’s lots of differences between theclasses in your school –

… Some have more boys than girls

… Less United fans than Rovers fans

… More cat-lovers than dog-lovers

… Less pizza-munchers than chicken-dippers



First Thoughts …

Form 6A has 30 pupils:

10 Rovers fans

20 United fans

Form 6B has 18 pupils:

9 Rovers fans

9 United fansYou’re a Rovers fan.

Which class would you rather be in?

Discuss and take a class vote.



Did You Pick 6A?

6A: 10 + 20 = 30 6B: 9 + 9 = 18

–

Rani, a mad Rovers fan, picked 6A:

“10 is bigger than 9,

so there’s more Rovers fans

in 6A than 6B. Yey!”



Did You Pick 6B?

6A: 10 + 20 = 30 6B: 9 + 9 = 18

- But other red Rovers fans picked 6B:

MARTIN SAYS“I’m not going to 6A - I’d

be outnumbered 2 United

to every 1 Rovers fan!” BECKY SAYS:

“Only one third

of 6A Roversfans. It’s one

half in 6B.

HANNAH SAYS:

“6A only has 10 outof 30 Rovers fans.

That’s 1 out of 3.”

Who is right?

Discuss and take a class vote!

2 to 1

is a ratiothird and half are fractions

1 out of 3 is a

proportion

All answers are correct! But - 3 different sorts of answer.

Which do you prefer? Why?



Recap – 3 Ways to Compare Numbers

Fraction?

Proportion?

Ratio?

Which questionis a … “6A only has 10 outof 30 Rovers fans.That’s 1 out of 3.”

“Only one third of 6ARovers fans.

It’s one half in 6B.”

“I’m not going to 6A.

I’d be outnumbered 2

to every 1.”



What’s the Difference - Summing Up: .

“1 to every 2” is a Ratio “1 Rovers fan to every 2 United fans” “The ratio of Rovers to United fans is 1 to 2”

“The ratio of United to Rovers fans is 2 to 1”

“1 out of 3” is a Proportion “1 out o f every 3 fans is a Rovers fan”

“The proportion of Rover fans is 1 out of 3”

“One third” is a Fraction “One third of all fans are Rovers fans

“1/3 of all fans are Rovers fans”

Ratios comparePART WITH

PART

Proportionscompare PART WITH WHOLE

Fractionscompare PART

WITH WHOLE

using shorthand

such as 1/3

3 different ways to

say the same thing

3 different ways to

compare numbers



So comparing totals isn’t the only way to

look at these numbers…

Form 6A has 30 pupils:

10 Rovers fans

20 United fans

Form 6B has 18 pupils:

9 Rovers fans

9 United fans

…You can compare part with part using RATIO

…You can compare part wi th who le using

PROPORTIONS or FRACTIONS

Eg: 1/3 are Rovers fansEg: 1 out of 3 are Rovers fans

Eg: Rovers : United = 1 to every 2 = 1:2



Ratio, Proportion or Fraction?two out of five

This is a … proportion

two fifths

This is a … fraction

four tenths


four to every ten

This is a … ratioten to every four

This is a … ratiofour out of ten

This is a … proportion4/10

This is a … fraction 4:10

This is a … ratio



Ratio, Proportion or Fraction?

3 United fans to every 2 Rangers fans

This is a … ratio

9 girls out of 10 use soap


3 boys out of 10 use deodorant





3 out of 4 pizza-munchers love olives


Half of all girls in 6D love History


One third of all road accidents involve drinking





3 out of 4 drivers speed at some time


Three quarters of drivers speed


3 drivers speed to every 1 which does not

This is a … ratio



Ratio and Proportion

Ratio and Proportion: Different Words!

Ratio: “to every”

1 Rovers fan to every 2 United fans

Proportion: “out of ”

1 out of 3 football fans is a Rovers fan



PART 2: Simplest Ratios and

Proportions



1 girl to every 2 boys

2 girls to every 4 boys



girls : boys = 4 : 8




But the simplest ratio is still 1 : 2



This is the simplest ratio is 1 : 2

The dinner queue

Ratio of girls

to boys?



2 boys to every 1 girl

4 boys to every 2 girls



boys : girls = 8 : 4







This is the simplest ratio is 2 : 1

Ratio of boys

to girls?

The dinner queue



Simplest ratios

2 : 1 is a simpler ratio than 4 : 2

but

They both mean the same

2 : 1 = 4 : 2

Can you explain why

2 : 1 = 6 : 3 ?

2 : 1 = 8 : 4 ?

2 : 1 = 100 : 50 ?



1 girl out of 3

2 girls out of 6

3 girls out of 9

4 girls out of 12

Simplest proportion of girls

is still 1 out of 3


is still 1 out of 3


is still 1 out of 3

This is the simplest

proportion of girls

= 1 out of 3

The dinner queue

What

proportionis girls?



Proportion of boys?

Simplest proportion of

boys?

Proportion of boys?


boys?

Proportion of boys?


boys?

Proportion of boys?

4 boys out of 6

6 boys out of 9

8 boys out of 12


boys is still 2 out of 3






boys?

