(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. Operations with fractions have the same meanings as operations with whole numbers, even though the algorithms differ.


GOAL 3a: I can represent fractions and their equivalents.

GOAL #3b: Comparing and Ordering Fractions and Mixed Numbers

GOAL #4a: Adding and Subtracting Fractions with Like Denominators

GOAL #4b: Adding and Subtracting Fractions with Unlike Denominators

GOAL #4c: Multiplying and Dividing Fractions by Whole Numbers


  • Represent, compare, and order decimals to hundredths and fractions, using a variety of tools (e.g., number lines, Cuisenaire rods, base ten materials, calculators);
  • Select and justify the most appropriate representation of a quantity (i.e., fraction, decimal, percent) for a given context (e.g., “I would use a decimal for recording the length or mass of an object, and a fraction for part of an hour.”);
  • Demonstrate an understanding of addition and subtraction of fractions…, and apply a variety of computational strategies to solve problems involving whole numbers and decimal numbers;
  • Divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials;
  • Use a variety of mental strategies to solve problems involving the addition and subtraction of fractions;
  • Add and subtract fractions with simple like and unlike denominators, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, calculators) and algorithms;
  • Demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number.