April 2, 2018

FRACTIONS, RATIOS AND RATES

BIG IDEAS:

(taken from “Big Ideas by Dr. Small”):
  1. Fractions can represent parts of regions, parts of sets, parts of measures, division, or ratios. These meanings are equivalent.
  2. A fraction is not meaningful without knowing what the whole is.
  3. Renaming fractions is often the key to comparing them or computing with them. Every fraction can be renamed in an infinite number of ways.
  4. Ratio and rates, just like fractions and decimals, are comparisons of quantities.
    • A ratio compares quantities with the same unit
    • A rate compares quantities with different units

STUDENT LEARNING GOALS:

GOAL: I can represent fractions and their equivalents.
GOAL: I can relate fractions to decimals.
GOAL: I can order fractions and mixed numbers with like denominators.
GOAL: I can identify and solve problems using ratios and rates.

CURRICULUM EXPECTATIONS:

  • represent, compare, and order fractional amounts with unlike denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, number lines, calculators) and using standard fractional notation (Sample problem: Use fraction strips to show that 1 is greater than .);
  • estimate quantities using benchmarks of 10%, 25%, 50%, 75%, and 100% (e.g., the container is about 75% full; approximately 50% of our students walk to school)
  • represent ratios found in real-life contexts, using concrete materials, drawings, and standard fractional notation (Sample problem: In a classroom of 28 students, 12 are female.What is the ratio of male students to female students?);
  • determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions (i.e., with denominators of 2, 4, 5, 10, 20, 25, 50, and 100), decimal numbers, and percents
  • represent relationships using unit rates (Sample problem: If 5 batteries cost $4.75, what is the cost of 1 battery?).

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