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Ratio simplification and proportion levels 4-5 lesson

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Ratio simplification and proportion levels 4-5 lesson
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Enterprise Skills
LESSON OBJECTIVES
Always aim
high!
We are learning to:
- Enhance our Mathematical learning skills.
(Which Enterprise skills?)
- Accurately simplify ratio and calculate proportions.
(Levels 4-5)
Where are we in
our journey?
AUTHOR
www.mistrymaths.co.uk
Real life
cross/curricular
links?
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EXAMPLE
DITDIONA can be rearranged to make ADDITION
TASK
Work out the following Mathematical anagrams:
PIMYLSIF
Simplify
ORAIT
Ratio
NIROOPPORT
Proportion
EXTENSION
Develop your own Mathematical anagrams as above as a
creative entrepreneur.
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TASK
1) Write 0.72
Independent
Learner
STARTER
as a fraction:
72 18
=
100 25
2) Write 12
25 as a decimal and percentage
= 0.48
= 48%
following:
3)WorkX 2out the
X3
(a) 2 + 1
6 X2 4
4
12
=
+
3
12
X3
(b) 3 X 2
4
8
=
6
32
7
3
=
12
16
4) Work out the following:
x
48 hours
x
3
4
of 2days
of £42 (b)
8
7
=
÷
=
£24
÷
=
18 hours
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EXTENSION
1) Find the nth term and
100th term of:
-5, 2, 9, 16, …..
+7
+7
+7
7n - 12
100th Term = 7 x 100 - 12
100th Term = 688
2) Use a calculator to write the
following as percentages:
(a) 78 out of 130
78
X 100 = 60%
130
(b) 22 out of 60
22
X 100 = 36.7%
60
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RATIO
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RATIO
Use it when sharing things out.
Use it when comparing one part with another (same units).
Written with a colon between two numbers e.g. 5:2, 3:1, 3:8
EXAMPLES 1
1)
(a) What is the ratio of BMW to Audi?
BMW : Audi
5: 3
(b) What proportion are BMW?
8 cars altogether
BMW =
5
8
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RATIO
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RATIO
Use it when sharing things out.
Use it when comparing one part with another (same units).
Written with a colon between two numbers e.g. 5:2, 3:1, 3:8
EXAMPLES 1
2)
(a) What is the ratio of Samsung to Iphone?
Samsung : Iphone
4: 5
(b) What proportion are Samsung?
9 phones altogether Samsung = 4
9
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RATIO
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RATIO
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Use it when sharing things out.
Use it when comparing one part with another (same units).
Written with a colon between two numbers e.g. 5:2, 3:1, 3:8
EXAMPLES 1
3)
(a) What is the shoe ratio of ladies to mens? (b) What proportion are men’s shoes?
8 shoes altogether
Ladies : Mens
2 ÷2 1
:2
6
=
Men’s
shoes
=
÷2
÷2
÷2 4
8
3: 1
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RATIO
TASK 1 (LEVEL 4) - BINGO
Draw a 3 x 3 grid as shown below:
Place any nine of the below into the grid (repeats forbidden)
4:5
1:2
3:4
5:6
3:1
2:3
2:7
8:1
2:1
5:2
1:9
5:3
1:3
3:4
3:2
10:7
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of bottles to cups:
5:2
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of kindles to books:
2:7
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of ligers to tigons:
4:5
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of samosas to dosas:
10:7
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of Buddhas to Hanumans:
3:4
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of Johnsons to Goves:
1:3
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of Harmoniums to Accordions:
5:3
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of scientific to basic calculators:
8:1
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of gramophones to hi-fis:
3:1
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of commodores to spectrums:
3:2
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of mullets to afros:
1:2
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of Chuck Norris’ to Bruce Lees:
2:3
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of Mr Motivators to Timmy Mallets:
2:1
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of Bananamans to Desperate Dans:
3:4
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TASK 1 (LEVEL 4) - BINGO
Write the ratio of Conservatives to Labour:
5:6
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RATIO
Enterprise Skills
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TASK 2 (LEVEL 4) – MATCHING ACTIVITY
Simplify the ratios and match them with their respective answers:
(a) 6:4 (b) 10:5 (c) 6:8 (d) 8:20 (e) 2:6 (f) 4:6 (g) 20:5 (h) 9:15
(i) 5:5
(j) 3:6 (k) 9:3 (l) 2:10 (o) 3:12 (p) 8:14 (q) 12:15
2:5
3:2
2:1
1:1
4:1
4:5
1:3
1:4
4:7
3:5
1:5
2:3
3:1
3:4
1:2
TASK 3 (LEVEL 4) – SIMPLIFYING RATIO CATCHPHRASE
2:4
5:15
2:5
15:48
5:70
3:9
6:12
12:36
24:60
10:12
9:90
14:70
22:99
120:25
6:6
10:45
3:18
4:17
5:100
9:117
5:65
4:10
6:18
4:15
2:70
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RATIO
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TASK 4 (LEVEL 5)
1)
2:4
2)
6:2
1:2
3:1
2:10
4:3
4:3
8:3
1:5
15:3
8:3
5:1
3:3
3:6
1:2
1:1
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TASK 5 (LEVEL 5) – CARD SORT
Match the picture with it’s respective ratio and proportion.
