Transcript Math I Period 1

CCGPS Coordinate Algebra
Day 2 (8-14-12)
UNIT QUESTION: Why is it
important to understand the
relationship between quantities?
Standard: MCC9-12.N.Q.1-3, MCC9-12.A.SSE.1, MCC9-12.A.CED.1-4
Today’s Question:
How are unit conversions performed,
and why is it important?
Standard: MCC9-12.N.Q.1 and N.Q.2
Measurement Words
How would you measure this?
Measurement Conversion
Graphic Organizer
Quantity- an exact amount or
measurement
A ratio is a comparison
of two quantitites
(numbers or measures).
A ratio can be written three
ways:
3:5
3/5
3 to 5
BACK
Ratios are often
expressed as fractions
in simplest or as a
decimal.
5
1
 or .25
20 4
BACK
A ratio is the comparison of two numbers with the same units by division. A
ratio may be written in three ways.
2 to 3
2:3
2
3
What ratios can we form from the tiles
above?
part  12 to 8
part 
part 
whole 
12
20
whole 
part 
20
12
BACK
Create as many ratios as
possible. Write each ratio
three different ways.
BACK
Simplest Form
• Write the ratio 50 to 300
in simplest form.
1
50

300 6
BACK
Simplest Form
• Write the ratio 60¢ per dozen
in simplest form.
5
60

1
12
BACK
Look over the ratios you have written.
Is there another way that you can write
those ratios?
The ratio illustrated here
is four filled cells to ten
total cells.
The ratio shown here
is two filled cells to
five total cells.
What do you know about these two
ratios? How can you prove your
BACK
Proportion
• An equation that sets two
ratios equal to one another
2
5
8

20
BACK
Unit Rate
A comparison of two
measurements in which
the second term has a
value of 1
“How much for just 1?”
BACK
Unit Rate
If it costs $78 for 13
sandwiches, What is the
unit rate?
$78 13  $6 each
BACK
The cost of a 12-ounce
box of Cheerios is $3.29.
Publix brand Cheerios
cost $4.89 for an 18ounce box. Find the unit
rate to find the better
buy.
3.29
4.89
 .274
 .271
12
18
BACK
Mile per Gallon
• M.P.G. stands
for miles per
gallon and is
usually used for
gas mileage in
cars.
BACK
Unit Rate
• If it takes 11 gallons
to drive 250 miles,
What is the unit rate
or m.p.g.?
BACK
Solving Word Problems
250
x
•Write problem as proportions:

11
1
•Solve using cross multiplication
250(1)  11X
250 11X

11
11
.
BACK
Measurements
Problem Solving Using Conversion
Factors
Example 1
1. Bob studied for 2.5 hrs. How many minutes
did he study for?
Initial unit = hr.
Multiply by:
Final unit = _______
What you want
What you have
How many minutes are in 2.5 hours?
Initial unit
2.5 hr
Conversion
factor
2.5 hr x 60 min
1 hr
cancel
Final
unit
= 150 min
Answer (2 SF)
Learning Check
A rattlesnake is 2.44 m long. How long is the
snake in cm?
1) 2440 cm
2) 244 cm
3) 24.4 cm
Solution
A rattlesnake is 2.44 m long. How long is the
snake in cm?
2) 244 cm
2.44 m x 100 cm
1m
= 244 cm
Example 2
How many seconds are in 1.4 days?
Unit plan: days
hr
1.4 days x 24 hr x
1 day
min
seconds
??
LecturePLUS Timberlake
26
Solution
Unit plan: days
hr
min
seconds
1.4 day x 24 hr x 60 min x 60 sec
1 day
1 hr
1 min
= 120,000 sec
Learning Check
If the ski pole is 3.0 feet in length, how long is
the ski pole in mm?
Solution
3.0 ft x 12 in
1 ft
x 2.54 cm x 10 mm =
1 in.
1 cm
= 214.4 mm.
Example 3
John Isner serves 140 miles per hour. How fast
is that feet per second?
Solution
140 miles
1 hr
x 5,280 ft. x 1 hr x 1 min =
1 mile
60 min 60 sec.
= 205.3 ft/sec.
Why are unit conversions
important?