Rates and Unit Rates 6.1.2.3 Determine the rate for ratios of quantities with different units 6.1.2.4 Use reasoning about multiplication and division to solve ratio and rate problems

I can… Write rates Write equivalent rates Calculate unit rates Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

RATIO REVIEW A ratio makes a comparison. There are 3 green aliens and 4 purple aliens. The ratio of green aliens to purple aliens is 3 to 4.

RATIOS A ratio makes a comparison. Ratios can be written in three different ways. 3 to 4 3:4

RATES 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. Speed can be measured in many different ways. This spaceship can travel 100 miles in 5 seconds. 100 miles in 5 seconds is a rate.

RATES Rates are often written in fraction form. A rate is a ratio that compares quantities that are measured in different units. Rates are often written in fraction form. 100 miles in 5 seconds is a rate. It can be written as….. Miles Seconds

RATES A rate is a ratio that compares quantities that are measured in different units. One key word that often identifies a rate is PER. Miles per gallon, Points per free throw, Dollars per pizza, Sticks of gum per pack

UNIT RATES = Most of the time when we work with rates we use a unit rate. A unit rate compares a quantity to one unit of another quantity. This alien can walk at a rate of 10 miles in 2 hours. His speed is a unit rate of 5 miles per 1 hour or simply 5 miles per hour. Miles Hours Hour =

2 people riders per dog rider UNIT RATES A unit rate compares a quantity to one unit of another quantity. These are all examples of unit rates. 6 tentacles per head 1 tail per body 2 eyes per alien 1 foot per leg 3 windows per spaceship 3 riders per spaceship 2 people riders per dog rider

EQUIVALENT RATES The International Space Station orbits Earth at an average rate of 15 miles every 3 seconds. How long will it take the space station to travel 150 miles? x 10   x 10

EQUIVALENT RATES The International Space Station orbits Earth at an average rate of 15 miles every 3 seconds. How long will it take the space station to travel 150 miles? x 10   x 10

UNIT RATES   ÷ 3   ÷ 3

UNIT RATES   ÷ 3   ÷ 3 5 miles per second

YOUR TURN Water is filling a storage tank at an average rate of 25 gallons in 5 minutes. Write this as a unit rate. ÷ 5   ÷ 5

5 gallons per minute YOUR TURN ÷ 5 ÷ 5 Water is filling a storage tank at an average rate of 25 gallons in 5 minutes. Write this as a unit rate. ÷ 5   ÷ 5 5 gallons per minute

USING UNIT RATES There are 5.54 centimeters in 1 inch. How many centimeters are in 3 inches? x 3   x 3

There are 7.62 cm in 3 inches. USING UNIT RATES x 3 x 3 There are 2.54 centimeters in 1 inch. How many centimeters are in 3 inches? x 3   x 3 There are 7.62 cm in 3 inches.

YOUR TURN There are 30.48 centimeters in a foot. How many centimeters are in 5 feet? x 5   x 5

There are 152.4 cm in 5feet. YOUR TURN x 5 x 5 There are 30.48 centimeters in a foot. How many centimeters are in 5 feet? x 5   x 5 There are 152.4 cm in 5feet.

COMPARING UNIT RATES ÷ 4 ÷ 4 ÷ 3 ÷ 3 A 12 ounce tub of popcorn costs $3.00. A 20 ounce tub of popcorn costs $4.00. Which tub is the better buy? We need to find the UNIT RATE of each ÷ 4   ÷ 4 ÷ 3   ÷ 3

COMPARING UNIT RATES ÷ 4 ÷ 4 ÷ 3 ÷ 3 A 12 ounce tub of popcorn costs $3.00. A 20 ounce tub of popcorn costs $4.00. Which tub is the better buy? ÷ 4   ÷ 4 ÷ 3   ÷ 3

20 oz. tub COMPARING UNIT RATES ÷ 4 ÷ 4 ÷ 3 ÷ 3 A 12 ounce tub of popcorn costs $3.00. A 20 ounce tub of popcorn costs $4.00. Which tub is the better buy? 20 oz. tub ÷ 4   ÷ 4 ÷ 3   ÷ 3

YOUR TURN A 3 ounce tube of toothpaste costs $0.75. A 15 ounce tube of toothpaste costs $6.00. Which tube is the better buy? ÷ 15   ÷ 15 ÷ 3   We need to find the UNIT RATE of each ÷ 3

YOUR TURN A 3 ounce tube of toothpaste costs $0.75. A 15 ounce tube of toothpaste costs $6.00. Which tube is the better buy? ÷ 15   ÷ 15 ÷ 3   We need to find the UNIT RATE of each ÷ 3

YOUR TURN A 3 ounce tube of toothpaste costs $0.75. A 15 ounce tube of toothpaste costs $6.00. Which tube is the better buy? 3 oz. ÷ 15   ÷ 15 ÷ 3   ÷ 3

I can… Write rates Write equivalent rates Calculate unit rates Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Rates = = 8.2 Notes 15 miles 150 miles 3 seconds 30 seconds You can only compare rates by using UNIT RATES Rates a rate is a ratio of two measures that have different units a unit rate has a denominator of 1 unit x 10 15 miles 150 miles 3 seconds 30 seconds = x 10 15 miles 5 miles 3 seconds 1 second =