Thursday, October 23, 2014

Ratios, Proportions, and Unit Rates

published on: 9/9/2008

Contributing Teacher(s): Nichole McDaniel

Subject Area: Math/Number Sense- Add, Subtract, Multiply, Divide, Estimate, Algebra

Grade Range: Middle Grades (6-8)

Materials Needed:

  • Computer
  • Dry erase boards
  • Dry erase markers and erasers

Objective: The learner will solve problems involving rates, ratios, and proportions including scaling and converting area and volume with in the same system of measure.

Essential Question:

  1. Is it important to know how to solve proportions and unit rates?

Instructional Strategy: Evaluating Student Understanding

Process Standards:

  • Goal 1.6 discover and evaluate patterns and relationships in information, ideas and structures

Content Standards:

  • Mathematics 2. Geometric and spatial sense involving measurement (including length, area, volume), trigonometry, ...

    Time Allowance: 4/50 minute class periods to teach and one for the Are You Smarter Than a Fifth Grader Assessment

    Technological Resources:
    Power Point Template

    Assessment:
    Students will write their answers on dry erase boards as we complete the Are You Smarter than a Fifth Grader game together as a class.

    Description: Students will solve problems involving rates, ratios and proportions including scaling and converting area and volume with in the same system of measure.

    Comments:


    Classroom Component:

    Please click here for 5th Grade Template Powerpoint


    7-1 Ratios and Proportions

    Objective: The learner will find equivalent ratios to create proportions.

    Vocabulary:
    Ratio- A comparison of two quantities by division (usually a fraction).
    Equivalent Ratio- Ratios that make the same comparison.
    Proportion- Ratios that are equivalent.

    ***NOTE- As long as you multiply OR divide a fraction by the same number, it is equivalent.

    Math question



    Math Questions


    7-3 Analyze Units

    Objective: The learner will use one or more conversion factors to solve rate problems.

    Vocabulary:
    To convert units, multiply by one or more ratios of equal quantities called Conversion Factors.

    Find the unit rate.

    1. $27.99
      9 ounces

    Find the better buy.

    1. 54 lbs. for $153.84 OR 48 lbs. for $136.77

    Complete each equation. All answers much be in unit rates with labels.

    1. 15 students . 42 classes = _________
      1 class 1 school




    2. 3 mi . ________ = 7,920 ft
      2 hours 1 hour




    3. 300 cm . _____ = ______ m
      6 hr hr




    4. 180 ft . ______ . ______ = ____ in
      5 sec




    7-4 Solving Proportions

    Objective: The learner will solve proportions.

    Vocabulary:
    Cross Products- in proportions are equal.


    1. A mixture of fuel for a certain small engine should be 4 parts gasoline to 1 part oil. If you combine 5 quarts of oil with 15 quarts of gasoline, will the mixture be correct?

     

     

     

     Math Questions


    7-4 Solving Proportions


    Objective: The learner will solve proportions.

    Vocabulary:
    Cross Products- in proportions are equal.

    **NOTE- This is different than Unit rates in that with proportions you MUST compare like units and they are EQUAL.

    Set up each proportion and solve.

    1. If there are 320 calories in 6 ounces of meat, how many calories are in 2 ounces of meat?








    2. If it takes 3 ounces of concentrate to make 11 ounces of perfume, how much perfume can be made with 7 ounces of concentrate?









    3. At a certain middle school, the ratio of 7th graders to 8th graders is 4 to 3. If there are 600 8th graders, how many 7th graders are there at the middle school?










    For additional information contact :
    Nichole McDaniel
    Pleasant Lea Middle
    Lee's Summit R-VII
    (816) 986-1175
    EMAIL:
    niki.mcdaniel@leesummit.k12.mo.us

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