# Ratio_n_Proportion_FINAL_PUPILS_F3

Document Sample

```					Problem-Solving
Pupils’ Version
Bridging the Gap
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:

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TO START POWERPOINT: F5       OR    Slide Show > View Show

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 CLICK ON YOUR CHOICE)
DO’s and DON’Ts
Working Through
DO 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 the

… 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:   Form 6B has 18 pupils:

10 Rovers fans           9 Rovers fans
20 United fans           9 United fans
You’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
2 to fans picked 6B:
- But other red Rovers 1
third and half      is a ratio MARTIN SAYS                 1 out of 3
are fractions                                                is a
“I’m not going to 6A - I’d
be outnumbered 2 United         proportion
to every 1 Rovers fan!”
BECKY SAYS:
“Only one third                               HANNAH SAYS:
of 6A Rovers                               “6A only has 10 out
fans. It’s one                              of 30 Rovers fans.
half in 6B.                               That’s 1 out of 3.”

Who is different
Discuss and take a class vote!
Which do you prefer? Why?
Recap – 3 Ways to Compare Numbers
Which question
“6A only has 10 out           is a …
of 30 Rovers fans.
That’s 1 out of 3.”           Fraction?

“I’m not going to 6A.         Ratio?
I’d be outnumbered 2
to every 1.”
Proportion?
“Only one third of 6A
Rovers fans.
It’s one half in 6B.”
What’s the Difference - Summing Up: .
3 different ways to    3 different ways to
say the same thing     compare numbers
Ratios compare
“1 to every 2” is a Ratio                         PART WITH
“1 Rovers fan to every 2 United fans”                 PART
“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                      Proportions
“1 out of every 3 fans is a Rovers fan”          compare PART
“The proportion of Rover fans is 1 out of 3”     WITH WHOLE

Fractions
“One third” is a Fraction                         compare PART
“One third of all fans are Rovers fans            WITH WHOLE
“1/3 of all fans are Rovers fans”                using shorthand
such as 1/3
So comparing totals isn’t the only way to
look at these numbers…
Form 6A has 30 pupils:        Form 6B has 18 pupils:
10 Rovers fans                9 Rovers fans
20 United fans                9 United fans

…You can compare part with part using RATIO
Eg: Rovers : United = 1 to every 2 = 1:2

…You can compare part with whole using
PROPORTIONS            or FRACTIONS
Eg: 1 out of 3 are Rovers fans Eg: 1/3 are Rovers fans
Ratio, Proportion or Fraction?
two out of five               two fifths
This is a … proportion This is a … fraction
four tenths
four to every ten
This is a … fraction
ten to every four    This is a … ratio
four out of ten
This is a … ratio
4/10        This is a … proportion

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
This is a … proportion

3 boys out of 10 use deodorant
This is a … proportion
Ratio, Proportion or Fraction?
3 out of 4 pizza-munchers love olives

This is a … proportion

Half of all girls in 6D love History

This is a … fraction

One third of all road accidents involve drinking

This is a … fraction
Ratio, Proportion or Fraction?
3 out of 4 drivers speed at some time
This is a … proportion

Three quarters of drivers speed
This is a … fraction

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
4 girls to every 8 boys
The dinner queue
girls : boys = 4 : 8
Ratio of girls
But the simplest ratio is still 1 : 2
to boys?
3 girls to every 6 boys

girls : boys = 3 : 6

But the simplest ratio is still 1 : 2

2 girls to every 4 boys

girls : boys = 2 : 4

But the simplest ratio is still 1 : 2

1 girl to every 2 boys

girls : boys = 1 : 2

This is the simplest ratio is 1 : 2
8 boys to every 4 girls
The dinner queue
boys : girls = 8 : 4
Ratio of boys
But the simplest ratio is still 2 : 1
to girls?
6 boys to every 3 girls

boys : girls = 6 : 3

But the simplest ratio is still 2 : 1

4 boys to every 2 girls

boys : girls = 4 : 2

But the simplest ratio is still 2 : 1

2 boys to every 1 girl

boys : girls = 2 : 1

This is the simplest ratio is 2 : 1
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 ?
The dinner queue                            4 girls out of 12

Simplest proportion of girls
What                                  is still 1 out of 3

proportion                       3 girls out of 9

is girls?            Simplest proportion of girls
is still 1 out of 3

2 girls out of 6

Simplest proportion of girls
is still 1 out of 3

1 girl out of 3

This is the simplest
proportion of girls
= 1 out of 3
The dinner queue                           8 boys out boys?
Proportion of of 12

Simplest proportion of
Simplest proportion of
What                                         boys?
boys is still 2 out of 3

proportion                     6 boys out of 9
Proportion of boys?

is boys?                  Simplest proportion of
Simplest proportion of
boys is still 2 out of 3
boys?

4 boys out of 6
Proportion of boys?

Simplest proportion of
Simplest proportion of
boys is still 2 out of 3
boys?

Proportion of boys?
2 boys out of 3

Simplest proportion of
boys?
This is the simplest
proportion of boys
= 2 out of 3
What fraction is girls?