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TASK 5 (LEVEL 5) – CARD SORT ANSWERS
Match the picture with it’s respective ratio and proportion.
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EXAMPLES 2
(a) A fruit drink is made by mixing lemon squash with water in the ratio 4:5. How
much water needs to be added to 28cl of lemon squash to make the drink?
SQUASH : WATER
x7
: 5
4
?
28cl : 35cl
x7
Therefore, 35cl of water needs to be added to make the drink.
(b) To make Squirrel Grey paint, you need to mix Snow White and Beetle Black
together in a ratio of 3:2. How much Snow White will you need if you’re
using 18 litres of Beetle Black?
WHITE : BLACK
x9
: 2
3
: 18litres
27litres
?
x9
Therefore, 27litres of Snow White needs to be mixed to make Squirrel Grey.
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TASK 6 (LEVEL 5)
EXTENSION 1 (LEVEL 5)
1) In a room, the ratio of men to women is
4:1. If there are 20 men, how many women
are there? 5 women
1) The ratio of male to female spectators at ice
hockey games is 4 : 5. At the Steelers’ last
5625
match, 4500 men watched the match. What
was the total attendance at the game? 10125
2) A teacher always arranged the content of
each of his lessons to Year 10 as ‘teaching’
and ‘practising learnt skills’ in the ratio 2 : 3.
a) If a lesson lasted 35 minutes, how much
teaching would he do? 14 minutes
b) If he decided to teach for 30 minutes, how
long would the lesson be? 75 minutes
3) A ‘good’ children’s book is supposed to
have pictures and text in the ratio 17 : 8. In a
book I have just looked at, the pictures occupy
272 pages.
a) Approximately how many pages of text
should this book have to be deemed a ‘good’
children’s book? 128 pages
b) What percentage of a ‘good’ children’s book
will be text? 32%
2) In a box, the ratio of nails to screws is
5:3. If there are 15 nails, how many screws
are there? 9 screws
3) An alloy consists of copper, zinc and tin
in the ratios 1:3:4. If there is 10g of copper
in the alloy, find the weights of zinc and tin.
30g zinc
40g tin
4) In a shop the ratio of oranges to apples
is 2:5. If there are 60 apples, how many
oranges are there? 24 oranges
5) In a train the ratio of adults to children is
7:2. If there are 126 adults, how many
children are there? 36 children
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EXAMPLES 3
1) The recipe to make stuffed
chicken Parma parcels is
shown below:
QUESTION
Write down the recipe to serve 20 people.
x5
Serves 20
Stuffed chicken Parma parcels
Serves 4
4 chicken legs, skinned and boned
50g dried porcini mushrooms
2 shallots, finely chopped
50g butter
2 garlic cloves, crushed
150g baby spinach
100g mozzarella cheese, grated
250g ricotta cheese
8 slices of Parma ham
3 tbsp olive oil
1 tsp balsamic vinegar
x5
x5
x5
x5
x5
x5
x5
x5
x5
x5
x5
20 chicken legs, skinned and boned
250g dried porcini mushrooms
10 shallots, finely chopped
250g butter
10 garlic cloves, crushed
750g baby spinach
500g mozzarella cheese, grated
1250g ricotta cheese
40 slices of Parma ham
15 tbsp olive oil
5 tsp balsamic vinegar
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EXAMPLE 3
2) The recipe to make
chocolate cake is shown
below:
Chocolate Cake
Serves 2
150ml milk
200ml double cream
2 tbsp cocoa powder
2 tbsp honey
200g couscous
55g butter
3 egg whites
2tbsp caster sugar
÷2
÷2
÷2
÷2
÷2
÷2
÷2
÷2
÷2
QUESTION
Write down the recipe to serve 7 people.
x7
Serve 1
Serves 7
2 is not a factor of 7, so
75ml milk
x7
what
do we do?
