4.3 Extending Operations to Fractions

Unit Goals

• Students learn that a fraction $\frac{a}{b}$ is a product of a whole number $a$ and a unit fraction $\frac{1}{b}$, or $\frac{a}{b} = a \times \frac{1}{b}$, and that $n \times \frac{a}{b} = \frac{(n \space \times \space a)}{b}$. Students learn to add and subtract fractions with like denominators, and to add and subtract tenths and hundredths.

Section A Goals

• Recognize that $n \times \frac{a}{b} = \frac{(n \space \times \space a)}{b}$.
• Represent and explain that a fraction $\frac{a}{b}$ is a multiple of $\frac{1}{b}$, namely $a \times \frac{1}{b}$.
• Represent and solve problems involving multiplication of a fraction by a whole number.

Section B Goals

• Create and analyze line plots that display measurement data in fractions of a unit ($\frac18, \frac14, \frac12$).
• Represent and solve problems that involve the addition and subtraction of fractions and mixed numbers, including measurements presented in line plots.
• Use various strategies to add and subtract fractions and mixed numbers with like denominators.

Section C Goals

• Reason about equivalence to add tenths and hundredths.
• Reason about equivalence to solve problems involving addition and subtraction of fractions and mixed numbers.