Mathematics 15. Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or separating parts referring to the same whole.
a. Decompose a fraction as a sum of unit fractions and as a sum of fractions with the same denominator in more than one way using area models, length models, and equations.
b. Add and subtract fractions and mixed numbers with like denominators using fraction equivalence, properties of operations, and the relationship between addition and subtraction.
c. Solve word problems involving addition and subtraction of fractions and mixed numbers having like denominators, using drawings, visual fraction models, and equations to represent the problem.
Unpacked Content
Evidence Of Student Attainment:
Students:
When given any fraction or mixed number, apply unit fraction understanding to decompose the given fraction or mixed number into the sum of smaller fractions, including unit fractions.
When given a problem solving situation involving addition and subtraction of fractions or mixed numbers with like denominators, explain and justify solutions using unit fractions, visual models, and equations involving a single unknown. Teacher 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.
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. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.4.15.1: Recognize that a whole can be partitioned into differing equal parts (halves, fourths, eighths, etc.).
M.4.15.2: Identify numerator and denominator.
M.4.15.3: Recall basic addition and subtraction facts.
M.4.15.4: Demonstrate an understanding of fractional parts.
M.4.15.5: Recall basic addition and subtraction facts.
M.4.15.6: Define mixed numbers.
M.4.15.7: Recall basic addition and subtraction facts.
M.4.15.8: Demonstrate an understanding of fractional parts.
M.4.15.9: Solve basic word problems using whole numbers.
M.4.15.10: Express parts of a whole as a fraction.
M.4.15.11: Write number sentences for word problems.
M.4.15.12: Identify key terms in word problems.
M.4.15.13: Recall basic addition and subtraction facts.
Prior Knowledge Skills:
Define fraction, numerator, and denominator.
Identify the parts of a fraction a/b as the quantity formed by a parts and size 1/b.
Label numerator, denominator, and fraction bar.
Identify parts of a whole with two, three, or four equal parts.
Distinguish between equal and non-qual parts.
Partition circles and rectangles into two and four equal shares; describe the shares using the words halves, fourths, and quarters; and use the phrases half of, fourth of, and quarter of.
Recognize fractions as lengths from zero to one.
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
Alabama Alternate Achievement Standards
AAS Standard:
