Objective
Students will be able to add and subtract fractions with unlike denominators by finding common denominators. Students will solve at least 8 out of 10 fraction addition and subtraction problems correctly on an exit ticket, including at least 2 word problems.
Standards
- CCSS.MATH.CONTENT.5.NF.A.1 — Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions.
- CCSS.MATH.CONTENT.5.NF.A.2 — Solve word problems involving addition and subtraction of fractions.
Materials
- Fraction strips (physical or printed, 1 set per student)
- Whiteboard and marker per student
- Anchor chart: "Steps for Adding Fractions with Unlike Denominators"
- Practice worksheet (10 problems)
- Word problem cards (6 cards)
- Exit ticket (10 problems)
Warm-Up (5 minutes)
Write on the board: 1/4 + 1/4 = ? and 2/5 + 1/5 = ?. Students solve on whiteboards. Review: when denominators are the same, we just add the numerators. Then write: 1/3 + 1/4 = ?. Ask: "Can we just add 1 + 1 and 3 + 4?" (No — that gives 2/7, which is wrong.) "Why not?" Because the pieces are different sizes — thirds and fourths. Today we learn how to add fractions when the denominators are different.
Direct Instruction (12 minutes)
Model the problem 1/3 + 1/4 step by step. Build the anchor chart as you go:
Step 1: Find a common denominator. List multiples of 3 (3, 6, 9, 12, 15...) and multiples of 4 (4, 8, 12, 16...). The least common multiple (LCM) is 12.
Step 2: Create equivalent fractions. 1/3 = ?/12. Since 3 x 4 = 12, multiply both numerator and denominator by 4: 1/3 = 4/12. Similarly, 1/4 = ?/12. Since 4 x 3 = 12, multiply both by 3: 1/4 = 3/12.
Step 3: Add the numerators. 4/12 + 3/12 = 7/12.
Step 4: Simplify if possible. 7/12 is already in simplest form.
Use fraction strips to verify: lay out the 1/3 strip and the 1/4 strip, then show that together they match the length of 7/12. This visual confirmation builds conceptual understanding.
Model a subtraction problem: 3/4 - 1/6. LCM of 4 and 6 is 12. 3/4 = 9/12, 1/6 = 2/12. 9/12 - 2/12 = 7/12. Model one more problem with an answer that needs simplifying: 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3.
Guided Practice (10 minutes)
Write 4 problems on the board. Students solve each independently on whiteboards, then hold up their answers:
- 1/2 + 1/3 (LCD = 6, answer: 5/6)
- 3/4 - 1/2 (LCD = 4, answer: 1/4)
- 2/5 + 1/4 (LCD = 20, answer: 13/20)
- 5/6 - 1/3 (LCD = 6, answer: 3/6 = 1/2)
After each problem, call on a student to walk through their steps. Address the most common errors: forgetting to multiply the numerator when creating equivalent fractions, and adding denominators instead of keeping the common denominator.
Independent Practice (10 minutes)
Students complete a worksheet with 10 problems: 6 computation problems (mix of addition and subtraction with unlike denominators) and 4 word problems. Example word problems:
- "Sarah ran 3/4 of a mile on Monday and 1/3 of a mile on Tuesday. How far did she run in total?"
- "A recipe calls for 2/3 cup of flour. Marco has already added 1/4 cup. How much more flour does he need?"
Students may use fraction strips as a tool but should show their steps numerically. Early finishers check their work with a partner and explain any differences.
Assessment
- Formative: Monitor whiteboard responses during guided practice. Check for correct LCM identification and accurate equivalent fraction conversions.
- Summative: Exit ticket with 10 problems (7 computation, 3 word problems). Target: 8 out of 10 correct. Students below target join a small reteaching group.
Differentiation
- Struggling learners: Limit to denominators of 2, 3, 4, and 6 (easier LCMs). Provide a multiplication chart for finding LCMs. Allow fraction strips for all problems. Use a step-by-step checklist they follow for each problem.
- ELL students: Pre-teach vocabulary: numerator, denominator, equivalent, least common denominator, simplify. Use visual diagrams alongside word problems. Simplify word problem language and include pictures. Provide sentence frames for explaining steps.
- Advanced learners: Include mixed numbers (e.g., 2 1/3 + 1 1/4). Add problems requiring simplification of improper fractions. Challenge them to create their own word problems and trade with a partner. Introduce problems with 3 fractions being added.
- Students with IEPs: Provide a printed step-by-step reference card. Allow use of a calculator for multiplication facts when finding LCMs. Reduce the worksheet to 6 problems (4 computation, 2 word problems). Offer graph paper to organize work neatly.
Closure (3 minutes)
Ask: "What is the most important step when adding fractions with different denominators?" (Finding a common denominator.) "Why can we not just add the denominators?" (Because the fractions are different sizes — we need equal-sized pieces to add them.) Give a quick "thumbs up, sideways, down" check: How confident are you with adding and subtracting fractions? Preview tomorrow's lesson on adding and subtracting mixed numbers.