This is the simplest proportion of boys

= 2 out of 3

2 boys out of 3

The dinner queue

What

proportionis boys?

What fraction is girls?

4 / 12





girls?


Simplest fraction of girls?


Simplest fraction of girls?


2 / 6

3 / 9

4 / 12

Simplest fraction of girls

is still 1 / 3

Simplest fraction of girls

is still 1 / 3

Simplest fraction of girls is

still 1 / 3

Simplest fraction of girls?This is the simplest

fraction of girls = 1 / 3

1 / 3

The dinner queue

What

fraction isgirls?



What fraction is boys?


boys?


Simplest fraction of

boys?



boys?

4 / 6

6 / 9

8 / 12

Simplest fraction of boys is

still 2 / 3


still 2 / 3


still 2 / 3


boys?

This is the simplest

fraction of boys = 2 / 3

The dinner queue

What

fraction isboys?

What fraction is boys?2 / 3



Does order matter?

There are 20 boys and 10 girls in 6D.

Which of these are correct?

b) girls : boys = 2 : 1

a) boys : girls = 2 : 1

c) boys : girls = 1 : 2

ORDER MATTERS!

Be careful what you write!

Click to check your answer boys : girls = 2 : 1 means 2 boys to every girlgirls : boys = 2 : 1 means 2 girls to every boy



True or Not True?

Ratio of teachers to pupils = 30 : 1

Ratio of fans to players = 1 : 1000

This would mean all the players

would be sitting in the stadium!

Ratio of weekdays to weekend days = 2 : 5

You wish!

Ratio of porridge lovers to pizza guzzlers = 100 : 1

- Not until they invent Porridge Takeaways ..



PART 3: Recipes and Proportion

How to scale a recipe for 10 people down to 4 people

without disaster!



Biscuits and Bananas Skins

Enjoy cooking? Check out these fantastic recipes!

Some of them need changing to suit the number of people,

- But remember to keep them in proportion,

- And watch out for the or else …



+ =

You r omelette tastes amazing! - So o f cou rse your mates start turning up .

Can you scale up you r ingredients to feed them al l?

It’s supper time! You make a simple omelette like this:

? eggs + ? tsp of butter = 2 omelettes




2 eggs + 1 teaspoon of butter = 1 omelette

4 eggs + 2 tsp of butter = 2 omelettes






+ =

… word’s getting around and more mates turn up the next day.

Can you scale up you r ingredients to feed them?

And the next week …

4 eggs + ? tsp of butter = ? omelettes

10 eggs + ? tsp of butter = ? omelettes

? eggs + 10 tsp of butter = ? omelettes

? eggs + 11 tsp of butter = ? omelettes

2 eggs + 1 teaspoon of butter = 1 omelette







STEP 1: CHOOSE the maths!x or ÷ ?

BIGGER AMOUNTS mean X SMALLER AMOUNTS mean ÷

STEP 2: DO the maths! DO THE SAME X or ÷ to ALL ingredients

(This is called ‘keeping it in proportion’)

STEP 3: CHECK the maths!- using ratio !

Eg: If there are 2 eggs to every 1 tsp butter, the‘eggs number’ is ALWAYS twice the ‘butter number’.

RECAPHow did you work these out?

Hungry for more? Try these recipes …

REMEMBER THE 3 STEPS



Recipe for Shortbread Biscuits

Makes 20 shortbread biscuits

Ingredients

200g butter

200g plain flour

100g golden caster sugar

100g fine semolina

Pre-heat the oven to gas mark 2, 300 °F (150 °C).

You will also need an 8 in (20 cm) diameter fluted flan tin,1¼ in (3 cm) deep with a loose base.



10 Mouth-watering Shortbread Biscuits!

+ + + =400g flour

400g

butter

200g

sugar

200g semolina

This is th e recipe for 20 biscu its. Can you scale down th e recipe for 10?

Remember to keep your recipe in prop ort ion – i f you halve the sugar,remember to halve the rest as well or it won’t taste good!

?

+ + + =10

biscuits200g

flour

200g

butter

100g

sugar

100g

semolina

? ? ? ? ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2

STEP 1: Choose the maths!x or ÷ ?

BIGGER means XSMALLER means ÷

STEP 2: Do the maths!DO THE SAME X or ÷ toALL ingredients

STEP 3: CHECK the maths!- using ratio.

Eg: The weight of the butteris always 2 times the weight

of the sugar.

20

biscuits



RECAP3 Steps for ScalingSTEP 1: CHOOSE the maths!

CHOOSE FROM x or ÷

… BIGGER means X … SMALLER means ÷

STEP 2: DO the maths!

DO THE SAME X or ÷ to ALL ingredients


Eg: If the weight of the butter is always 2 timesthe weight of the sugar…



… Nirmal makes 2 shortbread biscuits

+ + + =20

biscuits400g

flour

400g

butter

200g

sugar

200g semolina

Nirmal scaled down the recipe for 2 biscuits, but they don’t taste right!

Did he scale down correctly and keep the recipe in proportion?

?

