8-5 6th grade math

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8-56th grade math

• Rates

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Objective

• To use rates to solve problems
• Why? To know how to convert miles per hour,
  miles per gallon, revolutions per minute, per
  hour, per pound, etc.

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California State Standards

• AF 2.2 Demonstrate an understanding that
  rate is a measure of one quantity per unit of
  value of another quantity.
• NS 1.2 Interpret and use ratios in
  different contexts to show the relative sizes
  of two quantities, using appropriate notations
  (x/y, x to y, x y)
• NS 1.3 Use proportions to solve problems
  
• AF 2.3 Solve problems involving rates, average
  speed, distance, and time.
• MR 1.1 Analyze problems by identifying
  relationships

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Vocabulary

• Rate
• A ratio that compares different kinds of units
• 25 feet in 3 hours, 5 cans of peaches for 2,
  etc.
• Unit
• Meaning 1 (uni 1)
• 1 teacher, 1 box of Kleenex, etc.
• Unit rate
• A ratio that compares a quantity to a unit of one
• 8 1/3 feet per hour, 0.40 per can, etc.
• Per
• Each or divide
• Miles per hour mi/hr

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How to Solve Rates

• Traveled 99 miles in 90 minutes. What is average
  rate of speed in miles per hour?
• 99 x
• 1.5 1
• 99 1.5 66 mph
• Or
• 99 x
• 90 1
• (99 90) x 60 66 mph

• Write a proportion
• First ratio is using the known rate
• Second ratio is placing an unknown value in
  numerator and 1 in the denominator
• 2) Solve by cross multiplying.
• 3) Check for reasonableness

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• Who scored more points?
• R 72 pts in 8 games
• B 57 pts in 6 games
• 72 / 8 9 pts per game
• 57 / 6 9.5 pts per game
• B scored more pts per game

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Try It!

1. 1.2 miles per minute
2. 28 miles per gallon
3. 8 chairs per table
4. 32 students per classroom

• Find the unit rate.
• 90 miles in 75 minutes
• 252 miles every 9 gallons
• 48 chairs for 6 tables
• 96 students in 3 classrooms

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Objective Review

• To use rates to solve problems

• Why? You now know how to convert miles per hour,
  miles per gallon, revolutions per minute, per
  hour, per pound, etc.
• A rate is a special ratio involving two
  quantities with different units, such as miles
  per hour.
• Miles per hour miles/hour
• miles hour

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Independent Practice

• Complete problems 6-10
• Copy original problem first.
• Show all work!

• If time, complete Mixed Review 12-18
• If still more time, work on Accelerated Math.