Proportional Reasoning

BIG IDEAS:

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

  1. Proportional thinking involves the use of multiplicative relationships, in the form of rates, ratios, and percents, to solve problems.
  2. 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.
  3. 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).
  4. 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.

GOAL #2: I can identify a rate and can calculate unit rates in order to solve real-world problems.

GOAL #3: I can demonstrate how a percent is a ratio of a number to 100.

GOAL #4: I can solve problems involving whole number percents.

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.).