Grade 4: Composing and Decomposing Fractions for Addition and Subtraction


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Number and Operations-Fractions

4.NF.B.3(a) Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

4.NF.B.3(b) 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. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

4.NF.B.3(c) 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.

4.NF.B.3(d) 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.

Standards for Mathematical Practice

MP.2  Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.4  Model with mathematics.

MP.7  Look for and make use of structure.


This 4th grade unit titled “Composing and Decomposing Fractions for Addition and Subtraction- Unit 3” from LearnZillion is made up of twelve 40-50 minute lessons. In this unit, students extend their understanding of partitioning wholes into unit fractions, and then use those unit fractions to compose and decompose fractions. They apply this understanding to the addition and subtraction of fractions and mixed numbers. Models and representations used in this unit include area models, bar models and number lines. Students also use various real-world tools and models including rulers, jars, and miniature obstacle courses. In the final lesson, students apply their knowledge and understanding of decomposition of mixed numbers to a real-life situation and explicitly engage in MP 3 and 4. The unit has a 13-item summative assessment with open-ended response questions.


Connecticut educators are cautioned that prior to teaching the lesson, they should thoroughly review the materials and make modifications or adjustments to meet the needs of their learners and to determine proper pacing. Prior knowledge required of students is noted in the unit materials.


This unit is a good example of a progression of learning where concepts and skills advance and deepen over time. Instruction reflects evidence of the key shifts required by the CCSS and targets the major work of the grade. Tasks, assessments and guidance provide support for teachers in differentiation and facilitate the use of multiple representations. An answer key with guidance for interpreting students’ answers to drive future instruction is included.