Ratio_n_Proportion_FINAL_PUPILS_F3

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					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

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                                   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
 classes 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:   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
 All answers are correct! But - 3right? sorts of answer.
             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
            Click to check your answer
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
  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!
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
                                                                INSTEAD OF
                                                                 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)
Still not had enough?
       Why not try …
        THE SCHOOL CANTEEN?
         - for FRIENDLY PROBLEMS
                   about
                Money

     THE HISTORY CLASSROOM?
         - for FRIENDLY PROBLEMS
                   about
          Area and Perimeter

     THE SPANISH CLASSROOM?
         For FIENDISH PROBLEMS
                  about
    Money with Area and Perimeter!

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