Course 2 Online!
Henrico County Public Schools, Virginia
7.4 - Proportions
Number, Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
Computation and Estimation
Focus: Integer Operations and Proportional Reasoning


The student will solve single-step and multistep practical problems, using proportional reasoning. 
Essential Knowledge and Skills 
  • Write proportions that represent equivalent relationships between two sets.
  • Solve a proportion to find a missing term.
  • Apply proportions to convert units of measurement between the U.S. Customary System and the metric system. Calculators may be used.
  • Apply proportions to solve practical problems, including scale drawings. Scale factors shall have denominators no greater than 12 and decimals no less than tenths.  Calculators may be used.
  • Using 10% as a benchmark, mentally compute 5%, 10%, 15%, or 20% in a practical situation such as tips, tax and discounts.
  • Solve problems involving tips, tax, and discounts. Limit problems to only one percent computation per problem.
Essential Understandings
  • What makes two quantities proportional? Two quantities are proportional when one quantity is a constant multiple of the other.
Vertical Articulation
  • SOL 6.1 - describe/compare data using ratios
  • SOL 8.3a - solve practical problems involving rational numbers, percent, ratios, and prop
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Proportions (PDF) - Solving a proportion to find a missing term (Word)
  2. VDOE Enhanced Scope and Sequence Lesson: Sales Tax and Tip (PDF) - Solving problems, using proportional reasoning (Word)
  3. Notes: Proportions (flipchart)
  4. Notes: Proportional Reasoning (flipchart)
  5. Notes: Percents and Proportions (ppt)
  6. Notes: Tax, Tip, and Total Cost (flipchart)
  7. Notes: Discounts (flipchart)
  8. Guided Notes: Proportional Reasoning (doc)
  9. Activity: Solving Proportions (doc)
  10. Activity: Proportions Jeopardy Review (flipchart)
  11. Activity: Restaurant Math (pdf)
  12. Activity: Menu Order with Coupons (doc)
  13. Activity: Menu and Tip with Guided Questions (doc)
  14. VDOE Algebra Readiness Curriculum Companion: Working with Percents (pdf)
  15. VDOE Algebra Readiness Curriculum Companion: Working with Ratios and Proportions (pdf)
Real World Lessons
  1. Dan Meyer 3-Act Lessons:
    • Dueling Discounts - Which coupon should I use?
    • Bubble Wrap - Guess how long the other bubble wrap pieces will take to pop.
    • Leaky Faucet - How long will it take the sink to fill up?
    • Pain Relief - Which pain reliever is the best deal?
    • Hot Coffee - How many gallons fit into that coffee cup?
    • Super Bear - How many regular bears equals the super bear?
    • Shower v Bath - Which is cheaper: a shower or a bath?
    • Print Job - How long will it take to print all those pages?
    • Bone Collector - How big is the killer's shoe size?
    • Sugar Packets - How many sugar packets are in a bottle of soda?
    • Partial Product - What's the total grocery bill?
    • Split Time - What should his split time on the indoor track be?
    • Bolt - How fast is Usain Bolt running?
    • Speed of Light - What does the speed of light look like?
    • Coin Carpet - If you were going to carpet the room with a single kind of coin, which would be the cheapest option?
  1. Mathalicious Lessons:
    • Pizza Pi - Pizza Hut pizzas come in three sizes: large, medium and personal. Which size is the best deal, and is it ever a good idea to buy the personal? 
    • 1600 Pennsylvania - How much would it cost to paint and heat the home of the president?
    • 22 Minutes - How does watching television affect your lifespan?
    • Beauty Shopp of Horrors - If you stopped cutting your hair and fingernails, how long would they be in a year? Two years? Ten?
    • Biggest Loser - What's the best way to determine weight loss?
    • Civic Hybrid - Is it ever worth it to buy a hybrid car. If so, when?
    • Face Value - How much of a concert ticket's face value actually goes toward the concert?
    • Family Plan - What's a fair way to share the cost of a family cell phone plan?
