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.
Glossary Entries
- common denominatorThe same denominator in two or more fractions. For instance, \(\frac{1}{4}\) and \(\frac{5}{4}\) have a common denominator.
- composite numberA whole number with more than 1 factor pair.
- denominatorThe bottom part of a fraction that tells how many equal parts the whole was partitioned into.
- equivalent fractionsFractions that have the same size and describe the same point on the number line. For example, \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent fractions.
- factor pair of a whole numberA pair of whole numbers that multiply to result in that number. For example, 5 and 4 are a factor pair of 20.
- mixed numberA number expressed as a whole number and a fraction less than 1.
- multiple of a numberThe result of multiplying that number by a whole number. For example, 18 is a multiple of 3, because it is a result of multiplying 3 by 6.
- numerator
The top part of a fraction that tells how many of the equal parts are being described.
- prime numberA whole number that is greater than 1 and has exactly one factor pair: the number itself and 1.