Learning target: Regroup a fractional sum of at least one whole and write simplified mixed-number answers.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Explore · mixed-number addition
Add 3 3/4 + 1 1/2. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 5 1/4
How it works: Whole-number parts: 3+1=4. Fractions: 3/4+1/2=5/4. Combining the wholes and fractional sum gives 4+5/4=5 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
What mixed number is equivalent to 6/4?
Show answer and worked explanation
Answer: 1 1/2
How it works: 6/4 = 1 2/4 = 1 1/2; exchange four fourths for one whole.
Understand the idea
Regroup a fractional sum of at least one whole and write simplified mixed-number answers.
When mixed-number fractional parts add to one or more wholes, regroup the result. For example, two fractional pieces totaling 6/4 create 1 2/4, not a mixed number with an improper fractional part. Simplify after regrouping.
Vocabulary focus: same whole, equivalent fractions, mixed numbers. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Leaving an improper fractional part in a mixed number.
Model to study: Fraction strips crossing one-whole threshold.
Worked examples
Worked examples 1 · mixed-number addition
Add 3 3/4 + 3 1/2. Express the result as a simplified mixed number.
Solution: 7 1/4
Why: Whole-number parts: 3+3=6. Fractions: 3/4+1/2=5/4. Combining the wholes and fractional sum gives 6+5/4=7 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Worked examples 2 · mixed-number addition
Add 1 3/4 + 1 1/2. Express the result as a simplified mixed number.
Solution: 3 1/4
Why: Whole-number parts: 1+1=2. Fractions: 3/4+1/2=5/4. Combining the wholes and fractional sum gives 2+5/4=3 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Worked examples 3 · mixed-number addition
Add 2 3/4 + 2 1/2. Express the result as a simplified mixed number.
Solution: 5 1/4
Why: Whole-number parts: 2+2=4. Fractions: 3/4+1/2=5/4. Combining the wholes and fractional sum gives 4+5/4=5 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Check understanding
Check understanding 1 · mixed-number addition
Add 2 5/6 + 1 1/2. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 4 1/3
How it works: Whole-number parts: 2+1=3. Fractions: 5/6+1/2=4/3. Combining the wholes and fractional sum gives 3+4/3=4 1/3. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Check understanding 2 · mixed-number addition
Add 2 2/3 + 1 1/3. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 4
How it works: Whole-number parts: 2+1=3. Fractions: 2/3+1/3=1. Combining the wholes and fractional sum gives 3+1=4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Guided practice
Guided practice 1 · mixed-number addition
Add 3 3/4 + 2 1/2. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 6 1/4
How it works: Whole-number parts: 3+2=5. Fractions: 3/4+1/2=5/4. Combining the wholes and fractional sum gives 5+5/4=6 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Guided practice 2 · mixed-number addition
Add 2 3/4 + 3 1/2. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 6 1/4
How it works: Whole-number parts: 2+3=5. Fractions: 3/4+1/2=5/4. Combining the wholes and fractional sum gives 5+5/4=6 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Guided practice 3 · mixed-number addition
Add 2 7/8 + 1 1/2. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 4 3/8
How it works: Whole-number parts: 2+1=3. Fractions: 7/8+1/2=11/8. Combining the wholes and fractional sum gives 3+11/8=4 3/8. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Independent practice
Independent practice 1 · mixed-number addition
Add 2 7/8 + 3 1/4. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 6 1/8
How it works: Whole-number parts: 2+3=5. Fractions: 7/8+1/4=9/8. Combining the wholes and fractional sum gives 5+9/8=6 1/8. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Independent practice 2 · mixed-number addition
Add 1 3/4 + 2 1/2. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 4 1/4
How it works: Whole-number parts: 1+2=3. Fractions: 3/4+1/2=5/4. Combining the wholes and fractional sum gives 3+5/4=4 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Independent practice 3 · mixed-number addition
Add 1 5/6 + 3 1/3. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 5 1/6
How it works: Whole-number parts: 1+3=4. Fractions: 5/6+1/3=7/6. Combining the wholes and fractional sum gives 4+7/6=5 1/6. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Independent practice 4 · mixed-number addition
Add 1 3/4 + 3 1/2. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 5 1/4
How it works: Whole-number parts: 1+3=4. Fractions: 3/4+1/2=5/4. Combining the wholes and fractional sum gives 4+5/4=5 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Independent practice 5 · mixed-number addition
Add 3 5/6 + 1 1/3. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 5 1/6
How it works: Whole-number parts: 3+1=4. Fractions: 5/6+1/3=7/6. Combining the wholes and fractional sum gives 4+7/6=5 1/6. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “For 31/8 and 11/8, my answer is 21/8; I added both numerators and denominators without making equal parts.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Add 3 7/8 + 1 3/8. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 5 1/4
How it works: Wrong step/assumption: Learner notebook (LESSON): “For 31/8 and 11/8, my answer is 21/8; I added both numerators and denominators without making equal parts.” Diagnosis: Use the same whole with equivalent denominators; exchange one whole before subtracting when fractional parts require it. Correct computation: Whole-number parts: 3+1=4. Fractions: 7/8+3/8=5/4. Combining the wholes and fractional sum gives 4+5/4=5 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Challenge and error analysis 2 · reasoning transfer
Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). Add 2 3/4 + 1 1/2. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 4 1/4
How it works: Whole-number parts: 2+1=3. Fractions: 3/4+1/2=5/4. Combining the wholes and fractional sum gives 3+5/4=4 1/4. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction. Verification: show why the answer has a reasonable magnitude and matches the operation, referent and unit.
Exit check
Exit check 1 · mixed-number addition
Add 1 3/4 + 3 3/8. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 5 1/8
How it works: Whole-number parts: 1+3=4. Fractions: 3/4+3/8=9/8. Combining the wholes and fractional sum gives 4+9/8=5 1/8. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Exit check 2 · mixed-number addition
Add 3 5/6 + 2 1/2. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 6 1/3
How it works: Whole-number parts: 3+2=5. Fractions: 5/6+1/2=4/3. Combining the wholes and fractional sum gives 5+4/3=6 1/3. If the fraction sum is at least 1, exchange the improper fractional part for a whole and a proper fraction.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A tutor may reteach the concept if calculations are correct without meaningful reasoning.