Fractions, Rates, Ratios

NS/N: 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 (GRADE 5):

  • describe multiplicative relationships between quantities by using simple fractions and decimals (e.g.,“If you have 4 plums and I have 6 plums, I can say that I have 1 1/2 or 1.5 times as many plums as you have.”);
  • demonstrate an understanding of simple multiplicative relationships involving whole-number rates, through investigation using concrete materials and drawings (Sample problem: If 2 books cost $6, how would you calculate the cost of 8 books?).
  • demonstrate and explain the concept of equivalent fractions, using concrete materials (e.g., use fraction strips to show that 3/4 is equal to 9/12)
  • represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using standard fractional notation;
  • determine and explain, through investigation using concrete materials, drawings, and calculators, the relationship between fractions (i.e., with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) and their equivalent decimal forms (e.g., use a 10 x 10 grid to show that 2/5 = 40/100 , which can also be represented as 0.4);

CURRICULUM EXPECTATIONS (GRADE 4):

  • represent fractions using concrete materials, words, and standard fractional notation, and explain the meaning of the denominator as the number of the fractional parts of a whole or a set, and the numerator as the number of fractional parts being considered
  • compare and order fractions (i.e., halves, thirds, fourths, fifths, tenths) by considering the size and the number of fractional – compare fractions to the benchmarks of 0, is more than parts
  • demonstrate and explain the relationship between equivalent fractions, using concrete materials (e.g., fraction circles, fraction strips, pattern blocks) and drawings
  • count forward by halves, thirds, fourths, and tenths to beyond one whole, using concrete materials and number lines (e.g., use fraction circles to count fourths: “One fourth, two fourths, three-fourths, four fourths, five fourths, six fourths, …”)