Primary Standards:
MAFS.4.NF.2.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
- Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
- Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.
- Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
- Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
MAFS.4.MD.2.4: Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
Content Knowledge:
In this Unit, students will begin to apply their understanding of operations to add and subtract fractions. Addition and subtraction of fractions with like denominators can easily be solved by using an algorithm – adding or subtracting the numerators and keeping the same denominator – but being able to get an answer using that algorithm does not mean that our students understand what they are doing. (And will develop misunderstanding when students work with operations of fractions with unlike denominators in 5th grade)
Concrete materials should be used to introduce work with fractions prior to moving to the algorithm so that students understand why they add or subtract the numerators when working with fractions with the same denominator. Through creating, observing, and discussing models, students discover the simple way to add and subtract fractions. Estimation should also be used to check the reasonableness of answers.
As students add and subtract, they will also learn to decompose fractions in flexible ways. They will begin by decomposing into multiple groups of unit fractions, e.g. 3/8 = 1/8 + 1/8 + 1/8 and can then explore the varied ways a fraction can be broken apart, e.g. 5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 or 4/6 + 1/6 or 2/6 + 3/6, etc. Students will also record these decompositions using equations, and justify using models why the decompositions are equivalent.
In 3rd grade, students created and interpreted data from line plots using whole units as well as halves and fourths. Students in this Unit will apply their work with addition and subtraction of fractions with like denominators to solve word problems involving data from line plots.
GCG 1 – Learning Goal: As a mathematician, I can decompose fractions and mixed numbers in different ways
- Step 1: Model decomposing fractions as combinations of fractions, record using addition notation
- Step 2: Decompose fractions in various ways, record using addition notation
- Step 3: Identify fractions equal to wholes and decompose mixed numbers in various ways, record using addition notation
GCG 2 – Learning Goal: As a mathematician, I can represent addition and subtraction of fractions with concrete and pictorial models
- Step 1: Represent and solve problems involving addition and subtraction of fractions using concrete models
- Step 2: Represent and solve problems involving addition and subtraction of fractions using drawings
- Step 3: Represent and solve problems involving addition and subtraction of fractions using number lines
GCG 3 – Learning Goal: As a mathematician, I can represent addition and subtraction of mixed numbers with concrete and pictorial models
- Step 1: Represent and solve problems involving addition and subtraction of mixed numbers using concrete models
- Step 2: Represent and solve problems involving addition and subtraction of mixed numbers using drawings
- Step 3: Represent and solve problems involving addition and subtraction of mixed numbers by regrouping wholes
GCG 4 – Learning Goal: As a mathematician, I can create line plots involving fractional measurements and solve simple word problems
- Step 1: Record and interpret data on a line plot (with fractional measures) using halves, fourths, and eighths
- Step 2: Record and interpret data on a line plot (with mixed number measures) using halves, fourths, and eighths
- Step 3: Solve problems involving addition and subtraction of fractions and mixed numbers using data from line plots