Adding Fractions with Unlike Denominators Using Equivalent Fractions

Adding Fractions with Unlike Denominators Using Equivalent Fractions

Grade 5 · Math · NYS NY-5.NF.1 · 55 Minutes

Math Teacher Review Pilot: This resource is eligible for review by a NYS-certified Mathematics teacher.

NYS-Aligned Standard

NY-5.NF.1 — Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. NYS Next Generation Mathematics Learning Standards (2017)

Learning Objectives — “I Can” Statements

• I can explain why you can only add fractions when the denominators are the same.
• I can find equivalent fractions using the least common denominator (LCD).
• I can add fractions with unlike denominators by renaming them with a common denominator.
• I can add mixed numbers with unlike denominators.

Essential Question

Why can’t you add fractions with different denominators until you rename them?

Lesson Sequence

Hook / Warm-Up (8 minutes)

1. Present: “½ cup of sugar + ⅓ cup of sugar. How much sugar do you have?” Let students estimate or guess.
2. Show a fraction bar model: ½ and ⅓ both visually — “Do the pieces look the same?”
3. Ask: “Why can’t we just say 1/2 + 1/3 = 2/5?” (The pieces are different sizes — we’d be adding unlike units.)
4. Bridge: “Before we can add, we need to rename both fractions to use the SAME size pieces.”

Direct Instruction (15 minutes)

1. Step 1 — Find the LCD: “½ and ⅓. Multiples of 2: 2, 4, 6, 8. Multiples of 3: 3, 6, 9. LCD = 6.”
2. Step 2 — Rename: ½ = 3/6 (multiply top and bottom by 3). ⅓ = 2/6 (multiply by 2).
3. Step 3 — Add: 3/6 + 2/6 = 5/6.
4. Check with fraction bar: draw a bar split into sixths; shade 3/6 and 2/6; total = 5/6. ✓
5. Model ¾ + ⅔: LCD = 12; 9/12 + 8/12 = 17/12 = 1 5/12.
6. Mixed numbers: 2¾ + 1⅓: convert to improper fractions OR add whole numbers and fractions separately.

Guided Practice (12 minutes)

1. Class works through 2/3 + 1/4 together on whiteboards:
   • LCD? (12) → 8/12 + 3/12 = 11/12
2. Pairs try: ½ + 2/5 (LCD = 10; 5/10 + 4/10 = 9/10)
3. Teacher projects student work; discuss: “Did anyone get a different LCD? Does it still work?”

Independent Practice (12 minutes)

Students solve the 5-problem practice set:

1. 1/3 + 1/4
2. 2/5 + 3/10
3. 5/6 + 1/4
4. 1½ + 2⅓ (mixed numbers)
5. 3¾ + 1⅝ (challenge)

For each problem: show the LCD, show renamed fractions, show the sum (simplified or as mixed number).

Closure (8 minutes)

1. Return to the hook question: “½ + ⅓ — now can you solve it? What is the LCD?”
2. Exit ticket: “Add 3/4 + 2/3. Show each step: LCD → renamed fractions → sum.”

SDI & Differentiation Block

Supports for MLLs/ELLs

Entering/Emerging (NYSESLAT Levels 1–2):

• Fraction vocabulary card with visuals: numerator (top number), denominator (bottom number), equivalent (same value), sum (answer to addition)
• Provide fraction bar manipulatives or pre-printed fraction strips
• Reduce to simpler unlike denominators with smaller LCDs (e.g., 1/2 + 1/4, LCD = 4)
• Sentence frame: “The LCD of ___ and ___ is ___. I renamed the fractions as ___ and ___. The sum is ___.”

Transitioning/Expanding (NYSESLAT Levels 3–4):

• Provide a step-by-step “fraction addition algorithm” card at desk
• Pre-teach LCD strategy the day before with a visual anchor
• Academic vocabulary: denominator, numerator, equivalent, least common multiple, simplify

Supports for Students with IEPs

SDI Adaptation Dimensions: content, methodology, delivery

• Content: Reduce to fractions with denominators that are multiples of each other (e.g., 1/2 + 1/4 — only need to rename one); limit to 3 problems; skip mixed numbers
• Methodology: Use fraction strips physically; provide a filled-in LCD table so student only needs to rename and add; use color-coding (numerators in blue, denominators in red)
• Delivery: Allow calculator for multiplication when finding equivalent fractions; provide a reference card showing LCD strategy with worked example; allow extended time per IEP

Suggested Placement: ICT, Resource Room

Suggested IEP Goal Reference (Teacher Reference Only — Not Legal Advice): Given fraction addition problems with a visual fraction bar and a step-by-step algorithm card, the student will correctly identify the LCD and rename fractions with 80% accuracy across 4 of 5 problems, supporting progress toward NY-5.NF.1.

Extensions for Advanced Learners

• Subtract fractions with unlike denominators (extension of NY-5.NF.1)
• Add three fractions with unlike denominators
• Explore “why does the LCD give the simplest answer?” compared to using any common multiple

Answer Key

1. 1/3 + 1/4: LCD=12; 4/12 + 3/12 = 7/12
2. 2/5 + 3/10: LCD=10; 4/10 + 3/10 = 7/10
3. 5/6 + 1/4: LCD=12; 10/12 + 3/12 = 13/12 = 1 1/12
4. 1½ + 2⅓: 1 3/6 + 2 2/6 = 3 5/6
5. 3¾ + 1⅝: 3 6/8 + 1 5/8 = 4 11/8 = 5 3/8 Exit ticket: 3/4 + 2/3: LCD=12; 9/12 + 8/12 = 17/12 = 1 5/12

Alignment Record