4 / 12
The dinner queue
Simplest proportion girls
Simplest fraction of of
is still 1 / 3
girls?
What
fraction is                            3 9
What fraction /is girls?

girls?                      Simplest fraction girls?
Simplestfraction ofof girls
is still 1 / 3
2 6
What fraction /is girls?
Simplest fraction of girls is
Simplest fraction of girls?
still 1 / 3

1 3
What fraction /is girls?

This is the simplest
Simplest fraction of girls?
fraction of girls = 1 / 3
The dinner queue                       What fraction is boys?
8 / 12

Simplest proportion of
Simplest fraction of boys is
What                                             boys?
still 2 / 3

fraction is                           6 9
What fraction /is boys?

boys?                      Simplest fraction of boys is
Simplest fraction of
still 2 / 3
boys?

4 6
What fraction /is boys?

Simplest fraction of boys is
Simplest fraction of
still 2 / 3
boys?

2 3
What fraction /is boys?

Simplest fraction of
This is the simplest
boys?
fraction of 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
boys : girls = 2 : 1 means 2 boys to every girl
girls : boys = 2 : 1 means 2 girls to every boy
ORDER MATTERS!
Be careful what you write!
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 …
It’s supper time! You make a simple omelette like this:

+                           =

2 eggs        +        1 teaspoon of butter = 1 omelette
Your omelette tastes amazing! - So of course your mates start turning up.
Can you scale up your ingredients to feed them all?

4 eggs
?             +        2 tsp of butter = 2 omelettes
?

?
6 eggs        +        ?
3 tsp of butter = 3 omelettes

?
8 eggs        +        ?
4 tsp of butter = 4 omelettes

? eggs
10 eggs       ++       ?
5 tsp of butter = 5 omelettes
And the next week …

+                         =

2 eggs      +         1 teaspoon of butter = 1 omelette
… word’s getting around and more mates turn up the next day.
Can you scale up your ingredients to feed them?

4 eggs      +         ?                 ?
2 tsp of butter = 2 omelettes
10 eggs       +       ?                 ?
5 tsp of butter = 5 omelettes
? eggs
20 eggs         10 tsp of butter = ? omelettes
++ 10 tsp of butter = 10 omelettes

? eggs
22 eggs     + 11 tsp of butter = ? omelettes
+ 11 tsp of butter = 11 omelettes
STEP 1: CHOOSE the maths!
RECAP
x you ?
How did or ÷work these out?
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’.

Hungry for more? Try these recipes …
REMEMBER THE 3 STEPS
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.
STEP is the recipemaths!
This 1: Choose the for 20                            STEP 3: recipe for 10?
biscuits. Can you scale down theCHECK the maths!
x or ÷ ?                                       - using ratio.
BIGGER means X                              Eg: The weight of the butter
STEP 2: Do the maths! – if you halve the sugar,
Remember to keep your recipe in proportion is always 2 times the weight
SMALLER means ÷ halve the rest asX or ÷or it won’t tastethe sugar.
remember to     DO THE SAME well to                of good!
ALL ingredients
20
400g       + 400g          + 200g        +    200g       =
flour        butter           sugar        semolina          biscuits

÷?2            ÷?2             ÷?2           ÷?
2                ÷?2

10
200g       + 200g          + 100g        +    100g       =
flour         butter          sugar        semolina
biscuits
STEP 1: CHOOSE the maths!
3 Steps for Scaling
CHOOSE FROM x or ÷
RECAP BIGGER means X
…
… SMALLER means ÷

STEP 2: DO the maths!

DO THE SAME X or ÷ to ALL ingredients

STEP 3: CHECK the maths!
- using ratio.
Eg: If the weight of the butter is always 2 times
the weight of the sugar…
… Nirmal makes 2 shortbread biscuits
Mistake in STEP 1: Choose the maths!
Nirmal               Check x ÷
CHOOSE FROM + - his for 2 biscuits,
scaled down the recipe working out but       they don’t taste right!
BIGGER means X        SMALLER means ÷
Did     BUT… Nirmal did X 10 instead of ÷ 10
he scale down correctly and keep the     recipe in proportion?
Then click to see if you’re right
20
20
400g         + 400g        + 200g        +    200g          =
flour                         sugar        semolina
biscuits
biscuits
butter

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

20 g                                        2
WHAT
40 g
4000 g       + 4000 g + 2000 g + 2000 g
40 g              20 g                      =       200
DIFFERENCE
flour           butter        sugar        semolina
biscuits
BISCUITS
DID THE
MISTAKE
2!
MAKE?
STEP 1: CHOOSE the maths!
3 Steps for Scaling
CHOOSE FROM x or ÷
RECAP BIGGER means X
…
… SMALLER means ÷

STEP 2: DO the maths!

DO THE SAME X or ÷ to ALL ingredients

STEP 3: CHECK the maths!
- using ratio.
Eg: If the weight of the butter is always 2 times
the weight of the sugar…
… Liana makes 5 shortbread biscuits
Check her Do biscuits,
Liana scaled down the recipe2:working outbut they don’t taste right!
Mistake in STEP for 5the maths!
