Add and Subtract Fractions

Overview

In this eighth lesson of “Build, Model, Solve,” students use fraction strips, area models, and number lines to add and subtract fractions with like denominators. They connect repeated unit fractions to decomposing mixed numbers and apply these ideas to measurement and word problems.

Learning intentions

Students will be able to:

• Model fractions as sums of unit fractions.
• Add and subtract fractions with like denominators.
• Decompose mixed numbers in more than one way.
• Represent and solve fraction word problems using equations and visual models.

Success criteria

• I can show a fraction using strips, an area model, or a number line.
• I can add or subtract fractions with the same denominator and explain why the denominator stays the same.
• I can decompose a mixed number in more than one way.
• I can use an equation and a model to solve a word problem.

Curriculum links

• Understand fractions greater than one as sums of unit fractions.
• Decompose a fraction into sums of fractions with the same denominator and justify each equation with a visual model.
• Understand fraction addition and subtraction as joining and separating parts of the same whole.
• Solve word problems involving addition and subtraction of fractions with like denominators.

Lesson structure (60 minutes)

1. 0–7 min · Hook and retrieval. Display the opening fraction challenge: “A recipe uses 3/8 cup of oats and 2/8 cup of raisins. How much is that altogether?” Students sketch or build the problem with fraction strips, then share strategies. Review that the denominator names equal parts and the numerator counts parts.

2. 7–17 min · Model unit fractions. Use the visual modeling slides to show 5/6 as five copies of 1/6 on a strip, area model, and number line. Teacher records 5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 and then 5/6 = 2/6 + 3/6. Students build both decompositions with strips and explain how the models prove the equations.

3. 17–29 min · Add and subtract. Demonstrate 3/8 + 2/8 and 7/10 − 4/10 with a fraction strip and number line, emphasizing that only the number of same-sized parts changes. Students complete two examples on the fraction modeling and problem-solving worksheet, drawing a model before writing each equation. Pause for a check: students show with fingers whether the answer should be greater than or less than the first fraction.

4. 29–43 min · Collaborative problem solving. Place students in groups of four or five and assign roles using the group role cards. Distribute the fraction modeling and problem-solving worksheet. Groups solve three tasks: combine two measured lengths, find the amount remaining after subtraction, and represent one fraction in two decomposed forms. Require a strip, area model, or number line plus an equation and a written explanation for each task. Circulate, asking, “What is the whole?” and “How does your model match your equation?”

5. 43–53 min · Mixed numbers and discussion. Use the mixed-number and discussion slides to model 2 3/5 as 5/5 + 5/5 + 3/5 and as 1 + 1 + 3/5. Students solve 1 2/6 + 2 3/6 and explain one decomposition to a partner. Invite two groups to compare different but equivalent representations. Address the misconception that denominators are added when combining like-denominator fractions.

6. 53–60 min · Independent assessment and close. Students complete the final worksheet problem independently: “A trail is 4 3/8 miles long. Maya walks 2 5/8 miles. How much farther does she need to walk?” They must include an equation and a visual model. Finish with the success criteria exit ticket slips; students identify one criterion they met and explain one fraction model in words.

Resources

• the Build, Model, Solve fraction slide deck
• the fraction modeling and problem-solving worksheet
• Fraction strips or fraction tiles
• Blank number-line strips
• Grid paper and plain paper
• Pencils, colored pencils, and erasers
• Chart paper or whiteboard
• the group role cards
• the success criteria exit ticket slips

Assessment

• During modeling, check whether students represent the denominator as the number of equal parts and the numerator as the number selected.
• During group work, review models and equations for matching denominators, accurate operations, and a clearly identified whole.
• Use the independent problem and exit ticket to identify students who need additional practice with mixed-number decomposition or explaining their models.

Differentiation

• Support students with pre-partitioned fraction strips, color-coded numerator and denominator labels, and sentence frames: “I used ___ equal parts,” “I added/subtracted ___ parts,” and “My model proves ___.”
• Pair students strategically and allow students to explain orally before writing. Provide reduced-number examples, such as denominators of 4 or 6, for students needing additional scaffolding.
• For multilingual learners, preview terms such as equal parts, numerator, denominator, sum, difference, and remaining; connect each word to a model and gesture.
• Extend ready students by asking them to find three decompositions of a mixed number or create a new measurement problem with two valid solution representations.