# Proportional Reasoning

**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.).