DO THE SAME X or ÷ to ALL ingredients
BUT …Liana did not do ÷ 2 to the sugar.
Then click to see if keep the recipe
Did she scale down correctly and you’re right in proportion?

20
400g     + 400g        + 200g          +     200g         =
flour        butter          sugar         semolina           biscuits

÷4
÷4            ÷4              ÷2                ÷4             ÷4
?

50 g                  5
WHAT
100 g    + 100 g          50 g
+ 100g          +                  =       THE
DIFFERENCE
flour        butter          sugar         semolina
biscuits
BISCUITS
DID THE
WERE TOO
MISTAKE
SWEET!
MAKE?
STEP 1: CHOOSE the maths!
3 Steps for Scaling
CHOOSE FROM x or ÷
RECAP BIGGER means X
…
… SMALLER means ÷

STEP 2: DO the maths!

DO THE SAME X or ÷ to ALL ingredients

STEP 3: CHECK the maths!
- using ratio.
Eg: If the weight of the butter is always 2 times
the weight of the sugar…
Further Practical Examples
Recipe No.1 Melon Merenga
Serves 8 people

Ingredients
300 g raspberries
200 g bananas
100 g melon
Method
Place ingredients in a juicer and
switch on power for 30 seconds.

Pour and serve with ice or ice-cream.
STEP 1: Choose the maths!                             STEP 3: CHECK the maths!
x or ÷ ?                                            - using ratio.
BIGGER means X
Can you work outSTEP 2:missing amounts?
the Do the maths!                  Eg: The bananas’ weight is
SMALLER means   ÷        DO THE SAME X or ÷ to     ALWAYS twice the melons’
ALL ingredients                    weight.

Melon
600 g +         400 g +         200 g    =   Merenga for 8

Melon
300 g g + 200 g g + 100 g g =
?         ?         ?                        Merenga for 4   General Method:
1) Work out the
recipe for 1.
Melon      2) Multiply by the
? g g + 100 g g +
150      ?                      ? g
50 g      =   Merenga for 2    number you need

Melon            Shortcut:
75 gg +
?              ? g
50 g        + 25 g
? g         =                 You can work this out
Merenga for 1 1) Work out from the
from the quantities
quantities BUT
for 1 person,for 2 …
Can you
people. see a
Melon      2) X 3shortcut?
450 g g + 300 gg + 150 gg
?         ?        ?                     =   Merenga for 6   (easier than X6)
Further Practical Examples
Recipe No.2 Raspberry Fruitloop
(Same ingredients. Different amounts)

Serves 10 people

Ingredients
500 g raspberries
250 g bananas
150 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!
x or ÷ ?                                              - using ratio.
BIGGER means X
Can you work outSTEP 2:missing amounts?
the Do the maths!                   Eg: The raspberries’ weight
SMALLER means   ÷        DO THE SAME X or ÷ to     is ALWAYS twice the melons’
ALL ingredients                      weight.

Raspberry
500 g +         250 g +         150 g    =   Fruitloop for 10

Raspberry
250gg +
?              125gg
?           +    ? g
75 g     =   Fruitloop for 5 General Method:
1) Work out the
recipe for 1.
Raspberry     2) Multiply by the
? 50 g
g       +     ? g
25         +    ? g
15       =   Fruitloop for 1    number you need

Shortcut:
? gg +                     +             =     Raspberry
You can out from
1) Workwork this out
200            ?
100gg            ? g
60 g                            the quantities
Fruitloop for 4 from the quantities
for 4 people.
for 1 person, BUT …
Can you see any
2) Just double it!
Raspberry           shortcuts?
? gg +
400            ?
200gg       +   120gg
?         =                      (Easier than X8)
Fruitloop for 8
Further Practical Examples
Recipe No.3 Bombastic Banana Boat
(Same ingredients. Different amounts)

Serves 12 people

Ingredients
120 g raspberries
600 g bananas
120 g melon
Method
Place ingredients in a juicer and
switch on power for 30 seconds.

Pour into a scooped out melon half . Serve
with fresh raspberries
STEP 1: Choose the maths!                            STEP 3: CHECK the maths!
x or ÷ ?                                           - using ratio.
BIGGER means X
Can you work outSTEP 2:missing amounts?
the Do the maths!                Eg: The weight of bananas is
SMALLER means   ÷        DO THE SAME X or ÷ to   always 5 times the weight of
ALL ingredients                  the melon.

Banana Boat
120 g +         600 g +         120 g    =      for 12

Banana Boat
? g
60 g      +    ? g
300g        +    ? g
60 g     =      for 6
General Method:
1) Work out the
Banana Boat         recipe for 1.
g
?40 g      +    200g
? g         +    ? g
40 g     =      for 4        2) Multiply by the
number you need

Banana Boat         Shortcut:
? g
10 g      +     ? g
50 g       +    ? g
10 g     =                  You can work this out
for 1         1) Work out from
from the quantities
for 1the quantities…
person, BUT
for 4 see a
Can youpeople.
Banana Boat           shortcut?
2) Just double it!
? g
80 g      + 400g
? g            +    ? g
80 g     =      for 8          (Easier than X8)
Why not try …
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