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LESSON SNAPSHOT

Lesson Title: Making the Denominators Match
Grade Level: 5th Grade
Topic: Adding Fractions with Unlike Denominators
Total Instructional Time: 45 minutes
Standard/Alignment: CCSS.MATH.CONTENT.5.NF.A.1 — This lesson addresses adding fractions with unlike denominators by using equivalent fractions to create common denominators.

Prerequisite Skills

Students should already be able to:

Identify the numerator and denominator of a fraction.

Generate simple equivalent fractions.

Add fractions with like denominators.

Materials and Teacher Preparation

Whiteboard or chart paper

Markers

Student paper or math notebooks

Pencils

Optional: fraction strips or fraction circles

Optional: multiplication chart for students who benefit from support

Teacher preparation:
Write the hook problem and independent-work problems on the board or prepare copies. Have fraction strips available if using manipulatives.

Key Academic Vocabulary

Numerator: The top number in a fraction; it tells how many parts are being used.

Denominator: The bottom number in a fraction; it tells how many equal parts make one whole.

Equivalent fractions: Fractions that name the same amount, such as 1/2 and 2/4.

Common denominator: A denominator shared by two or more fractions.

Simplify: Write a fraction in an equivalent form using smaller numbers when possible.

LEARNING OBJECTIVE

By the end of the lesson, students will be able to add two fractions with unlike denominators by creating equivalent fractions with a common denominator and correctly simplify the sum when appropriate.

Student-Friendly “I Can” Statement

I can add fractions with different denominators by finding a common denominator and using equivalent fractions.

Success Criteria

Students will:

Identify or create an appropriate common denominator.

Rewrite both fractions as equivalent fractions when needed.

Add the numerators while keeping the common denominator.

Simplify the final answer when possible.

SIX CORE LESSON SECTIONS
1. HOOK — 5 minutes
Teacher Action

Display:

Maya ate 1/2 of a small pizza at lunch and 1/4 of the same-size pizza later. How much pizza did she eat altogether?

Ask students to think silently for about 20 seconds, then discuss with a partner.

Draw a simple rectangle or circle divided into fourths if students need a visual.

Student Action

Students:

Think about the problem.

Discuss possible strategies with a partner.

Share how they might combine 1/2 and 1/4.

Opening Question

“Can we add 1/2 + 1/4 immediately, or do we need to change something first?”

Teacher Looks/Listens For

Listen for students who recognize that:

The denominators are different.

1/2 can be renamed as 2/4.

2/4 + 1/4 = 3/4.

Do not require every student to already know the procedure. Use responses to transition into instruction.

2. DIRECT INSTRUCTION — 10 minutes
Essential Concept

Fractions can only be added directly when they refer to pieces of the same size.

The denominator tells the size of the pieces. When denominators differ, students first rename the fractions using equivalent fractions so both fractions have the same denominator.

Suggested Teacher Language

“Imagine adding pieces of pizza. One piece that is half a pizza is not the same size as one piece that is one-fourth of a pizza. Before we count the pieces together, we need to describe them using pieces of the same size.”

Write:

1/2 + 1/4

Explain:

“The denominators are 2 and 4. We need a common denominator.”

Because fourths can represent both fractions:

1/2 = 2/4

Now:

2/4 + 1/4 = 3/4

Reinforce:

“When the denominators match, we add the numerators. We do not add the denominators.”

Fully Worked Example

Solve:

2/3 + 1/4

Step 1: Find a common denominator.

Multiples of 3:

3, 6, 9, 12, 15...

Multiples of 4:

4, 8, 12, 16...

A common denominator is 12.

Step 2: Rewrite each fraction.

For 2/3:

3 × 4 = 12, so multiply both numerator and denominator by 4.

2/3 = 8/12

For 1/4:

4 × 3 = 12, so multiply both numerator and denominator by 3.

1/4 = 3/12

Step 3: Add.

8/12 + 3/12 = 11/12

Correct Answer

2/3 + 1/4 = 11/12

Important Vocabulary Reinforcement

Point out:

12 is the common denominator.

8/12 and 3/12 are equivalent fractions.

Check for Understanding

Ask:

“Why can't we say 2/3 + 1/4 = 3/7?”

Expected student idea:

Because thirds and fourths are different-size pieces. The denominators must represent the same-size pieces before adding.

Also ask:

“Once our denominators match, which numbers do we add?”

Expected answer:

The numerators.

3. GUIDED PRACTICE — 10 minutes
Student Directions

“Work each problem with me. First identify a common denominator. Then rewrite the fractions as equivalent fractions, add, and simplify if needed.”

