## Rates, Ratios and Percents

**BIG IDEAS****:**

*(taken from “Big Ideas by Dr. Small”)***:**

- Proportional thinking involves the use of multiplicative relationships, in the form of rates, ratios, and percents, to solve problems.
- A ratio is a comparison between two numbers. A part-to-part ratio compares two parts of something. A part-to-whole ratio compares one part of something to the whole thing.
- A rate is a ratio that involves two quantities with different units. In order to compare rates, you must make the second value the same (e.g. unit rates).
- A percent is a ratio where the second number is 100.

**STUDENT LEARNING GOALS:**

**GOAL #1: I can represent and identify ratios.**

- VIDEO: Introduction to Ratios
*(Source: Khan Academy)* - VIDEO: Ratios as Fractions
*(Source: Khan Academy)* - QUIZ: Ratios
*(Source: Nelson Education)* - QUIZ: Ratio II
*(Source: Nelson Education)*

**GOAL #2: I can solve problems involving proportions.**

- VIDEO: Reducing Ratios to Simplest Terms
*(Source: Khan Academy)* - VIDEO: Ratio Word Problem Example I
*(Source: Khan Academy)* - VIDEO: Ratio Word Problem Example II
*(Source: Khan Academy)* - QUIZ: Proportions
*(Source: Nelson Education)* - QUIZ: Solving Ratio Problems
*(Source: Nelson Education)* - GAME: Ratio Martian
*(Source: Math Playground)* - GAME: Thinking Block Ratios
*(Source: Math Playground)* - GAME: Ratio Rumble
*(Source: BrainPop)* - GAME: Ratio Stadium
*(Source: Math Playground)*

**GOAL #3: I can solve problems involving rates.**

- VIDEO: Introduction to Rate
*(Source: Khan Academy)* - VIDEO: Solving for Unit Rate
*(Source: Khan Academy)* - VIDEO: Solving Unit Price Problem
*(Source: Khan Academy)* - VIDEO: Comparing Rates Problem
*(Source: Khan Academy)* - QUIZ: Rates
*(Source: Nelson Education)* - QUIZ: Decimal Division
*(Source: Nelson Education)* - GAME: Matching Rates
*(Source: Sheppard Software)* - GAME: Ratios and Rates Jeopardy
*(Source: Jeopardy Labs)*

**GOAL #4: I can solve problems involving percents.**

- VIDEO: The Meaning of 109%
*(Source: Khan Academy)* - VIDEO: Converting Percents to Decimals and Fractions
*(Source: Khan Academy)* - VIDEO: Converting Decimals to Percents
*(Source: Khan Academy)* - VIDEO: Finding a Percent
*(Source: Khan Academy)* - VIDEO: Percent of Whole Number Values
*(Source: Khan Academy)* - VIDEO: Finding Percentages from Ratios
*(Source: Khan Academy)* - VIDEO: Finding Amount based on Percentage
*(Source: Khan Academy)* - VIDEO: Percent Problem Example
*(Source: Khan Academy)* - VIDEO: Discount Problem Example
*(Source: Khan Academy)* - QUIZ: Ratios as Percents
*(Source: Nelson Education)* - QUIZ: Estimating and Calculating Percents
*(Source: Nelson Education)* - QUIZ: Solving Percent Problems
*(Source: Nelson Education)* - PRACTICE: Converting Percents to Decimals
*(Source: XP Math)* - GAME: Balloon Invaders
*(Source: Math Playground)* - GAME: Percent Proportion Jeopardy
*(Source: Jeopardy Labs)* - GAME: Balloon Pop Math
*(Source: Sheppard Software)* - GAME: Decention
*(Source: Math Playground)*

**CURRICULUM EXPECTATIONS:**

- Translate between equivalent forms of a number (i.e., decimals, fractions, percents)
- Solve problems involving percents expressed to one decimal place (e.g., 12.5%) and whole-number percents greater than 100 (e.g., 115%) (Sample problem:The total cost of an item with tax included [115%] is $23.00. Use base ten materials to determine the price before tax.);
- Identify and describe real-life situations involving two quantities that are directly proportional (e.g., the number of servings and the quantities in a recipe, mass and volume of a substance, circumference and diameter of a circle);
- Solve problems involving proportions, using concrete materials, drawings, and variables (Sample problem:The ratio of stone to sand in HardFast Concrete is 2 to 3. How much stone is needed if 15 bags of sand are used?);
- Solve problems involving percent that arise from real-life contexts (e.g., discount, sales tax, simple interest) (Sample problem: In Ontario, people often pay a provincial sales tax [PST] of 8% and a federal sales tax [GST] of 7% when they make a purchase. Does it matter which tax is calculated first? Explain your reasoning.);
- Solve problems involving rates (Sample problem: A pack of 24 CDs costs $7.99. A pack of 50 CDs costs $10.45. What is the most economical way to purchase 130 CDs?).