Teaching Addition and Subtraction of Fractions in 5th Grade Small Groups

Fractions can only be combined once students see that they refer to same-sized parts. This guide builds common-denominator reasoning from equivalent fractions and visual models, so "find the LCD" grows out of understanding rather than replacing it.

Direct Answer

Adding and subtracting fractions with unlike denominators means combining or comparing parts that are currently different sizes. Before students can add 1/3 and 1/4, those pieces need to be rewritten as parts of the same size — a common unit — using equivalent fractions. Students need to understand that a fraction's denominator tells you how big each piece is, not just a number to manipulate. The teacher's job is to keep that idea visible: every time a common denominator is found, connect it back to "these pieces are now the same size, so we can combine them." A common 5th grade instructional focus is building this reasoning with visual models before moving toward more efficient procedures, and specific grade-level expectations and number ranges vary by state and curriculum.

Where This Skill Fits

Equivalent fractions and comparing fractions (4th grade) → Adding and subtracting fractions with unlike denominators using common-unit reasoning (5th grade) → Multiplying and dividing fractions, and fraction operations with mixed numbers (5th grade)

Prerequisite Skills

Essential:

Generating equivalent fractions (understanding why multiplying numerator and denominator by the same number doesn't change the value)
Comparing fractions with unlike denominators
Understanding a fraction's denominator as the size of the piece, and the numerator as how many pieces

Helpful but not required:

Fluency with multiplication facts, which speeds up finding a common denominator
Familiarity with mixed numbers and improper fractions

Common Student Thinking / Misconceptions

Student may think: "1/3 + 1/4 = 2/7 — I just add the tops and add the bottoms."

What this may reveal: The student may be treating the numerator and denominator as two separate whole numbers rather than as a single value describing part of a whole. This is one of the most common fraction-addition errors and often persists even after students can find common denominators in isolation.

Possible teacher response: Return to a visual model — show 1/3 and 1/4 as fraction strips and ask the student to combine them physically. Ask, "What would 2/7 mean here? Are the pieces the same size?" This is worth linking explicitly to the Adding the Numerator and Denominator misconception, since it can resurface even after a student demonstrates the correct procedure once.

Student may think: "1/8 is bigger than 1/4 because 8 is a bigger number."

What this may reveal: The student may be applying whole-number reasoning to the denominator instead of recognizing that a larger denominator means smaller pieces. This can interfere with judging whether a common-denominator rewrite is reasonable. See Bigger Denominator Means Bigger Fraction.

Possible teacher response: Compare the two fractions with fraction strips side by side and ask the student to point to the larger piece.

Student may think: "I need to find the LCD, but I don't know why — I just multiply the bottoms."

What this may reveal: The student may have learned a procedure without the underlying reason: that both fractions need to be described in the same-size pieces before they can be combined. This can work for simple problems but tends to break down with three or more fractions, or when a smaller common denominator would make the work easier.

Possible teacher response: Ask, "Why do we need the same denominator before we add?" and have the student explain using a visual model before returning to the numeric shortcut.

Student may think: "After I subtract, I don't need to simplify — 4/8 and 1/2 aren't the same thing."

What this may reveal: The student may not yet see equivalent fractions as different names for the same value, which connects back to the 4th grade prerequisite skill.

Possible teacher response: Show both fractions on the same fraction strip model and ask what the student notices.

Visual Models

Fraction Strips — useful for physically lining up pieces of different sizes and seeing why they can't be combined until they're the same size. A limitation is that fraction strips become harder to draw precisely as denominators grow (e.g., sevenths or ninths), so they work best for introducing the concept rather than for every problem.
Fraction Area Models — useful for showing equivalent fractions by subdividing the same shape, which makes the "same-size pieces" idea concrete. A limitation is that area models can get visually cluttered with larger denominators or mixed numbers, and some students find them harder to read precisely than a linear strip.

