algebra 2.6 rates, ratios, and proportions. learning targets language goal students will be able to...

Algebra 2.6Rates, Ratios, and Proportions

Learning TargetsLanguage Goal Students will be able to write and use

ratios, rates, and unit rates.Math Goal Students will be able to write and solve

proportions.Essential Question Where do you see ratios, rates, and

proportions in real-life situations?

Warm-up

Go over Quiz

Vocabulary Ratio:

Rate:

Scale:

Unit Rate:

A comparison of two quantities.

A ratio of two quantities with different unitsEx. 34 mi/2 gal

A ratio between two sets of measurement.Ex. 1 in : 5 mi

A rate with a second quantity of 1 unit.Ex. 17 mi / 1 gal

Vocabulary Conversion Factor:

Proportion:

Cross Products:

Scale Drawings/Scale Model:

Two quantities are equal but use different unitsEx. 12 in / 1 ft

A statement that two ratios are equivalent.Ex.

In proportion ,

Uses a scale to represent an object as smaller or larger than the actual object

Ex. A map

Cross Product PropertyWords Numbers Algebra

In a proportion, cross products

are equal.

Example 4: Solving ProportionsA. B.

C. D.

Extra Whiteboard Practice!A.

Extra Whiteboard Practice!B.

Extra Whiteboard Practice!C.

Extra Whiteboard Practice!D.

Extra Whiteboard Practice!E.

Extra Whiteboard Practice!F.

Example 1: Using Ratios A. The ratio of faculty members to

students at a college is 1:15. There are 675 students how many faculty members are there?

Example 1: Using Ratios B. The ratio of games won to games lost

for a baseball team is 3:2. The team won 18 games. How many games did the team lose

Example 1: Using Ratios C. The ratio of the number of bones in

the human skull to the number of bones in the ears is 11:3. There are 22 bones in the skull. How many bones are in the ears?

Example 2: Finding Unit Rates A.Takeru Kobayashi of Japan ate 53.5

hotdogs in 12 minutes to win a contest. Find the unit rate. Round your answer to the nearest hundredth.

Example 2: Finding Unit Rates B. Cory earns $52.50 in 7 hours. Find

the unit rate.

Example 2: Finding Unit Rates C. Ralf Laue of Germany flipped a

pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth.

Example 3: Converting Rates A. As you go deeper underground, the

earth’s temperature increases. In some places, it may increase by 25C per kilometer. What is this rate in degrees per meter?

Example 3: Converting Rates B. The dwarf sea horse swims at a rate

of 52.68 feet per hour. What is this speed in inches per minute?

Example 3: Converting Rates C. A cyclist travels 56 miles in 4 hours.

What is the cyclist’s speed in feet per second? Round your answer to the nearest tenth.

Practice B WS (if time)

Lesson Quiz