100ml double cream
x7
May help to find 1 serving and
1tbsp cocoa powder
x7
7
mutliply by …….
x7
1tbsp honey
100g couscous
x7
x7
27.5g butter
1.5 eggs
x7
1tbsp caster sugar
x7
525ml milk
700ml double cream
7tbsp cocoa powder
7tbsp honey
700g couscous
192.5g butter
10.5 eggs
7tbsp caster sugar
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TASK 7 (LEVEL 5)
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RATIO
1) The recipe to make flapjacks is shown below:
Flapjacks
Serves 10
120g butter
100g dark brown soft sugar
4 tbsp golden syrup
250g rolled oats
40g sultanas or raisins
How much of each ingredient would you need to make flapjacks for:
(a) 30 people? x3
(b) 2 people? ÷5
(c) 9 people? ÷10 x9
360g butter
300g dark brown soft sugar
12 tbsp golden syrup
750g rolled oats
120g sultanas or raisins
24g butter
20g dark brown soft sugar
0.8 tbsp golden syrup
50g rolled oats
8g sultanas or raisins
108g butter
90g dark brown soft sugar
3.6 tbsp golden syrup
225g rolled oats
36g sultanas or raisins
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RATIO
2) The recipe to make tomato soup is shown below:
Tomato Soup
Serves 6
30g butter
1 chopped onion
2 tbsp plain flour
1200ml tomato juice
480ml milk
How much of each ingredient would you need to make flapjacks for:
(a) 24 people? x4
(b) 3 people? ÷2
(c) 7 people? ÷6
120g butter
4 chopped onions
8 tbsp plain flour
4800ml tomato juice
480ml milk
15g butter
0.5 chopped onion
1 tbsp plain flour
600ml tomato juice
240ml milk
x7
35g butter
1.17 chopped onion
2.34 tbsp plain flour
1400ml tomato juice
560ml milk
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RATIO
3) The recipe to make tomato soup is shown below:
Shortbread Biscuits
Serves 6
240g butter, softened
90g caster sugar
0.75 tsp ground allspice
0.5 tsp salt
420g plain flour
How much of each ingredient would you need to make flapjacks for:
(a) 72 people? x12
(b) 2 people? ÷3
(c) 10 people? ÷6
2880g butter, softened
1080g caster sugar
9 tsp ground allspice
6 tsp salt
5040g plain flour
80g butter, softened
30g caster sugar
0.25 tsp ground allspice
0.17 tsp salt
140g plain flour
x10
400g butter, softened
150g caster sugar
1.25 tsp ground all spice
0.83 tsp salt
700g plain flour
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EXTENSION 2 (LEVEL 6)
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1) The knifes and forks are out as you compete on ‘Come Dine With Me’
with strangers for the title of ultimate dinner party host for £1000.
Using the internet or a recipe book, come up with a winning three course
meal that you would like to serve. Work out how much of each ingredient
you would need to feed four people.
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RATIO
MINI-PLENARY ACTIVITY – AFL CARDS
SQUASH : WATER
x7
:
3
21cl :
7
?
x7
A)
56cl
B)
49cl
C)
17cl
D)
42cl
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RATIO
MINI-PLENARY ACTIVITY – AFL CARDS
NAILS : SCREWS
x5
4
20
:
:
5
?
x5
A)
24
B)
20
C)
25
D)
30
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RATIO
MINI-PLENARY ACTIVITY – AFL CARDS
POTS : PANS
x 11
6
66
:
:
10
?
x 11
A)
110
B)
111
C)
1010
D)
100
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RATIO
MINI-PLENARY ACTIVITY – AFL CARDS
BIKES : CARS
x6
3
18
:
:
15
?
x6
A)
30
B)
150
C)
90
D)
60
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RATIO
MINI-PLENARY ACTIVITY – AFL CARDS
A recipe requires 3 eggs for 6 people. How many
eggs would be required for 36 people?
A)
27
B)
16
C)
12
D)
18
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RATIO
MINI-PLENARY ACTIVITY – AFL CARDS
A recipe requires 40g of butter for 8 people. How
much butter would be required for 2 people?
A)
10g
B)
20g
C)
160g
D)
5g
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DISCOVERY
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LINK BACK TO OBJECTIVES
- Accurately simplify ratio and calculate
proportions.
What level
are we
working at?
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RATIO
PLENARY ACTIVITY – EXAM QUESTION
Leah, Chloe and Maya share £400 between them. Leah receives
the smallest amount of £90. The ratio of Leah’s share to Chloe’s
share is 2:3. Work out how much Maya receives.
Total of Chloe and Maya’s share
£400 - £90 = £310
x 45
Leah : Chloe
2:3
90 :135
?
x 45
Leah = £90
Chloe = £135
Maya = £400 - £90 - £135
Maya = £175
(3 marks)
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember simplifying
ratio and calculating proportions. It can be a skill or a reflection, or
something else that might be prominent in your brain.
Where are we
in our
journey?
What level
are we
working at?
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Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
How well do you understand the task?
.
I don’t
understand
I nearly
understand
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I fully
understand
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Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
WWW (What Went Well)
EBI (Even Better If)
On your post it
notes…
Think about how you
can improve your
work.
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