45-Minute Lesson Plan: Adding Fractions with Different Denominators
Subject: Mathematics
Grade: 5
Class size: 28 students, mixed levels
Topic: Adding fractions with different denominators
Time: 45 minutes
Learning Objectives
By the end of the lesson, students will be able to:
- Explain why fractions must have the same denominator before they can be added.
- Find a common denominator for two fractions with different denominators.
- Rewrite fractions as equivalent fractions with the common denominator.
- Add fractions with different denominators and simplify the answer when possible.
- Solve simple word problems involving addition of fractions with different denominators.
Key Vocabulary
- Fraction
- Numerator
- Denominator
- Equivalent fractions
- Common denominator
- Least common denominator
- Simplify / lowest terms
Materials
- Whiteboard or projector
- Fraction strips, fraction bars, or paper folding strips
- Worksheet with 6 questions
- Exit ticket slips
- Optional: colored markers for modeling
Lesson Procedure
1. Warm-Up: “Why Can’t We Just Add the Bottom Numbers?”
Time: 5 minutes
Teacher action:
Write on the board:
[ \frac{1}{2} + \frac{1}{3} ]
Ask students:
“Can we add this like (\frac{2}{5})? Why or why not?”
Give students 30 seconds to think, then ask 2–3 students to share.
Expected idea:
We cannot add denominators directly because the pieces are different sizes.
Quick model:
Use fraction strips or draw two rectangles: one divided into halves, one divided into thirds. Show that (\frac{1}{2}) and (\frac{1}{3}) are not the same size pieces.
Teacher statement:
“To add fractions, the pieces must be the same size. That means the denominators must be the same.”
2. Direct Instruction: Steps for Adding Fractions
Time: 10 minutes
Write the steps on the board:
- Look at the denominators.
- Find a common denominator.
- Rewrite each fraction as an equivalent fraction.
- Add the numerators.
- Keep the denominator the same.
- Simplify if possible.
Model one example:
[ \frac{1}{2} + \frac{1}{3} ]
Step 1: Denominators are 2 and 3.
Step 2: Common denominator could be 6.
Step 3: Rewrite:
[ \frac{1}{2} = \frac{3}{6} ]
[ \frac{1}{3} = \frac{2}{6} ]
Step 4: Add:
[ \frac{3}{6} + \frac{2}{6} = \frac{5}{6} ]
Step 5: Simplify? No.
Answer:
[ \frac{5}{6} ]
Model a second example with simplification:
[ \frac{1}{4} + \frac{1}{6} ]
Common denominator: 12.
[ \frac{1}{4} = \frac{3}{12} ]
[ \frac{1}{6} = \frac{2}{12} ]
[ \frac{3}{12} + \frac{2}{12} = \frac{5}{12} ]
Answer:
[ \frac{5}{12} ]
Model a third example where the answer needs simplifying:
[ \frac{1}{6} + \frac{1}{3} ]
Common denominator: 6.
[ \frac{1}{3} = \frac{2}{6} ]
[ \frac{1}{6} + \frac{2}{6} = \frac{3}{6} ]
Simplify:
[ \frac{3}{6} = \frac{1}{2} ]
3. Guided Practice: “Do It Together”
Time: 10 minutes
Write three problems on the board. Solve them with student participation.
- (\frac{1}{2} + \frac{1}{4})
- (\frac{2}{5} + \frac{1}{10})
- (\frac{1}{3} + \frac{1}{6})
Ask students to:
- Say the common denominator.
- Rewrite the fractions.
- Add.
- Simplify if needed.
Answers:
- (\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4})
- (\frac{2}{5} + \frac{1}{10} = \frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2})
- (\frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2})
Differentiation during guided practice:
- For struggling students, allow them to use fraction strips or a multiplication chart.
- For advanced students, ask them to find the least common denominator and explain why it works.
4. Independent Practice: Worksheet
Time: 15 minutes
Students complete the 6-question worksheet. The worksheet increases in difficulty.
Teacher role:
- Circulate and check work.
- Prompt students to say the common denominator before adding.
- Provide support to students who are stuck.
