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 write ratios in a variety of forms and simplify them when necessary. I can explain how order matters when writing a ratio.
- VIDEO: Introduction to Ratio (Source: Khan Academy)
- VIDEO: Ratios as Fractions (Source: Khan Academy)
- 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: 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 #2: I can identify a rate and can calculate unit rates in order to solve real-world problems.
- 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 #3: I can demonstrate how a percent is a ratio of a number to 100.
- VIDEO: The Meaning of Percent (Source: Khan Academy)
- 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)
- QUIZ: Ratios as Percents (Source: Nelson Education)
- PRACTICE: Converting Percents to Decimals (Source: XP Math)
- GAME: Balloon Pop Math (Source: Sheppard Software)
- GAME: Decention (Source: Math Playground)
- GAME: Dunk Tank (Source: PBS Learning Media)
GOAL #4: I can solve problems involving whole number percents.
- 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)
- QUIZ: Solving Percent Problems (Source: Nelson Education)
- GAME: Balloon Invaders (Source: Math Playground)
- GAME: Percent Proportion Jeopardy (Source: Jeopardy Labs)
CURRICULUM EXPECTATIONS:
- Demonstrate an understanding of proportional relationships using percent, ratio, and rate;
- Determine, through investigation, the relationships among … percents and ratios;
- Solve problems that involve determining whole number percents, using a variety of tools (e.g., base ten materials, paper and pencil, calculators);
- Use estimation when solving problems involving operations with … percents to help judge the reasonableness of a solution.
- Demonstrate an understanding of rate as a comparison, or ratio, of two measurements with different units (e.g., speed is a rate that compares distance to time and that can be expressed as kilometres per hour);
- Solve problems involving the calculation of unit rates (Sample problem:You go shopping and notice that 25 kg of Ryan’s Famous Potatoes cost $12.95, and 10 kg of Gillian’s Potatoes cost $5.78. Which is the better deal? Justify your answer.).