Problem 1 — Worked Together

1/3 + 1/6

Ask:

“What denominator could both fractions use?”

Expected response:

6

Rewrite:

1/3 = 2/6

Then:

2/6 + 1/6 = 3/6

Simplify:

3/6 = 1/2

Answer

1/2

Problem 2

3/4 + 1/8

Common denominator:

8

Equivalent fraction:

3/4 = 6/8

Add:

6/8 + 1/8 = 7/8

Answer

7/8

Problem 3

2/5 + 1/2

Common denominator:

10

Equivalent fractions:

2/5 = 4/10

1/2 = 5/10

Add:

4/10 + 5/10 = 9/10

Answer

9/10

Problem 4

1/6 + 3/4

Common denominator:

12

Equivalent fractions:

1/6 = 2/12

3/4 = 9/12

Add:

2/12 + 9/12 = 11/12

Answer

11/12

Teacher Questioning Prompts

Ask during practice:

“What tells us that these fractions cannot be added immediately?”

“What number could both denominators become?”

“Whatever we do to the denominator, what must we also do to the numerator?”

“How do you know your new fraction is equivalent to the original?”

“Do we need to simplify this answer?”

Check for Understanding

After Problem 3, have students show a thumbs-up, sideways thumb, or thumbs-down for:

“I can explain why 2/5 becomes 4/10.”

Ask one or two students to explain:

“Because 5 × 2 = 10, we multiply both 2 and 5 by 2.”

If Students Are Struggling

Pause before Problem 4.

Use fraction strips or draw models showing, for example:

1/2 = 2/4

Then emphasize the rule:

Multiply the numerator and denominator by the same number.

Provide students with multiples lists:

2: 2, 4, 6, 8, 10, 12

3: 3, 6, 9, 12

4: 4, 8, 12

5: 5, 10, 15

6: 6, 12, 18

4. INDEPENDENT WORK — 10 minutes
Student Directions

“Complete each problem independently. Show the equivalent fractions you create before adding. Simplify your answer when possible.”

Problems

1/2 + 1/6

2/3 + 1/6

3/5 + 1/4

2/3 + 3/8

1/4 + 5/6

Answer Key
1. 1/2 + 1/6

1/2 = 3/6

3/6 + 1/6 = 4/6

Answer: 2/3

2. 2/3 + 1/6

2/3 = 4/6

4/6 + 1/6 = 5/6

Answer: 5/6

3. 3/5 + 1/4

Common denominator: 20

3/5 = 12/20

1/4 = 5/20

12/20 + 5/20 = 17/20

Answer: 17/20

4. 2/3 + 3/8

Common denominator: 24

2/3 = 16/24

3/8 = 9/24

16/24 + 9/24 = 25/24

Answer: 25/24 or 1 1/24

Accept either form if improper fractions have already been established in class.

5. 1/4 + 5/6

Common denominator: 12

1/4 = 3/12

5/6 = 10/12

3/12 + 10/12 = 13/12

Answer: 13/12 or 1 1/12

Accept either form if improper fractions have already been established in class.

What Successful Work Should Demonstrate

Students should:

Find a valid common denominator.

Produce equivalent fractions correctly.

Add numerators accurately.

Keep the common denominator.

Simplify when appropriate.

For students who have not yet worked extensively with improper fractions or mixed numbers, Problems 4 and 5 may remain as improper fractions.

5. EXIT TICKET — 6 minutes

Students complete independently.

Question 1

Solve:

1/3 + 1/4

Show your equivalent fractions.

Answer

Common denominator: 12

1/3 = 4/12

1/4 = 3/12

4/12 + 3/12 = 7/12

Question 2

Solve:

3/5 + 1/10

Answer

3/5 = 6/10

6/10 + 1/10 = 7/10

Question 3

A student writes:

1/2 + 1/3 = 2/5

Explain what the student did incorrectly and describe what should be done instead.

Expected Response

The student incorrectly added the denominators.

The fractions must first be rewritten with a common denominator.

For example:

1/2 = 3/6

1/3 = 2/6

3/6 + 2/6 = 5/6

Interpretation Rule

Ready to move on:
Correctly solves both computation problems and gives an accurate explanation for Question 3.

Needs brief review:
Correctly completes two of the three questions or shows the correct process with one minor calculation error.

Needs reteaching:
Cannot consistently create equivalent fractions with a common denominator or continues adding denominators.

6. OBJECTIVE / CLOSURE CHECK — 4 minutes

Return to the objective:

“By the end of the lesson, students will be able to add two fractions with unlike denominators by creating equivalent fractions with a common denominator and correctly simplify the sum when appropriate.”

Student Reflection

Ask students to complete this statement verbally with a partner:

“When two fractions have different denominators, the first thing I should do is ______ because ______.”

Expected response should communicate:

Find or create a common denominator because the fractions need to represent equal-size parts before they can be added.

Teacher Prompt

“What steps could you give another fifth grader who does not know how to add 2/3 + 1/4?”

Listen for students to describe:

Find a common denominator.

Create equivalent fractions.

Add the numerators.

Keep the common denominator.

Simplify when needed.

Evidence of Meeting the Success Criteria

Students demonstrate mastery when they can independently:

Find an appropriate common denominator.

Write correct equivalent fractions.

Add accurately.

Simplify the result when appropriate.

Explain why denominators must match.

DIFFERENTIATION
Students Needing Additional Support

Provide fraction strips or fraction circles so students can physically compare equivalent fractions.

Give a multiplication chart or short multiples list to help locate common denominators.

Use a four-step organizer:

1. Find common denominator → 2. Rename fractions → 3. Add → 4. Simplify

Begin with problems where one denominator is a multiple of the other, such as 1/2 + 1/4.

Reduce the independent task from five problems to three while keeping the same core skill.

Highlight the numerator and denominator in different ways on the board to emphasize their roles.

Students Ready for an Extension

Ask students to:

Solve problems where neither denominator is a multiple of the other.

Compare two possible common denominators and decide which is more efficient.

Create their own unlike-denominator addition problem with an answer greater than 1.

Explain why different common denominators can still lead to equivalent correct answers.

Example extension:

“Could you solve 1/3 + 1/4 using 24 as the common denominator instead of 12? Would the final value change? Explain.”

Expected reasoning:

1/3 = 8/24 and 1/4 = 6/24.

8/24 + 6/24 = 14/24 = 7/12.

The value does not change.

English Learners / Students Who Benefit From Language Scaffolds

Pair mathematical vocabulary with visuals.

Point to the top and bottom of a written fraction when saying numerator and denominator.

Display vocabulary throughout the lesson.

Provide sentence stems:

“The common denominator is ___ because ___.”

“I changed ___ into ___ by multiplying the numerator and denominator by ___.”

“These fractions can now be added because ___.”

Allow students to explain the process using drawings, numbers, gestures, or short verbal responses before requiring a complete written explanation.

COMMON MISCONCEPTIONS
Misconception 1: Adding Both Numerators and Denominators

Example:

1/2 + 1/3 = 2/5

How to Recognize It

Students consistently add the top numbers and bottom numbers.

Correction

Use a visual model showing halves and thirds as different-size pieces.

Say:

“The denominator names the size of the pieces. We can't combine different-size pieces until we rename them as equal-size pieces.”

Misconception 2: Changing Only the Denominator

Example:

A student changes:

1/3 into 1/6

instead of:

2/6

How to Recognize It

The denominator changes but the numerator remains unchanged.

Correction

Emphasize:

“Whatever you multiply the denominator by, multiply the numerator by the same number.”

Show:

1/3 × 2/2 = 2/6.

Explain that multiplying by 2/2 is multiplying by 1, so the value does not change.

Misconception 3: Adding Before Finding a Common Denominator

Example:

Students begin combining fractions despite unlike denominators.

How to Recognize It

Students start adding numerators immediately without checking the denominators.

Correction

Teach the quick self-check:

“Look down before you add up.”

Students check the denominators first.

If they are different, create equivalent fractions before adding.

Misconception 4: Forgetting to Simplify

Example:

Student leaves:

4/6

instead of:

2/3

How to Recognize It

The addition procedure is correct but the final fraction can still be reduced.

Correction

Add a final question to the routine:

“Can both numbers be divided by the same whole number greater than 1?”

If yes, simplify.

Lesson Plan Check
Section	Minutes
Hook	5
Direct Instruction	10
Guided Practice	10
Independent Work	10
Exit Ticket	6
Objective / Closure Check	4
TOTAL	45

Time check: PASS — section times total exactly 45 minutes.

Objective check: PASS — exit ticket measures the stated objective.

Answer check: PASS — worked examples/practice answers were checked for internal consistency.

Grade-level check: PASS — language, task difficulty, workload, and pacing were designed for the stated grade.

I can also turn this into a matching student worksheet + teacher answer key if you want to test the prompt as a fuller classroom-product example.