Ratio of objects 3-Oct-15 Calculate ratios from a real life situation Level 6+ D+
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Transcript of Ratio of objects 3-Oct-15 Calculate ratios from a real life situation Level 6+ D+
Ratio of objects 19 Apr 2023
Calculate ratios from a real life
situation
Calculate ratios from a real life
situation
Level 6+ D+
STARTER
The string of beads contains 6 red and 12 black beads. This can be written as a ratio
RED : BLACK6 : 12
By dividing both numbers by 6, the ratio can be written in a way that tells you that there are twice as many black
beads
Red : Black1 : 2
6 ÷ 6 = 16 ÷ 6 = 1 12 ÷ 6 = 2
12 ÷ 6 = 2
2 cm
5 cm
This can be done to any ratio. The rectangle has a width of 2 cm and a height of 5 cm so the ratio of width to height is
W : H
2 : 5
1 : 2.52 ÷ 2 =
12 ÷ 2 =
15 ÷ 2 =
2.55 ÷ 2 =
2.5
This rectangle is 2.5 times
higher than its width
This rectangle is 2.5 times
higher than its width
1.8 cm
5.8 cm
This rectangle has a width of 1.8 cm and a height of 5.8 cm so the ratio of width to height is
W : H
1.8 : 5.8
1 : 3.22 (to 2 dp)
1.8 ÷ 1.8 = 1
1.8 ÷ 1.8 = 1
5.8 ÷ 1.8 = 3.22…
5.8 ÷ 1.8 = 3.22…
This rectangle is 3.22 times higher than its
width
This rectangle is 3.22 times higher than its
width
4 cm
8 cm
W : H
4 : 8
1 : 2
8 ÷ 4 = 2
8 ÷ 4 = 2
3 cm
12 cm
W : H
3 : 12
1 : 4
This rectangle is 2 times higher than
its width
This rectangle is 2 times higher than
its width
12 ÷ 3 = 4
12 ÷ 3 = 4
This rectangle is 4 times higher than
its width
This rectangle is 4 times higher than
its width
How many times higher than the width?
1.2 cm
6.6 cm
W : H
1.2 : 6.6
1 : 5.5
6.6 ÷ 1.2 = 5.5
6.6 ÷ 1.2 = 5.5
0.9cm
7.2 cm
W : H
0.9 : 7.2
1 : 6
This rectangle is 5.5 times higher than its width
This rectangle is 5.5 times higher than its width
7.2 ÷ 0.9 = 8
7.2 ÷ 0.9 = 8
This rectangle is 8 times higher than
its width
This rectangle is 8 times higher than
its width
How many times higher than the width?
2.7 cm
5.2 cm
W : H
2.7 : 5.2
1 : 1.93
5.2 ÷ 2.7 = 1.925…
5.2 ÷ 2.7 = 1.925…
1.2 cm
6.5 cm
W : H
1.2 : 6.5
1 : 5.42
This rectangle is 1.93 (to 2dp) times
higher than its width
This rectangle is 1.93 (to 2dp) times
higher than its width
6.5 ÷ 1.2 = 5.4166…
6.5 ÷ 1.2 = 5.4166…
This rectangle is 5.42 (to 2 dp)
times higher than its width
This rectangle is 5.42 (to 2 dp)
times higher than its width
How many times higher than the width?
Do You Look Like a Greek God or Goddess?
The Greeks believed that the ratio 1 : 1.62 was attractive. The 1.62 is an approximation for something called the Golden Ratio.
12 cm
19.4 cm
W : H
12 : 19.4
1 : 1.62
This rectangle is 1.62 (to 2dp) times
higher than its width
This rectangle is 1.62 (to 2dp) times
higher than its width
Everyday Objects
Object Length Width Ratio
Textbook
Passport
Whiteboard
Computer
Building Brick
Door Frame
Extension
• What else can you find that will have this same ratio?
• Go around the room and see what you can find that has a ratio of 1 : 1.618 ( or as close to it as you can get)
Ratio of objects 19 Apr 2023
Be able to construct a
spiral
Be able to construct a
spiral
Level 6+ D+
Creating the golden spiral.