Small-Group Teaching Sequence (about 15–30 minutes)

Activate Prior Knowledge (2–4 min): Ask students to name a fraction equivalent to 1/2 and explain how they know, to bring equivalent-fraction reasoning back to the surface.
I Do (4–6 min): Model rewriting two fractions with unlike denominators as same-size pieces using fraction strips, then combine them.
We Do (5–8 min): Guide students through one or two problems together, asking questions that keep the "same-size pieces" reasoning visible.
You Do (4–8 min): Students try problems independently, with fraction strips or area models available if needed.
Quick Check (2–3 min): One problem to gauge whether the reasoning, not just the steps, has taken hold.

I Do Example

Problem: 1/3 + 1/4

The teacher draws a fraction strip divided into thirds and shades one part, then a second strip divided into fourths and shades one part. "These two pieces are not the same size, so I can't combine them yet — I need to rename them using a common unit." The teacher subdivides the thirds strip into twelfths (3 × 4) and the fourths strip into twelfths (4 × 3), showing 1/3 = 4/12 and 1/4 = 3/12. "Now every piece on both strips is the same size — a twelfth — so I can combine them: 4/12 + 3/12 = 7/12." The teacher writes the notation step by step: 1/3 + 1/4 = 4/12 + 3/12 = 7/12, emphasizing the language "same-size pieces" and "common unit" throughout rather than just "common denominator."

We Do Example

Problem 1: 2/5 + 1/2. "What size are the pieces in each fraction right now? Are they the same size? What common unit could we rename both fractions with?" Guide students to rewrite as 4/10 + 5/10 = 9/10.

Problem 2: 3/4 − 1/6. "Before we subtract, what do these fractions need first?" Guide students to rename using twelfths: 9/12 − 2/12 = 7/12.

You Do Example

1/2 + 1/5
2/3 − 1/4
3/8 + 1/4
5/6 − 1/3

Quick Check

Ask the student to solve 1/4 + 1/6 and explain, in their own words, why the denominators had to change before adding. If understanding is demonstrated → move toward mixed numbers and more efficient common-denominator strategies. If not yet secure → return to fraction strips with smaller, more familiar denominators (like halves, thirds, and fourths) before reintroducing the notation.

If Students Are Ready

Extend to adding and subtracting mixed numbers with unlike denominators, and begin connecting this reasoning to multiplying and dividing fractions.

If Students Need More Support

Return to fraction strips or area models with denominators that are more familiar (halves, thirds, fourths) rather than moving to numeric-only work. Revisit generating equivalent fractions as a standalone skill before combining it with addition or subtraction, and keep the teacher prompt "are these pieces the same size?" present at every step.

Related Skills

Before: Equivalent Fractions and Compare Fractions (4th grade)
Current: Adding and subtracting fractions with unlike denominators using common-unit reasoning
Next: 5th Grade Fractions, including multiplying and dividing fractions

Related Misconceptions

Related Visual Models

Relevant SMS Resources

Browse more 5th grade fraction routines in the full catalog.

Teacher FAQ

Should I teach "find the LCD" as the first step?

Not before students understand why they need it. Introduce common-denominator work through visual models first, then connect it to the more efficient numeric procedure once the reasoning is solid.

Do students need to use the least common denominator, or can they use any common denominator?

Any common denominator works mathematically; the least common denominator just keeps the numbers smaller and often makes simplifying easier. It's reasonable to accept a larger common denominator from a student who reasons correctly, and revisit efficiency later.

What if a student can find common denominators but still can't explain why?

That's worth treating as a sign to slow down. A student who can complete the steps without understanding the reasoning often struggles when the numbers get harder or the context changes.

How does this connect to comparing fractions from 4th grade?

Comparing fractions with unlike denominators already requires rewriting fractions with a common unit. If that skill is shaky, it's often worth a quick review before introducing addition and subtraction.

Should mixed numbers be introduced at the same time?

It's generally more effective to secure the common-unit reasoning with simple fractions first, then extend to mixed numbers once that foundation is steady.