Practice
  1. Worksheet: Ratios, Rates, Proportions and ACC Basketball (doc)
  2. Worksheet: Comparing Unit Rates (doc)
  3. Worksheet: Proportion Word Problems (pdf)
  4. Worksheet: Proportion Word Problems #2 (doc)
  5. Worksheet: Proportion Word Problems #3 (doc)
  6. Worksheet: Proportion Word Problems #4 (doc)
  7. Worksheet: Percent Proportions Problems - Color Coded (doc)
  8. Worksheet: Proportions (doc)
  9. Worksheet: Discount Sale Price Worksheet (pdf)
  10. Worksheet: Discount Sale Price #2 Worksheet (pdf)
  11. Worksheet: Discount Sale Price #3 Worksheet (pdf)
  12. Worksheet: Practical Sales Problems (doc)
  13. Worksheet: Tax, Tip, and Discount (doc)
  14. Worksheet: Sales Tax and Tip (doc)
SOL Mini Quiz
  1. SOL 7.4 Mini Quiz: Proportional Reasoning (pdf) | (doc)
Skills
  1. Mathematics Assessment Project:
    • A01:25% sale - Apprentice - In a sale, the store reduces all prices by 25% each week. Does this mean that, after 4 weeks, everything in the store will cost $0? If not, why not?
    • A03:A Million Dollars - Apprentice - In this task, you will figure out questions such as: How much does a million Dollars in Dollar bills weigh? How many burgers can you buy for a million Dollars?
    • A18:Giantburgers - Apprentice - Every day 7% of Americans eat at Giantburger restaurants! Your task is to  decide whether this newspaper headline can be true.
    • A19:Leaky Faucet - Apprentice - How much water might a dripping faucet waste in a year?
    • A21:Sale! - Apprentice - In this task, you use mathematics to decide which special offers give the biggest and smallest price reductions.
    • A22:Photographs - Apprentice - In this task, you need to figure out how to fit three different-sized photographs on a single sheet.
    • A23:T-Shirt Sale - Apprentice - A store sells T-shirts at various prices and offers "Any 3 T-shirts for $14.50". Your task is to work out how much people have saved.
    • A24:Yogurt - Apprentice - In this task, you must calculate how much yogurt is produced by a machine at a food company.
    • E02:Counting Trees - Expert - In this task, you must estimate the number of trees on a tree farm - without counting every tree.
    • E05:Ice Cream - Expert - In this task, you use math to plan how to sell ice cream at a school sports event.
  2. Proportional Reasoning: Cats and Rats! (doc)
  3. Proportional Reasoning: Square Buildings (doc)
  4. Practical Problem: Sales Tax (doc)
Videos
  1. YouTube: Percents and Proportions - Solving Percent Problems
  2. YouTube: Sales Tax and Discount
  3. Virtual Nerd: Setting Up a Proportion from a Word Problem
  4. PH: Finding sales tax
  5. PH: Finding percent of discount
  6. PH: Identifying proportions
  7. PH: Identifying whether two ratios are proportional
  8. PH: Solving proportions using number sense or mental math
  9. PH: Solving proportions using cross products
Explore Learning
  1. None
Websites
  1. PBS: Dunk Tank Activity
  2. The Math Page: The Method of Proportions
  3. The Math Lab: Solving Percents with Problems
  4. Math Goodies: Percents and Proportions
  5. Manga High: Ratio and Proportion - Using Proportions Game
  6. Quia: Rates, Ratios, and Proportions
  7. Quia: Ratios & Proportions - Rags to Riches Game
  8. Arcademic: Ratio Blaster Game
  9. Arcademic: Ratio Stadium Game
  10. Wisc-Online: Ratios and Proportions
VDOE Interventions
  1. VDOE Algebra Readiness Curriculum Companion: Working with Ratios and Proportions - The lessons focus on the meaning of ratios and proportions. Students practice writing ratios and build on their knowledge of ratios to work with proportions. Using proportional reasoning to solve practical problems is a common element in this section. (pdf)
Common Core Standards
6.RP.1
6.RP.2
6.RP.3a
6.RP.3b
6.RP.3c
6.RP.3d
7.RP.1
7.RP.2a
7.RP.2b
7.RP.2c
7.RP.2d
7.RP.3
7.EE.3
7.G.1
8.EE.5
N-Q.1
N-Q.2
N-Q.3