CCGPS Coordinate AlgebraDay 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 A ratio is a comparison of two quantitites of two quantitites (numbers or measures).(numbers or measures).

A A ratioratio can be written three ways: can be written three ways:3:53:5 3/5 3/5 3 to 53 to 5

BACK

Ratios are often expressed as fractions in simplest or as a decimal.

20

5.25or

4

1

BACK

A ratio is the comparison of two numbers with the same units by division. A ratio may be written in three ways.

3

2 3:2 3 to2

What ratios can we form from the tiles above?

part

whole

whole

part

part

part 12 to 8

20

12

12

20BACK

Create as many ratios as possible. Write each ratio three different ways. BACK

Simplest Form

• Write the ratio 50 to 300 in simplest form.

300

50

6

1

BACK

Simplest Form

• Write the ratio 60¢ per dozen in simplest form.

12

60

1

5

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 answer?

BACK

Proportion

• An equation that sets two ratios equal to one another

5

220

8

BACK

Unit RateA comparison of two measurements in which the second term has a value of 1

“How much for just 1?”BACK

If it costs $78 for 13 sandwiches, What is the unit rate?

Unit Rate

1378$ each 6$

BACK

The cost of a 12-ounce box of Cheerios is $3.29. Publix brand Cheerios cost $4.89 for an 18-ounce box. Find the unit rate to find the better buy.

12

29.3274.

18

89.4271.

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

•Write problem as proportions:

111

250 x

•Solve using cross multiplication.

11X250(1)

11

11X

11

250

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. Final unit = _______

Multiply by:What you wantWhat you have

How many minutes are in 2.5 hours?

Initial unit

2.5 hr

Conversion Final

factor unit

2.5 hr x 60 min = 150 min

1 hr

cancel 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 = 244 cm

1 m

LecturePLUS Timberlake 26

Example 2

How many seconds are in 1.4 days?

Unit plan: days hr min seconds

1.4 days x 24 hr x ??

1 day

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

Solution

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 x 2.54 cm x 10 mm =

1 ft 1 in. 1 cm

= 214.4 mm.

John Isner serves 140 miles per hour. How fast is that feet per second?

Example 3

Solution

140 miles x 5,280 ft. x 1 hr x 1 min =

1 hr 1 mile 60 min 60 sec.

= 205.3 ft/sec.

Why are unit conversions important?