Explore · mixed-number subtraction
Subtract 4 1/2 − 2 1/2. Explain any exchange needed.
Great Inheritance Mathematics Term A · Independent learning
Subtracting Mixed Numbers— Part 1
Learning target: Subtract mixed numbers without renaming a whole; justify the order of terms.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
Compute 5/6 − 2/6.
Understand the idea
Subtract mixed numbers without renaming a whole; justify the order of terms.
Subtract the second mixed number from the first in the stated order. When the first fractional part is large enough, subtract fractional parts and wholes separately. A number line provides a quick estimate of the difference.
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: Subtracting the smaller fractional part from the larger regardless of expression order.
Model to study: Mixed-number partition blocks.
Worked examples
Worked examples 1 · mixed-number subtraction
Subtract 8 1/2 − 2 1/4. Explain any exchange needed.
Solution: 6 1/4
Why: Subtract wholes 8−2=6, then fractions 4/8−2/8=1/4, giving 6 1/4.
Worked examples 2 · mixed-number subtraction
Subtract 7 1/2 − 3 1/2. Explain any exchange needed.
Solution: 4
Why: Subtract wholes 7−3=4, then fractions 4/8−4/8=0, giving 4.
Worked examples 3 · mixed-number subtraction
Subtract 7 5/6 − 1 2/3. Explain any exchange needed.
Solution: 6 1/6
Why: Subtract wholes 7−1=6, then fractions 5/6−4/6=1/6, giving 6 1/6.
Check understanding
Check understanding 1 · mixed-number subtraction
Subtract 5 7/8 − 1 5/8. Explain any exchange needed.
Check understanding 2 · mixed-number subtraction
Subtract 7 2/3 − 3 1/3. Explain any exchange needed.
Guided practice
Guided practice 1 · mixed-number subtraction
Subtract 6 5/8 − 1 1/4. Explain any exchange needed.
Guided practice 2 · mixed-number subtraction
Subtract 7 2/3 − 1 1/2. Explain any exchange needed.
Guided practice 3 · mixed-number subtraction
Subtract 6 1/2 − 3 1/4. Explain any exchange needed.
Independent practice
Independent practice 1 · mixed-number subtraction
Subtract 7 5/6 − 1 1/6. Explain any exchange needed.
Independent practice 2 · mixed-number subtraction
Subtract 6 2/3 − 3 1/3. Explain any exchange needed.
Independent practice 3 · mixed-number subtraction
Subtract 8 2/3 − 1 1/2. Explain any exchange needed.
Independent practice 4 · mixed-number subtraction
Subtract 5 3/4 − 2 1/4. Explain any exchange needed.
Independent practice 5 · mixed-number subtraction
Subtract 8 1/2 − 1 1/4. Explain any exchange needed.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “For 9/2 and 9/8, my answer is 9/5; 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: Subtract 4 1/2 − 1 1/8. Explain any exchange needed.
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). Subtract 5 3/4 − 1 1/4. Explain any exchange needed.
Exit check
Exit check 1 · mixed-number subtraction
Subtract 6 7/8 − 1 5/8. Explain any exchange needed.
Exit check 2 · mixed-number subtraction
Subtract 5 1/2 − 2 1/4. Explain any exchange needed.
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.