+ + + =2

biscuits4000 g

flour

4000 g

butter

2000 g

sugar

2000 g

semolina

? ? ? ? x10 x 10 x 10 x 10 x 10

Mistake in STEP 1: Choose the maths!CHOOSE FROM + - x ÷

BIGGER means X SMALLER means ÷ BUT… Nirmal did X 10 instead of ÷ 10

÷ 10 ÷ 10 ÷ 10 ÷ 10

40 g

butter

20 g

sugar

20 g

semolina 40 g flour

WHAT DIFFERENCE

DID THE

MISTAKEMAKE?

200BISCUITS

INSTEAD OF2!

Check his working out

Then click to see if you’re right

20

biscuits

÷ 10




CHOOSE FROM x or ÷








… Liana makes 5 shortbread biscuits

+ + + =20

biscuits400g

flour

400g

butter

200g

sugar

200g semolina

Liana scaled down the recipe for 5 biscuits, but they don’t taste right!

Did she scale down correctly and keep the recipe in proportion?

+ + + =5

biscuits100 g

sugar

? ÷ 2

100 g

butter

50 g

sugar

50 g

semolina 100 g

flour

Check her working out

Then click to see if you’re right

WHAT DIFFERENCE

DID THE

MISTAKEMAKE?

THE

BISCUITS

WERE TOO

SWEET!

÷ 4 ÷ 4

÷ 4

÷ 4 ÷ 4

Mistake in STEP 2: Do the maths!DO THE SAME X or ÷ to ALL ingredients

BUT …Liana did not do ÷ 2 to the sugar.




CHOOSE FROM x or ÷








Serves 8 people

Ingredients300 g raspberries

200 g bananas100 g melon

Method Place ingredients in a juicer and

switch on power for 30 seconds.

Pour and serve with ice or ice-cream.

Further Practical ExamplesRecipe No.1 Melon Merenga

STEP 1: Choose the maths! STEP 3 CHECK th th !



Can you work out the missing amounts?

+ + =600 g 400 g 200 g Melon

Merenga for 8

+ + =? g ? g ? g

Melon

Merenga for 4

+ + =? g ? g ? gMelon

Merenga for 2

+ + =? g ? g ? g

Melon

Merenga for 6

300 g 200 g 100 g

150 g 100 g 50 g

+ + =

450 g 300 g 150 g

Melon

Merenga for 1? g ? g ? g75 g 50 g 25 g


BIGGER means X

SMALLER means ÷ STEP 2: Do the maths!

DO THE SAME X or ÷ toALL ingredients


Eg: The bananas’ weight isALWAYS twice the melons’

weight.

You can work this oufrom the quantitiesfor 1 person, BUT …

Can you see ashortcut?

General Method:1) Work out the

recipe for 1.

2) Multiply by the

number you need

Shortcut:

1) Work out from th

quantities for 2

people.

2) X 3

(easier than X6)

F th P ti l E l



Further Practical ExamplesRecipe No.2 Raspberry Fruitloop

(Same ingredients. Different amounts)

Serves 10 people

Ingredients

500 g raspberries250 g bananas150 g melon

Method Place ingredients in a juicer and switch on power for 30 seconds.

Pour and serve with fresh raspberries

STEP 1: Choose the maths! STEP 3: CHECK the maths!




+ + =500 g 250 g 150 g Raspberry

Fruitloop for 10

+ + =? g ? g ? g

Raspberry

Fruitloop for 5

+ + =? g ? g ? gRaspberry

Fruitloop for 1

+ + =? g ? g ? g

Raspberry

Fruitloop for 8

250 g 125 g 75 g

50 g 25 g 15 g

+ + =

400 g 200 g 120 g

Raspberry

Fruitloop for 4? g ? g ? g200 g 100 g 60 g


BIGGER means X




Eg: The raspberries’ weightis ALWAYS twice the melons’

weight.


Can you see anyshortcuts?

General Method:1) Work out the

recipe for 1.2) Multiply by the

number you nee

Shortcut: 1) Work out from

the quantitiesfor 4 people.

2) Just double it!(Easier than X8

Further Practical Examples



Further Practical ExamplesRecipe No.3 Bombastic Banana Boat

(Same ingredients. Different amounts)

Serves 12 people

Ingredients120 g raspberries600 g bananas120 g melon

Method Place ingredients in a juicer and

switch on power for 30 seconds.

Pour into a scooped out melon half . Servewith fresh raspberries

STEP 1: Choose the maths! STEP 3: CHECK the maths!




+ + =120 g 600 g 120 g Banana Boat

for 12

+ + =? g ? g ? g

Banana Boat

for 6

+ + =? g ? g ? gBanana Boat

for 4

+ + =? g ? g ? g

Banana Boat

for 8

60 g 300 g 60 g

40 g 200 g 40 g

+ + =

80 g 400 g 80 g

Banana Boat

for 1? g ? g ? g10 g 50 g 10 g


BIGGER means X




Can you see ashortcut?


Eg: The weight of bananas isalways 5 times the weight of

the melon.

General Method:

1) Work out the

recipe for 1.

2) Multiply by the

number you nee

Shortcut:

1) Work out from

the quantities

for 4 people.

2) Just double it!

(Easier than X8)

ll h d h



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ratio n proportion final pupils f3

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