Question: 7.)(7 − 3)² + 36 ÷ 9
Show work here:
Answer:
8.)50 − 2 × (3 + 4)² ÷ 7
Show work here:
Answer:
Part III: Error Analysis & Critical Thinking
Directions: Analyze the student work below. Identify if it is Correct or Incorrect. If Incorrect, find the mistake and write the correct answer.
9. Problem: 16 ÷ 4 × 2
Student Solution: 16 ÷ (4 × 2) = 16 ÷ 8 = 2
Status: [ ] Correct [ ] Incorrect
If incorrect, correct answer is: ______
10. Problem: 10 − 3 + 4
Student Solution: 10 − 7 = 3
Status: [ ] Correct [ ] Incorrect
If incorrect, correct answer is:______
1. **Problem 7:** Calculate $$(7 - 3)^2 + \frac{36}{9}$$.
2. **Step 1:** Simplify inside the parentheses: $7 - 3 = 4$.
3. **Step 2:** Square the result: $$4^2 = 16$$.
4. **Step 3:** Divide $36$ by $9$: $$\frac{36}{9} = 4$$.
5. **Step 4:** Add the two results: $$16 + 4 = 20$$.
**Answer for Problem 7:** $20$
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6. **Problem 8:** Calculate $$50 - 2 \times (3 + 4)^2 \div 7$$.
7. **Step 1:** Simplify inside the parentheses: $3 + 4 = 7$.
8. **Step 2:** Square the result: $$7^2 = 49$$.
9. **Step 3:** Multiply $2$ by $49$: $$2 \times 49 = 98$$.
10. **Step 4:** Divide $98$ by $7$: $$\frac{98}{7} = 14$$.
11. **Step 5:** Subtract from $50$: $$50 - 14 = 36$$.
**Answer for Problem 8:** $36$
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12. **Problem 9:** Analyze student solution for $$16 \div 4 \times 2$$.
13. **Student's work:** $16 \div (4 \times 2) = 16 \div 8 = 2$.
14. **Step 1:** According to order of operations, division and multiplication are performed left to right.
15. **Step 2:** Correct calculation: $$16 \div 4 = 4$$.
16. **Step 3:** Then multiply by $2$: $$4 \times 2 = 8$$.
17. **Conclusion:** Student's solution is **Incorrect**.
18. **Correct answer:** $8$
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19. **Problem 10:** Analyze student solution for $$10 - 3 + 4$$.
20. **Student's work:** $10 - 7 = 3$.
21. **Step 1:** According to order of operations, addition and subtraction are performed left to right.
22. **Step 2:** Calculate $10 - 3 = 7$.
23. **Step 3:** Then add $4$: $$7 + 4 = 11$$.
24. **Conclusion:** Student's solution is **Incorrect**.
25. **Correct answer:** $11$