Explore · parentheses
Evaluate 29 × (5 + 4), explaining why parentheses matter.
Singapore Math 5A · Independent learning
Expressions with Parentheses
Learning target: Translate grouping into arithmetic expressions and explain why placement changes the result.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Prerequisite check (before instruction)
Attempt without help. A weak prerequisite signals review of 4A or 4B material, not a failed 5A lesson.
Compute 7 × 8 and 36 ÷ 6.
Explain what parentheses mean in a simple sum.
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
Find 9 + 4 and 4 × 6. Which operation is multiplication?
Understand the idea
Translate grouping into arithmetic expressions and explain why placement changes the result.
Parentheses say which group to combine first. The phrases “the total of A and B, multiplied by C” and “A plus B times C” may describe different quantities. Write the part-whole grouping before evaluating.
Vocabulary focus: grouping, expression, equal precedence. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Ignoring parentheses or placing them after computing.
Model to study: Part-whole and grouping diagrams.
Worked examples
Worked examples 1 · parentheses
Evaluate (23 + 3) × 5. Would 23 + 3 × 5 have the same value?
Solution: 130; no
Why: Parentheses first: 23+3=26; 26×5=130. Without parentheses: 23+15=38.
Worked examples 2 · parentheses
Evaluate 10 × (7 + 6), explaining why parentheses matter.
Solution: 130
Why: 7+6=13; 10×13=130.
Worked examples 3 · parentheses
Evaluate (24 + 7) × 5. Would 24 + 7 × 5 have the same value?
Solution: 155; no
Why: Parentheses first: 24+7=31; 31×5=155. Without parentheses: 24+35=59.
Check understanding
Check understanding 1 · parentheses
Evaluate 8 × (5 + 9), explaining why parentheses matter.
Check understanding 2 · parentheses
Evaluate (28 + 4) × 4. Would 28 + 4 × 4 have the same value?
Guided practice
Guided practice 1 · parentheses
Evaluate 18 × (3 + 3), explaining why parentheses matter.
Guided practice 2 · parentheses
Evaluate (25 + 6) × 5. Would 25 + 6 × 5 have the same value?
Guided practice 3 · parentheses
Evaluate 9 × (3 + 4), explaining why parentheses matter.
Independent practice
Independent practice 1 · parentheses
Evaluate (14 + 6) × 6. Would 14 + 6 × 6 have the same value?
Independent practice 2 · parentheses
Evaluate 19 × (2 + 3), explaining why parentheses matter.
Independent practice 3 · parentheses
Evaluate (20 + 3) × 7. Would 20 + 3 × 7 have the same value?
Independent practice 4 · parentheses
Evaluate 14 × (7 + 8), explaining why parentheses matter.
Independent practice 5 · parentheses
Evaluate (18 + 7) × 7. Would 18 + 7 × 7 have the same value?
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “I erased grouping from 23 × (2 + 6) and wrote 23 × 2 + 6 = 52. I claimed parentheses do not change the answer.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Evaluate 23 × (2 + 6), explaining why parentheses matter.
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). Evaluate (23 + 3) × 7. Would 23 + 3 × 7 have the same value?
Exit check
Exit check 1 · parentheses
Evaluate 11 × (7 + 4), explaining why parentheses matter.
Exit check 2 · parentheses
Evaluate (17 + 4) × 3. Would 17 + 4 × 3 have the same value?
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.