MA19.4.15
Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.
Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.
UP:MA19.4.15
Vocabulary
- Decomposition
- Unit fraction
- Area model
- Length model
- Equation
- Mixed number
- Visual fraction model
- Whole
- Sum
- Difference
- Recomposition
Knowledge
Students know:
- Situation contexts for addition and subtraction problems.
- A variety of strategies and models to represent addition and subtraction situations.
- The fraction a/b is equivalent to the unit fraction 1/b being iterated or "copied" the number of times indicated by the numerator, a.
- A fraction can represent a whole number or fraction greater than 1 and can be illustrated by decomposing the fraction.
Example: 6/3 = 3/3 + 3/3 = 2 and 5/3 = 3/3 + 2/3 = 1 2/3.
Skills
Students are able to:
- Decompose fractions as a sum of unit fractions.
- Model decomposition of fractions as a sum of unit fractions.
- Add and subtract fractions with like denominators using properties of operations and the relationship between addition and subtraction.
- Solve word problems involving addition and subtraction using visual models, drawings, and equations to represent the problem.
Understanding
Students understand that:
- A unit fraction (1/b) names the size of the unit with respect to the whole and that the denominator tells the number of parts the whole is partitioned, and the numerator indicates the number of parts referenced.
- A variety of models and strategies can be used to represent and solve word situations involving addition and subtraction.
- The operations of addition and subtraction are performed with quantities expressed in like units, and the sum or difference retains the same unit.
