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 singlestep 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 
 VDOE Enhanced Scope and Sequence Lesson: Proportions (PDF)  Solving a proportion to find a missing term (Word)
 VDOE Enhanced Scope and Sequence Lesson: Sales Tax and Tip (PDF)  Solving problems, using proportional reasoning (Word)
 Notes: Proportions (flipchart)
 Notes: Proportional Reasoning (flipchart)
 Notes: Percents and Proportions (ppt)
 Notes: Tax, Tip, and Total Cost (flipchart)
 Notes: Discounts (flipchart)
 Guided Notes: Proportional Reasoning (doc)
 Activity: Solving Proportions (doc)
 Activity: Proportions Jeopardy Review (flipchart)
 Activity: Restaurant Math (pdf)
 Activity: Menu Order with Coupons (doc)
 Activity: Menu and Tip with Guided Questions (doc)
 VDOE Algebra Readiness Curriculum Companion: Working with Percents (pdf)
 VDOE Algebra Readiness Curriculum Companion: Working with Ratios and Proportions (pdf)

Real World Lessons 
 Dan Meyer 3Act 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?
 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 
 Worksheet: Ratios, Rates, Proportions and ACC Basketball (doc)
 Worksheet: Comparing Unit Rates (doc)
 Worksheet: Proportion Word Problems (pdf)
 Worksheet: Proportion Word Problems #2 (doc)
 Worksheet: Proportion Word Problems #3 (doc)
 Worksheet: Proportion Word Problems #4 (doc)
 Worksheet: Percent Proportions Problems  Color Coded (doc)
 Worksheet: Proportions (doc)
 Worksheet: Discount Sale Price Worksheet (pdf)
 Worksheet: Discount Sale Price #2 Worksheet (pdf)
 Worksheet: Discount Sale Price #3 Worksheet (pdf)
 Worksheet: Practical Sales Problems (doc)
 Worksheet: Tax, Tip, and Discount (doc)
 Worksheet: Sales Tax and Tip (doc)

SOL Mini Quiz 
 SOL 7.4 Mini Quiz: Proportional Reasoning (pdf)  (doc)

Skills 
 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 differentsized photographs on a single sheet.
 A23:TShirt Sale  Apprentice  A store sells Tshirts at various prices and offers "Any 3 Tshirts 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.
 Proportional Reasoning: Cats and Rats! (doc)
 Proportional Reasoning: Square Buildings (doc)
 Practical Problem: Sales Tax (doc)

Videos 
 YouTube: Percents and Proportions  Solving Percent Problems
 YouTube: Sales Tax and Discount
 Virtual Nerd: Setting Up a Proportion from a Word Problem
 PH: Finding sales tax
 PH: Finding percent of discount
 PH: Identifying proportions
 PH: Identifying whether two ratios are proportional
 PH: Solving proportions using number sense or mental math
 PH: Solving proportions using cross products

Explore
Learning 
 None

Websites 
 PBS: Dunk Tank Activity
 The Math Page: The Method of Proportions
 The Math Lab: Solving Percents with Problems
 Math Goodies: Percents and Proportions
 Manga High: Ratio and Proportion  Using Proportions Game
 Quia:
Rates, Ratios, and Proportions
 Quia:
Ratios & Proportions  Rags to Riches Game
 Arcademic: Ratio Blaster Game
 Arcademic: Ratio Stadium Game
 WiscOnline: Ratios and Proportions

VDOE Interventions 
 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 
NQ.1 
NQ.2 
NQ.3 