Possible support prompts:
- “What are the denominators?”
- “Can you find a number both denominators divide into?”
- “What fraction is equivalent to (\frac{1}{2}) with denominator 6?”
- “Did you simplify your answer?”
5. Assessment and Closure
Time: 5 minutes
Use a quick exit ticket.
Write on the board:
[ \frac{2}{3} + \frac{1}{6} ]
Students solve on a slip and hand it in.
Expected answer:
[ \frac{4}{6} + \frac{1}{6} = \frac{5}{6} ]
Closure question:
“Why must the denominators be the same before we add fractions?”
Expected answer:
Because the pieces must be the same size.
Differentiation Plan for Mixed Levels
| Student Level | Support | Challenge |
|---|---|---|
| Emerging | Use fraction strips; give denominators that are easy multiples, such as 2 and 4; provide a multiplication chart | Ask them to explain each step in words |
| Developing | Provide step cards: find denominator → rewrite → add → simplify | Give one extra practice problem with simplification |
| Proficient | Work independently | Ask them to create their own fraction addition problem and solve it |
| Advanced | Ask them to use least common denominator | Include word problems or three-fraction addition |
6-Question Worksheet: Adding Fractions with Different Denominators
Name: ________________________
Date: ________________________
Instructions:
Add the fractions. Show your work. Simplify your answer if possible.
Question 1
[ \frac{1}{2} + \frac{1}{4} = ]
Question 2
[ \frac{1}{3} + \frac{1}{6} = ]
Question 3
[ \frac{2}{5} + \frac{1}{10} = ]
Question 4
[ \frac{1}{4} + \frac{1}{8} = ]
Question 5
[ \frac{3}{4} + \frac{1}{6} = ]
Question 6
Maya ate (\frac{1}{2}) of a pizza. Her brother ate (\frac{1}{3}) of the same pizza. How much of the pizza did they eat together?
Answer Key
Question 1
[ \frac{1}{2} + \frac{1}{4} ]
Common denominator: 4
[ \frac{1}{2} = \frac{2}{4} ]
[ \frac{2}{4} + \frac{1}{4} = \frac{3}{4} ]
Answer:
[ \frac{3}{4} ]
Question 2
[ \frac{1}{3} + \frac{1}{6} ]
Common denominator: 6
[ \frac{1}{3} = \frac{2}{6} ]
[ \frac{2}{6} + \frac{1}{6} = \frac{3}{6} ]
Simplify:
[ \frac{3}{6} = \frac{1}{2} ]
Answer:
[ \frac{1}{2} ]
Question 3
[ \frac{2}{5} + \frac{1}{10} ]
Common denominator: 10
[ \frac{2}{5} = \frac{4}{10} ]
[ \frac{4}{10} + \frac{1}{10} = \frac{5}{10} ]
Simplify:
[ \frac{5}{10} = \frac{1}{2} ]
Answer:
[ \frac{1}{2} ]
Question 4
[ \frac{1}{4} + \frac{1}{8} ]
Common denominator: 8
[ \frac{1}{4} = \frac{2}{8} ]
[ \frac{2}{8} + \frac{1}{8} = \frac{3}{8} ]
Answer:
[ \frac{3}{8} ]
Question 5
[ \frac{3}{4} + \frac{1}{6} ]
Common denominator: 12
[ \frac{3}{4} = \frac{9}{12} ]
[ \frac{1}{6} = \frac{2}{12} ]
[ \frac{9}{12} + \frac{2}{12} = \frac{11}{12} ]
Answer:
[ \frac{11}{12} ]
Question 6
Maya ate (\frac{1}{2}) of a pizza. Her brother ate (\frac{1}{3}) of the same pizza.
[ \frac{1}{2} + \frac{1}{3} ]
Common denominator: 6
[ \frac{1}{2} = \frac{3}{6} ]
[ \frac{1}{3} = \frac{2}{6} ]
[ \frac{3}{6} + \frac{2}{6} = \frac{5}{6} ]
Answer:
[ \frac{5}{6} ]
They ate (\frac{5}{6}) of the pizza together.