Proportions

Report
Constructed Response Assessment
October 17th
Day 1: Ratios
A ratio is a comparison of two quantities
using division.
Ratios can be written in three different
7
ways: 7 to 5, 7:5, and
5
Order matters when writing a ratio.
Find the ratio of boys to girls in Donnelly’s class.
Lucky Ladd Farms has:
16 cows, 8 sheep, and 6 pigs



cows to sheep
pigs to total animals
sheep to pigs
Always simplify your ratio to the lowest term.
The ratio of wings to beaks in the bird house
at the zoo was 2:1, because for every 2 wings
there was 1 beak.
 For every vote candidate A received,
candidate C received nearly three votes.
Make a table or model to represent one of the
above situations.

Beak
Wing
1
2
2
4
3
6
4
8
Remember, a ratio makes a
comparison.
The ratio of green aliens to total
aliens is 3 to 7.
****Make sure you write the ratio
just like they ask for it!****
The ratio of total aliens to purple
aliens is 7 to 4. Not 4 to 7




1. What is the ratio of
blue balloons to red
balloons?
2. What is the ratio of
total balloons to orange
balloons?
3. What is the ratio of
yellow balloons to total
balloons?
4. What is the ratio of
green balloons to purple
balloons?
Day 3: Equivalent Ratios
Ratios that make the same comparison
are equivalent ratios. To check
whether two ratios are equivalent, you
can write both in simplest form.
20 cars : 30 trucks
10 : 15
2 : 3 80 : 120
Check It Out! Example 1
Write the ratio 24 shirts to 9 jeans in
simplest form.
Write the ratio as
a fraction.
shirts = 24
jeans
9
=
24 ÷ 3
9÷3
= 8
3
Simplify.
The ratio of shirts to jeans is 8 , 8:3, or 8 to 3.
3
Lesson Quiz: Part I
Write each ratio in simplest form.
1
1. 22 tigers to 44 lions
2
30
2. 5 feet to 14 inches
7
Find a ratios that is equivalent to each given
ratio.
3. 4
15
Possible answer: 8 , 12
30 45
4. 7
21
Possible answer: 1 , 14
3 42
Determining Whether Two Ratios Are Equivalent
Simplify to tell whether the ratios are
equivalent.
A. 3 and 2
27
18
B. 12 and 27
15
36
Lesson Quiz: Part II
Simplify to tell whether the ratios are
equivalent.
5. 16 and 32 8 = 8; yes
10
20 5 5
6. 36 and 28
24
18
3 14 ; no
2 9
7. Kate poured 8 oz of juice from a 64 oz bottle.
Brian poured 16 oz of juice from a 128 oz bottle.
Are the ratios of poured juice to starting amount
of juice equivalent?
8 and 16 ; yes, both equal 1
64
8
128
A rate is a ratio that compares quantities that
are measured in different units.
This spaceship travels at a certain speed.
Speed is an example of a rate.
This spaceship can travel
100 miles in 5 seconds is a rate.
It can be written 100 miles
5 seconds
A rate is a ratio that compares quantities that
are measured in different units.
One key word that often identifies a rate is PER.
•Example: Miles per gallon, Points per free throw,
Dollars per pizza, Sticks of gum per pack
What other examples of rates can
your group think of?


Remember: A rate is a ratio that compares
two quantities measured in different units
(miles, inches, feet, hours, minutes, seconds).
The unit rate is the rate for one unit of a
given quantity. Unit rates have a
denominator of 1.
A unit rate compares a quantity to one unit of
another quantity. These are all examples of
unit rates.
6 tentacles per head
2 eyes per alien
1 tail per body
1 foot per leg
3 windows per spaceship
3 riders per spaceship
Rate
150 heartbeats
2 minutes
Unit Rate (divide to get it):
150 ÷ 2 = 75
75 heartbeats to 1minute OR
75 heartbeats per minute
Amy can read 88 pages in 4 hours (rate).
What is the unit rate? (How many pages can
she read per hour?)
88 pages
4 hours
22 pages / hour
Try this by yourself!
Unit rates are rates in which the second
quantity is 1.
The ratio 90 can be simplified by dividing:
3
90 = 30
3
1
unit rate: 30 miles, or 30 mi/h
1 hour
Check It Out! Can you solve?
Penelope can type 90 words in 2 minutes. How
many words can she type in 1 minute?
90 words
2 minutes
Write a rate.
90 words ÷ 2 = 45 words
2 minutes ÷ 2 1 minute
Divide to find words
per minute.
Penelope can type 45 words in one minute.



Unit price is a unit rate used to compare
price per item.
Use division to find the unit prices of the two
products in question.
The unit rate that is smaller (costs less) is the
better value.
Juice is sold in two different sizes. A 48fluid ounce bottle costs $2.07. A 32-fluid
ounce bottle costs $1.64. Which is the
better buy?
$2.07
48 fl.oz.
$1.64
32 fl.oz.
0.04312
5
0.05125
$0.04 per
fl.oz.
$0.05 per
fl.oz.
The 48 fl.oz. bottle is the better value.
Additional Example: Finding Unit Prices to Compare
Costs
Pens can be purchased in a 5-pack for $1.95
or a 15-pack for $6.20. Which pack has the
lower unit price?
price for package = $1.95 = $0.39 Divide the price
by the number
number of pens
5
of pens.
price for package = $6.20  $0.41
number of pens
15
The 5-pack for $1.95 has the lower unit price.
Try this by yourself
John can buy a 24 oz bottle of ketchup for
$2.19 or a 36 oz bottle for $3.79. Which
bottle has the lower unit price?
price for bottle
= $2.19  $0.09
number of ounces
24
Divide the price
by the number
of ounces.
price for bottle
= $3.79  $0.11
number of ounces
36
The 24 oz jar for $2.19 has the lower unit price.
Day 7: A proportion is an equation
stating that two ratios are equal.
x3
7 , 21
10 30
Yes, these two ratios DO form a proportion,
because the same relationship exists in both the
numerators and denominators.
x3
÷4
No, these ratios do NOT form a
proportion, because the ratios are not
equal.
8 , 2
9 3
÷3

A proportion is an equation stating that two
ratios are equal.
Example:
Example:
A piglet can gain 3 pounds in 36 hours. If
this rate continues, the pig will reach 18
pounds in _________ hours.
Jessica drives 130 miles every two hours.
If this rate continues, how long will it take
her to drive 1,000 miles?
Joe’s car goes 25 miles per gallon of
gasoline. How far can it go on 8
gallons of gasoline?
x8
Unit Rate
25 miles
1 gallon
=
8 gallons
x8
25 x 8 = 200. Joe’s car can go 200
miles on 8 gallons of gas.

similar documents