Construct a 1cm square, It should be about 7cm from the bottom of the page
7cm
1cm
This square represents the square that you have just constructed.
Creating the golden spiral
1 : 1What is the width : length ratio of the square?
Extend the top edge of the square 1cm to the left and draw the arc with centre at the top left-hand corner of the square and radius 1cm.
Creating the golden spiral
Extend the bottom edge of the square 1cm to the left and then complete the rectangle.
Creating the golden spiral
What is the width : length ratio of the rectangle? 2 : 1
Use these diagrams to complete the next steps of the construction.
Creating the golden spiral
2 : 3What is the width : length ratio of the new rectangle?
The last two diagrams show the next stage in the process. Describe it and then construct the new rectangle.
Creating the golden spiral
3 : 5What is the width : length ratio of this new rectangle?
Describe exactly how this process of creating new rectangles works.
Creating the golden spiral
The longer side of each rectangle is rotated 90° clockwise about a corner to form an extension to the shorter side. Together with the shorter side, this makes the longer side of a new rectangle. The corner used as centre of rotation is the next corner clockwise each time.
Constructing a spiral
• Continue with this pattern until the spiral no longer fits onto your page.
• How large does it get?
• What do you notice about the lengths of the sides?
Plenary
The spiral formed by the quarter-circle arcs is called the golden spiral.
Why is this an appropriate name for the spiral? As more rectangles are created, the ratio of width : length of the rectangles approaches 1 : Ø.)
Ratio of Gods and Goddesses
19 Apr 2023
Calculate ratios from a real life situation to find out if you are a Greek god or
goddess?
Calculate ratios from a real life situation to find out if you are a Greek god or
goddess?
Level 6+ D+
The Greek goddess called ‘Dike’ later became the Roman god with the name of ‘Justice’. Where have you seen her?
Video on Golden Ratio
Video on Golden Ratio 2
The Greeks also believed that their gods would have features that are in the ratio 1 : 1.62.
Working with a partner, measure and calculate the ratio of your features by following the instructions on the next three slides.
1
1.62
Width of head (w)
Top of the head to the chin (h)
Start by measuring the distance from the top of your head to the chin (h) and then the width of your head (w).
Now divide h by w and write down your answer.
h ÷ w = (Your Answer)
If your answer is near to 1.62, you are the shape of a Greek God/Goddess!
Pupils to where the lips meet (m)
Top of the head to the pupils (p)
Measure p and m then divide p by mand write down your answer.
p ÷ m = Answer
If your answer is near to 1.62, you are the shape of a Greek God/Goddess!
Write down the two numbers that you have found so far and calculate the mean average
m
p
h
w
n
f
ue
Now that you have the idea, measure these features and then divide. Find the mean average of all your answers
h ÷ w =
p ÷ m =
c ÷ s =
e ÷ f =
u ÷ n =
c
s
Measurements• a = Top-of-head to chin = ………cm• b = Top-of-head to pupil = ……… cm• c = Pupil to nosetip = ……… cm• d = Pupil to lip = ……… cm• e = Width of nose = ……… cm• f = Outside distance between eyes = ……… cm• g = Width of head = ……… cm• h = Hairline to pupil = ……… cm• i = Nosetip to chin = ……… cm• j = Lips to chin = ……… cm• k = Length of lips = ……… cm• l = Nosetip to lips = ……… cm
Ratios
• Now, find the following ratios:• a/g = ……… cm• b/d = ……… cm• i/j = ……… cm• i/c = ……… cm• e/l = ……… cm• f/h = ……… cm• k/e = ……… cm
Investigation
Find pictures of four people that are considered to be attractive.
Measure their features on the photograph and see which is the nearest to a Greek God or Goddess.
Put the four people into rank order and then do a survey to see if your people’s opinions are the same as the your ratio results.
Find out more about the Golden Ratio
A student in my class did the Greek Goddess test on a picture of Cheryl Cole and discovered that she fitted the ratio. Try it.