Lesson 8Lesson 8

Gears and RatiosGears and RatiosClick below for animationClick below for animation

http://www.dynamicscience.com.au/tester/solutions/hydraulicus/gears1.htm

Activity 1 Activity 1 GearsGears

10 minutes

First pairFirst pair

Question 1 Question 1 How many times do you have to turn the How many times do you have to turn the

small wheel to make the large one turn small wheel to make the large one turn twicetwice??

1. Small wheel turns ............. 1. Small wheel turns ............. (big wheel turns twice)(big wheel turns twice)

Question 2Question 2 Without doing it, work out how many times Without doing it, work out how many times

the small wheel would turn if you turned the small wheel would turn if you turned the large one once.the large one once.

2. Guess small wheel turns ............. 2. Guess small wheel turns ............. when big wheelturns oncewhen big wheelturns once

Question 3Question 3

3 Real answer is .............

Question 4Question 4

4 Ratio is .......... (big wheel : small 4 Ratio is .......... (big wheel : small wheel)wheel)

Question 5Question 5

5 Turn big wheel 20 times in a 5 Turn big wheel 20 times in a minute and the small wheel’s speed minute and the small wheel’s speed is .............is .............

Second pairSecond pair1 Small wheel turns ............. (big 1 Small wheel turns ............. (big

wheel turns twice)wheel turns twice)2 Guess small wheel turns ............. 2 Guess small wheel turns .............

when big wheel turns oncewhen big wheel turns once3 Real answer is .............3 Real answer is .............4 Ratio is ............. (big wheel : small 4 Ratio is ............. (big wheel : small

wheel)wheel)5 Turn big wheel 20 times in a minute 5 Turn big wheel 20 times in a minute

and the small wheel’s speed is .............and the small wheel’s speed is .............

Activity 2 Activity 2 Scale drawingScale drawingWho likes drawing? I need 2 Who likes drawing? I need 2

volunteers.volunteers.

Could you draw a mouse on the Could you draw a mouse on the board for me?board for me?

Could you draw an elephant. Next to Could you draw an elephant. Next to the mouse. the mouse. You have 3 minutes.

The elephant.The elephant. Is the drawing of the elephant bigger Is the drawing of the elephant bigger

or smaller than a real elephant?or smaller than a real elephant?

Why did the artists draw it this way?Why did the artists draw it this way?

How much smaller is the drawing How much smaller is the drawing than a real elephant?than a real elephant?

The mouse.The mouse. Is the drawing of the mouse bigger or Is the drawing of the mouse bigger or

smaller than a real elephant?smaller than a real elephant?

Why did the artists draw it this way?Why did the artists draw it this way?

How much bigger is the drawing than How much bigger is the drawing than a real mouse?a real mouse?

Activity 2 Activity 2 Scale drawingScale drawingAre the drawings ‘to scale’? Are the drawings ‘to scale’?

Are they both to the same scale?Are they both to the same scale?

Human EmbryosHuman Embryos

6 weeks old life size 12mm

3 months old. Life size 45mm

Human EmbryosHuman EmbryosNone of them are drawn ‘life size’. None of them are drawn ‘life size’.

Why not?Why not?

Which drawings have been scaled up Which drawings have been scaled up (made larger than life)?(made larger than life)?

Which drawings have been scaled Which drawings have been scaled down (made smaller than life)?down (made smaller than life)?

We can say more about how each of We can say more about how each of the drawings has been scaled up or the drawings has been scaled up or down if we take some down if we take some measurements.measurements.

Age of Age of embryoembryo

Drawing Drawing size (mm)size (mm)

Real size Real size (mm)(mm)

Ratio of Ratio of drawing : drawing : realreal

ScaleScale

6 weeks

3 months

9 months

Age of Age of embryoembryo

Drawing Drawing size (mm)size (mm)

Real size Real size (mm)(mm)

Ratio of Ratio of drawing : drawing : realreal

ScaleScale

6060

135135

9090

1212

4545

360360

5:15:1

3:13:1

1:41:4

x5x5

x3x3

x1/4x1/4

6 weeks

3 months

9 months

Work with the other people in your Work with the other people in your group to complete these sentences:group to complete these sentences:

When we draw a picture or a map When we draw a picture or a map to to scale scale we would do it by .............we would do it by .............

The word ratio means .............The word ratio means .............

It is useful to be able to work out It is useful to be able to work out scales and ratios because .............scales and ratios because .............

More thinking aboutMore thinking about

Gears and RatiosGears and Ratios

Work as a group doing the questions Work as a group doing the questions on “more thinking about gears and on “more thinking about gears and ratios.ratios.

Barbie DollBarbie Doll

Mattel manufactured the first Barbie Doll in 1959. She was 11 1/2 inches tall and was designed with the very distinctive shapely body.

Song

Barbie Doll Barbie Doll How long are her legs in relation to her How long are her legs in relation to her

height?height?Legs (Heel to Hip) ______ cmLegs (Heel to Hip) ______ cm

Height (Heel to Top of Head) ______ cmHeight (Heel to Top of Head) ______ cm

What is the doll ratio? ____ to ____What is the doll ratio? ____ to ____

Barbie Doll Barbie Doll How long are her legs in relation to How long are her legs in relation to

her height?her height?Legs (Heel to Hip) 15 cmLegs (Heel to Hip) 15 cm

Height (Heel to Top of Head) 30 cmHeight (Heel to Top of Head) 30 cm

What is the doll ratio? 1 to 2What is the doll ratio? 1 to 2

Real PeopleReal PeopleHow long are your legs in relation to How long are your legs in relation to

your height?your height?Legs (Heel to Hip) ______ cmLegs (Heel to Hip) ______ cm

Height (Heel to Top of Head) ______ cmHeight (Heel to Top of Head) ______ cm

What is the real ratio? ____ to ____What is the real ratio? ____ to ____

Whose legs are too long?Whose legs are too long?

Give an example where you need to Give an example where you need to think about scales or ratios outside think about scales or ratios outside school.school.