In Module 3, students’ understanding of addition and subtraction of fractions extends from earlier work with fractions and decimals. This module focuses on the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra.
In Topic A, students revisit the Grade 4 standards addressing equivalence. When equivalent, fractions represent the same amount of area of a rectangle and the same point on the number line. These equivalencies can also be represented symbolically.
In Topic A, students revisit the Grade 4 standards addressing equivalence. When equivalent, fractions represent the same amount of area of a rectangle and the same point on the number line. These equivalencies can also be represented symbolically.
In Topic B, students add and subtract fractions with unlike denominators by replacing different fractional units with an equivalent fraction or like unit. Throughout the module, a concrete to pictorial to abstract approach is used to convey this simple concept. This topic primarily uses the rectangular fractional model because it is useful for creating smaller like units by means of partitioning (e.g., thirds and fourths are changed to twelfths to create equivalent fractions as in the diagram below).
Topic C also uses the number line when adding and subtracting fractions greater than or equal to 1 so that students begin to see and manipulate fractions in relation to larger whole numbers and to each other. The number line allows the students to pictorially represent larger whole numbers. For example, “Between which two whole numbers does the sum of 1 and 3/4 and 5 and 3/5 lie?”
In Topic D, students strategize to solve multi-term problems and more intensely assess the reasonableness of their solutions to equations and word problems with fractional units.
In Topic D, students strategize to solve multi-term problems and more intensely assess the reasonableness of their solutions to equations and word problems with fractional units.