Great Inheritance Mathematics Term A · Independent learning
Adding Mixed Numbers— Part 1
Learning target: Add mixed numbers by combining whole and fractional parts with equivalent denominators.
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 1 1/3 + 1 1/3. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 2 2/3
How it works: Whole-number parts: 1+1=2. Fractions: 1/3+1/3=2/3. Combining the wholes and fractional sum gives 2+2/3=2 2/3. 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.
Write 9/4 as a mixed number.
Show answer and worked explanation
Answer: 2 1/4
How it works: 9 fourths contain 8 fourths (=2 wholes) plus 1 fourth.
Understand the idea
Add mixed numbers by combining whole and fractional parts with equivalent denominators.
A mixed number combines whole units and one proper fractional part. Add whole parts and fractions separately; for unlike denominators, rename the fractional parts first. The final result should use a reduced proper fraction beside the whole number.
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: Combining unlike fraction numerators without renaming.
Model to study: Whole-and-fraction bars.
Worked examples
Worked examples 1 · mixed-number addition
Add 3 1/4 + 1 1/4. Express the result as a simplified mixed number.
Solution: 4 1/2
Why: Whole-number parts: 3+1=4. Fractions: 1/4+1/4=1/2. Combining the wholes and fractional sum gives 4+1/2=4 1/2. 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 2 1/8 + 1 1/8. Express the result as a simplified mixed number.
Solution: 3 1/4
Why: Whole-number parts: 2+1=3. Fractions: 1/8+1/8=1/4. Combining the wholes and fractional sum gives 3+1/4=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 1 1/4 + 1 1/4. Express the result as a simplified mixed number.
Solution: 2 1/2
Why: Whole-number parts: 1+1=2. Fractions: 1/4+1/4=1/2. Combining the wholes and fractional sum gives 2+1/2=2 1/2. 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 3 1/3 + 1 1/3. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 4 2/3
How it works: Whole-number parts: 3+1=4. Fractions: 1/3+1/3=2/3. Combining the wholes and fractional sum gives 4+2/3=4 2/3. 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 1/8 + 2 1/4. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 4 3/8
How it works: Whole-number parts: 2+2=4. Fractions: 1/8+1/4=3/8. Combining the wholes and fractional sum gives 4+3/8=4 3/8. 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 2 1/4 + 2 1/4. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 4 1/2
How it works: Whole-number parts: 2+2=4. Fractions: 1/4+1/4=1/2. Combining the wholes and fractional sum gives 4+1/2=4 1/2. 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 1/4 + 3 1/4. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 5 1/2
How it works: Whole-number parts: 2+3=5. Fractions: 1/4+1/4=1/2. Combining the wholes and fractional sum gives 5+1/2=5 1/2. 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 3 1/4 + 3 1/8. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 6 3/8
How it works: Whole-number parts: 3+3=6. Fractions: 1/4+1/8=3/8. Combining the wholes and fractional sum gives 6+3/8=6 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 1 1/4 + 2 1/4. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 3 1/2
How it works: Whole-number parts: 1+2=3. Fractions: 1/4+1/4=1/2. Combining the wholes and fractional sum gives 3+1/2=3 1/2. 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 3 1/8 + 3 1/4. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 6 3/8
How it works: Whole-number parts: 3+3=6. Fractions: 1/8+1/4=3/8. Combining the wholes and fractional sum gives 6+3/8=6 3/8. 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 2 1/4 + 1 1/4. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 3 1/2
How it works: Whole-number parts: 2+1=3. Fractions: 1/4+1/4=1/2. Combining the wholes and fractional sum gives 3+1/2=3 1/2. 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 3 1/3 + 2 1/6. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 5 1/2
How it works: Whole-number parts: 3+2=5. Fractions: 1/3+1/6=1/2. Combining the wholes and fractional sum gives 5+1/2=5 1/2. 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 2 1/3 + 3 1/6. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 5 1/2
How it works: Whole-number parts: 2+3=5. Fractions: 1/3+1/6=1/2. Combining the wholes and fractional sum gives 5+1/2=5 1/2. 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 9/8 and 5/4, my answer is 7/6; 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 1 1/8 + 1 1/4. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 2 3/8
How it works: Wrong step/assumption: Learner notebook (LESSON): “For 9/8 and 5/4, my answer is 7/6; 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: 1+1=2. Fractions: 1/8+1/4=3/8. Combining the wholes and fractional sum gives 2+3/8=2 3/8. 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 1/4 + 1 1/8. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 3 3/8
How it works: Whole-number parts: 2+1=3. Fractions: 1/4+1/8=3/8. Combining the wholes and fractional sum gives 3+3/8=3 3/8. 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 2 1/3 + 1 1/6. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 3 1/2
How it works: Whole-number parts: 2+1=3. Fractions: 1/3+1/6=1/2. Combining the wholes and fractional sum gives 3+1/2=3 1/2. 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 1 1/4 + 3 1/4. Express the result as a simplified mixed number.
Show answer and worked explanation
Answer: 4 1/2
How it works: Whole-number parts: 1+3=4. Fractions: 1/4+1/4=1/2. Combining the wholes and fractional sum gives 4+1/2=4 1/2. 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 instructor may reteach the concept if calculations are correct without meaningful reasoning.