Course 3 Online!
Henrico County Public Schools, Virginia
8.3 - Applications with Real Numbers
Number and Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
Computation and Estimation
Focus: Practical Applications of Operations with Real Numbers


The student will
a)   solve practical problems involving rational numbers, percents, ratios, and proportions; and
b)   determine the percent increase or decrease for a given situation. 
Essential Knowledge and Skills 
  • Write a proportion given the relationship of equality between two ratios.
  • Solve practical problems by using computation procedures for whole numbers, integers, fractions, percents, ratios, and proportions. Some problems may require the application of a formula.
  • Maintain a checkbook and check registry for five or fewer transactions.
  • Compute a discount or markup and the resulting sale price for one discount or markup.
  • Compute the percent increase or decrease for a one-step equation found in a real life situation.
  • Compute the sales tax or tip and resulting total.
  • Substitute values for variables in given formulas. For example, use the simple interest formula I=prt to determine the value of any missing variable when given specific information.
  • Compute the simple interest and new balance earned in an investment or on a loan for a given number of years.
Essential Understandings
  • What is the difference between percent increase and percent decrease? Percent increase and percent decrease are both percents of change measuring the percent a quantity increases or decreases. Percent increase shows a growing change in the quantity while percent decrease shows a lessening change.
  • What is a percent? A percent is a special ratio with a denominator of 100.
Vertical Articulation
  1. SOL 6.1 - describe/compare data using ratios
  2. SOL 6.6b - solve practical problems involving add/sub/mult/div fractions
  3. SOL 6.7 - solve practical problems involving add/sub/mult/div decimals
  4. SOL 7.4 - single and multistep practical problems with proportional reasoning
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Do You Like to Spend Money? (PDF) - Solving problem involving percents (Word)
  2. VDOE Enhanced Scope and Sequence Lesson: The Scoop on Ice Cream (PDF) - Solving problems involving percent, ratios, and proportions (Word)
  3. VDOE Enhanced Scope and Sequence Lesson: Percent of Increase or Decrease (PDF) - Finding percent of increase or decrease (Word)
  4. Warm-Up: Percent Decrease TEI item (flipchart)
  5. Guided Notes : Percent Increase/Decrease (doc)
  6. Guided Notes: Sales Tax, Tip and Discount (doc)
  7. Guided Notes: Simple Interest (doc)
  8. Notes: Percent of Change (ppt)
  9. Notes: Ratios and Rates (doc)
  10. Activity: Math Academy Packet - Dining Out! Explorations in Fractions, Decimals, and Percents (pdf)
  11. Activity: Translating Verbal Phrases Into Symbols Chart (doc)
  12. Activity: Math Mall (doc)
  13. Activity: E-shopping (doc)
  14. Activity: Scale Drawings (doc)
  15. Activity: Shopping Activity (doc)
  16. VDOE Algebra Readiness Curriculum Companion: Exploring Decimals (pdf)
  17. VDOE Algebra Readiness Curriculum Companion: Working with Fractions (pdf)
  18. VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)
  19. VDOE Algebra Readiness Curriculum Companion: Working with Percents (pdf)
  20. VDOE Algebra Readiness Curriculum Companion: Working with Ratios and Proportions (pdf)
Real World Lessons
Practice
  1. Worksheet: Consumer Math Word Problem Test Review (doc)
  2. Quiz Review: Consumer Math (doc)
  3. Quiz: Consumer Math (doc)
  4. Worksheet: Practical Problems Practice (doc)
  5. Quiz: Proportions (doc)
  6. Worksheet: Similar Triangles & Indirect Measurement Practice (doc)
  7. Worksheet: Vocabulary Review (doc)
  8. Worksheet: Comparing Unit Rates (doc)
Self-Assessments
  1. SOL 8.3a Mini-Quiz: Problem Solving
  2. SOL 8.3b Mini-Quiz: Percent Increase/Decrease
Skills
  1. Mathematics Assessment Project:
    • A02:100 People - Apprentice - In this task, you are asked to estimate the real numbers, given that there are approximately seven billion people in the world.
    • 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.
    • 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. Practical Problem: Best Buy (doc)
Videos
  1. Khan Academy: Writing Proportions
Explore Learning
  1. Adding Real Numbers: Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation.
  2. Beam to Moon (Ratios and Proportions): Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights.
  3. Estimating Population Size: Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake.
  4. Part:Part and Part:Whole Ratios: Compare a ratio represented by an area with its percent, fraction, and decimal forms.
  5. Percent of Change: Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations.
  6. Percents and Proportions: Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model.
  7. Polling: Neighborhood: Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling.
  8. Proportions and Common Multipliers: Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator.
  9. Simple and Compound Interest: Find the current balance and the interest charged on an investment using the graph of the interest function and by directly calculating.
Websites
VDOE Interventions
  1. VDOE Algebra Readiness Curriculum Companion: Working with Ratios and Proportions - (SOL 8.3a) 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)
  2. VDOE Algebra Readiness Curriculum Companion: Exploring Decimals - The lessons focus on identifying place values, rounding decimals through hundredths, and performing operations of decimals and writing and solving problems with decimals.(pdf)
  3. VDOE Algebra Readiness Curriculum Companion: Working with Fractions - The lessons focus on fraction computation, factors, and multistep practical problems with fractions. Students are expected to model multiple representations of the multiplication and division of fractions. (pdf)
  4. VDOE Algebra Readiness Curriculum Companion: – Investigating Patterns, Functions, and Algebra - The lessons focus on algebraic reasoning. Students explore the relationships found in number patterns through arithmetic and geometric sequences using variables expressions. They use modeling to collect data, and they learn to record data so that they can see the relationship that exists among tables, graphs, words, and equations. (pdf)
  5. VDOE Algebra Readiness Curriculum Companion: Working With Percents - The lessons in this section focus on relating percents to decimals and fractions, comparing and ordering, solving multistep practical problems and determining the percent of increase or decrease for a give situation. (pdf)
Common Core Standards
6.RP.3c
7.NS.3
7.EE.3
N-Q.1
N-Q.2
N-Q.3