Ratio and Proportion Lesson for Geometry

7/27/2019 Ratio and Proportion Lesson for Geometry

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Geometry Name:_______________

Lesson 34 Date:_________

Ratio, Proportion and Triangle Midsegments Class Work

Do Now:

(1) Which pair of numbers is out of place? Explain why you chose that pair.

(a) 3 and 4

(b) 5 and 6

(c) 9 and 12

(d) 27 and 36

(2) Which pair of numbers is out of place? Explain why you chose that pair.

(a) 9 and 12

(b) 12 and 15

(c) 20 and 25

(d) 32 and 40

(3) You got a part-time job at The Pizza Hub. You just found out that your co-worker makes more

money. Which statement would make you angrier? Why?

(a) Your coworker makes $10 more than you.

(b) Your coworker makes double what you make.

Ratio and Proportion:

Exercise 1: Definitions

(1) You’ve heard these two words before. Give me what you know- a definition, an example, a picture.

(2) Consider the table below

Ratio Proportion Neither

Dave can eat three timesmore than me.

Dave works twice as hard as Ido, so when I work for 3hours, he works for 6 hours.

Dave is 5 years younger thanme, so when I’m 95, he’ll be90.

Based on the table above, can you explain the difference between ratio and proportion? Try.



(3) Let’s come up with some formal definitions.

(4) Let’s play with these definitions! Suppose the ratio of coffee drinkers to non-coffee drinkers is10

4

.

a. This says that for every 10____________________ there are 4 ______________________.

b. Use multiplication or division to come up with two more ratios.

c. Write three proportions using the original ratio and new ones you came up with.

d.

Suppose there are 100 coffee drinkers in the building right now. How many non-coffee drinkersmust there also be?

e. Suppose there are 168 people total. How many of them are coffee drinkers?

(5) Identify which two figures are proportional and explain why using the definitions presented above.

Ratio and Proportion Definitions

Ratio Notation: A ratio is expressed normally in two different ways

(1) : is read as “the ratio of to ”

(2)

is also read as “the ratio of to ” or is talked about just as we talk about fractions.

(3) In real life, we often read

as, “for every somethings, there are somethings”.

Informal definition of Ratio: conveying a relationship between two numbers as a fraction.

Because it’s fraction, the numerator and denominator can be multiplied or divided by the same

number to produce a new ratio equivalent to the first.

Informal definition of Proportion: A statement showing the equality between a ratio and

another ratio that is an equivalent fraction. i.e.

=



Exercise 2: So what seems to make figures proportional?

Suppose you’re trying to perfect your shrink ray.

Here’s how you want it to work

You decide to try it out on Mario (you had a previous

project where you invented a way to make video game

characters come to life). This is what happened.

(1) Why does your new shrunken Mario look weird?

(2) What adjustment needs to be made to the shrink-ray to make shrunken Mario look right again?

(3) Write the ratio of big Mario’s height to big Mario’s width. Then write the ratio of small Mario’s

height to small Mario’s width.

(4) Do these two ratios form a proportion?

(5) Write the ratio of what you think small Mario’s height to width should be to make him look not so

squashed.

(6) Does this ratio form a proportion with big Mario’s ratio of height to width?

6 ft

4 ft

3 ft

4 ft



Exercise 3: It WORKED!

(1) There are a BUNCH of different ratios

in the figure. (Remember, a ratio is

just comparing two numbers that have

some relationship to each other and

writing them as a fraction.)

Write down as many ratios as you can.

(2) Look at your list of ratios above. Find

pairs of ratios that are proportions.

Exercise 4: The Math

Why did so many proportions work out? Let’s play with this mathematically. Let big Mario be represented

with a , small Mario be represented with an . Let stand for width and ℎ stand for height.

(1) We saw that the proportion

=

was true. Multiply both sides by

and reduce. Is this newproportion one of the proportions we found to be true?

(2) Take the proportion

=

. Multiply both sides by

and reduce. Is this new proportion one of

the proportions we found to be true?

(3) Generalize: If you have the proportion

=

what two other proportions hold true?

6 ft

4 ft

2 ft

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Ratio and Proportion Lesson for Geometry