ratio and proportion lesson for geometry
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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.
7/27/2019 Ratio and Proportion Lesson for Geometry
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(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.
=
7/27/2019 Ratio and Proportion Lesson for Geometry
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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
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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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