Transcript Do Now 2/7/08 - Howell Township Public Schools

Do Now 3/28/11
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Copy HW in your planner.
 Text
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p. 272, #10-36 evens
Be ready to copy POTW #1 for the 4th
marking period.
Chapter 6 “Ratio, Proportion, and
Probability”
Section 6.1 “Ratios and Rates”
Section 6.2 “Writing and Solving Proportions”
Section 6.3 “Solving Proportions Using Cross Products”
Section 6.7 “Probability and Odds”
Section 6.8 “The Counting Principle”
Objective
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SWBAT find ratios and unit rates
Section 6.1 “Ratios and Rates”
RATIOuses division to compare two
quantities of the SAME
MEASURE.
You can write ratios three different ways:
a to b
a:b
a
b
Ratios
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What is the ratio of:
 Blue
to total
 Yellow to green
 green to red
 Red to blue
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1/17
6/7
7/3
3/1
Try It Out…
VOLLEYBALL
A volleyball team plays 14 home matches and 10 away
matches.
a.
Find the ratio of home matches to away matches.
b.
Find the ratio of home matches to all matches.
SOLUTION
home matches
7
14
a.
= 10 = 5
away matches
b.
home matches
all matches
=
14
14
7
14 + 10 = 24 = 12
RATIOa comparison of two numbers by
division. The two numbers must have the
same unit of measure.
5 ft
Find the ratio of the
height to the width.
9 ft
Find the ratio of the
width to the height.
Are the ratios the same?
5
9
NO!!
9
5
Find the Ratio…
On a set of house plans, an architect wants to represent
a 30ft length of a room by a 5 inch segment. What is the
ratio of the length of the segment to the length of the room?
A comparison of two numbers by division.
The two numbers must have the same unit of measure
Length of segment
5 inches
Length of room
30 ft
(x 12 inches) =
5
1
360
72
Convert feet to inches.
12 inches in 1 foot.
The ratio is 1 to 72.
“Rates”
RATEa fraction in which the numerator and the
denominator have different units of
measure.
Examples of rates: speed & distance, wages
45miles
hour
5 meters
second
8 dollars
hour
UNIT RATEa rate with a denominator of
90miles
2 hours
÷2
=
÷2
=
1
45 miles
1 hour
UNIT RATE
Finding a Unit Rate
A car travels 110 miles in 2 hours. Find the unit rate.
110 miles
2 hours =
110 miles
2 hours
2
55 miles
2 = 1 hour
Finding a Unit Rate
Arnold and Jena went mountain biking on some trails
in their town. Based on the information below, which
one of them rode at a faster pace?
Arnold rode 23 miles in 4 hours.
Jena rode 16 miles in 3.5 hours.
Arnold
23 miles
4 hours =
23 miles
4 hours
4
5.75 miles
4 = 1 hour
Jena
16 miles
3.5 hours
16 miles ÷ 3.5
3.5 hours ÷ 3.5
4.6 miles
1 hour
Your basic monthly charge for cell phone service is $30, which
includes 300 free minutes. You pay a fee for each extra minute you use.
One month you paid $3.75 for 15 extra minutes. Find your total bill if you
use 22 extra minutes.
STEP 1 Calculate the unit rate.
3.75
15
0.25
=
1
= $.25 per minute
STEP 2
Write a verbal model and then an expression. Let m be the number of
extra minutes.
30
+
0.25
m
STEP 3
Evaluate the expression when m = 22.
30 + 0.25(22) = 35.5
Total Bill: $35.50
“Rate or Ratio?”
8 people
11people
140 gallons
5 min utes
16apples
3apples
80 beats
1 min ute
10 miles
2hours
Rate
85 ft
13inches
Ratio
Writing Equivalent Rates
5m ? m
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1 sec 1 h
If you are walking 5
meters in 1 second, how
many meters will you
walk in a hour?
There are 60 seconds in
a minute and 60 minutes
in a hour, so multiply 5
meters by 3600.
5 m 18,000 m
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1 sec
1h
3 lb ? oz
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$1
$1
If you can buy 3 pounds
for a $1, how many
ounces can you buy for a
$1?
There are 16 ounces in a
pound, so multiply 3
pounds by 16.
3 lb 48 oz
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$1
$1
Homework
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Text p. 272, #10-36 evens, #44, & #47