Explore · equal precedence
Evaluate 100 ÷ 5 ÷ 5, showing the equal-priority order.
Singapore Math 5A · Independent learning
Order of Operations — Part 2
Learning target: Evaluate nested or longer expressions and handle same-priority operations left to right.
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 48 ÷ 6 ÷ 2 from left to right.
Understand the idea
Evaluate nested or longer expressions and handle same-priority operations left to right.
Operations tied at the same priority must be completed from left to right. This is particularly important for 18 − 5 + 2 and 48 ÷ 4 ÷ 3. Show one new expression after each step rather than moving numbers around informally.
Vocabulary focus: grouping, expression, equal precedence. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Doing addition before subtraction simply because it appears first in a mnemonic.
Model to study: Annotated equal-priority computation sequence.
Worked examples
Worked examples 1 · equal precedence
Evaluate 20 − 5 + 8, showing the equal-priority order.
Solution: 23
Why: At equal priority, go left to right: 20 − 5 = 15; then 15 + 8 = 23.
Worked examples 2 · equal precedence
Evaluate 36 ÷ 3 ÷ 2, showing the equal-priority order.
Solution: 6
Why: Divide from left to right: 36 ÷ 3 = 12; 12 ÷ 2 = 6.
Worked examples 3 · equal precedence
Evaluate 17 − 3 + 7, showing the equal-priority order.
Solution: 21
Why: At equal priority, go left to right: 17 − 3 = 14; then 14 + 7 = 21.
Check understanding
Check understanding 1 · equal precedence
Evaluate 84 ÷ 3 ÷ 4, showing the equal-priority order.
Check understanding 2 · equal precedence
Evaluate 27 − 2 + 4, showing the equal-priority order.
Guided practice
Guided practice 1 · equal precedence
Evaluate 50 ÷ 2 ÷ 5, showing the equal-priority order.
Guided practice 2 · equal precedence
Evaluate 23 − 4 + 7, showing the equal-priority order.
Guided practice 3 · equal precedence
Evaluate 105 ÷ 3 ÷ 7, showing the equal-priority order.
Independent practice
Independent practice 1 · equal precedence
Evaluate 20 − 5 + 5, showing the equal-priority order.
Independent practice 2 · equal precedence
Evaluate 60 ÷ 5 ÷ 4, showing the equal-priority order.
Independent practice 3 · equal precedence
Evaluate 18 − 3 + 6, showing the equal-priority order.
Independent practice 4 · equal precedence
Evaluate 80 ÷ 2 ÷ 5, showing the equal-priority order.
Independent practice 5 · equal precedence
Evaluate 18 − 2 + 3, showing the equal-priority order.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “100 ÷ 4 ÷ 5 = 100 ÷ (4 ÷ 5) = 125. I grouped the two divisors before working from the left.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Evaluate 100 ÷ 4 ÷ 5, showing the equal-priority order.
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 9 − 4 + 7, showing the equal-priority order.
Targeted mastery: model, calculate, explain
These additional original examples address specific 5A mastery requirements. Compare the visual and the reasoning before trying the independent questions.
Targeted 1 · targeted mastery: expression
Evaluate 72 ÷ (3 × (2 + 2)) + 5. Show nested-parentheses order.
Solution: 11
Why: Inner parentheses 2+2=4; 3×4=12; 72÷12=6; add 5 to get 11.
Targeted 2 · targeted mastery: expression
Evaluate 48 ÷ 4 × 3. Why is the answer not 4?
Solution: 36
Why: Division and multiplication have equal precedence. Left to right: 48÷4=12, then 12×3=36.
Targeted 3 · targeted mastery: expression
Evaluate 90 − (6 + 4) × 5.
Targeted 4 · targeted mastery: expression
Find 84 ÷ (2 × (3 + 4)).
Exit check
Exit check 1 · equal precedence
Evaluate 105 ÷ 5 ÷ 7, showing the equal-priority order.
Exit check 2 · equal precedence
Evaluate 23 − 3 + 8, showing the equal-priority order.
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.