Explore · multistep expression
9 shelves each hold 16 novels and 6 reference books. Then 2 books are removed from each shelf. Write one expression for the books remaining.
Singapore Math 5A · Independent learning
Word Problems — Part 2
Learning target: Solve complex multistep problems by choosing parentheses and explaining intermediate quantities.
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.
Seven baskets each contain 8 apples. Four are removed overall. How many remain?
Understand the idea
Solve complex multistep problems by choosing parentheses and explaining intermediate quantities.
Longer word problems often change an intermediate quantity: supplies per shelf, then items removed from each shelf, then number of shelves. Work out which quantities depend on the earlier change. Explain every intermediate value and confirm that the final unit answers the question.
Vocabulary focus: grouping, expression, equal precedence. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Calculating in the wrong sequence and losing a dependency.
Model to study: Before/after quantities with expression annotations.
Worked examples
Worked examples 1 · multistep expression
7 shelves each hold 16 novels and 2 reference books. Then 3 books are removed from each shelf. Write one expression for the books remaining.
Solution: 7 × (16 + 2 − 3) = 105 books
Why: One shelf starts with 18 books and ends with 15. Multiply by 7 shelves to get 105.
Worked examples 2 · multistep expression
9 shelves each hold 8 novels and 2 reference books. Then 2 books are removed from each shelf. Write one expression for the books remaining.
Solution: 9 × (8 + 2 − 2) = 72 books
Why: One shelf starts with 10 books and ends with 8. Multiply by 9 shelves to get 72.
Worked examples 3 · multistep expression
7 shelves each hold 16 novels and 7 reference books. Then 5 books are removed from each shelf. Write one expression for the books remaining.
Solution: 7 × (16 + 7 − 5) = 126 books
Why: One shelf starts with 23 books and ends with 18. Multiply by 7 shelves to get 126.
Check understanding
Check understanding 1 · multistep expression
3 shelves each hold 13 novels and 5 reference books. Then 5 books are removed from each shelf. Write one expression for the books remaining.
Check understanding 2 · multistep expression
9 shelves each hold 26 novels and 2 reference books. Then 5 books are removed from each shelf. Write one expression for the books remaining.
Guided practice
Guided practice 1 · multistep expression
9 shelves each hold 14 novels and 6 reference books. Then 2 books are removed from each shelf. Write one expression for the books remaining.
Guided practice 2 · multistep expression
5 shelves each hold 16 novels and 6 reference books. Then 3 books are removed from each shelf. Write one expression for the books remaining.
Guided practice 3 · multistep expression
9 shelves each hold 21 novels and 7 reference books. Then 2 books are removed from each shelf. Write one expression for the books remaining.
Independent practice
Independent practice 1 · multistep expression
4 shelves each hold 25 novels and 7 reference books. Then 4 books are removed from each shelf. Write one expression for the books remaining.
Independent practice 2 · multistep expression
6 shelves each hold 24 novels and 4 reference books. Then 4 books are removed from each shelf. Write one expression for the books remaining.
Independent practice 3 · multistep expression
6 shelves each hold 15 novels and 3 reference books. Then 5 books are removed from each shelf. Write one expression for the books remaining.
Independent practice 4 · multistep expression
5 shelves each hold 12 novels and 6 reference books. Then 4 books are removed from each shelf. Write one expression for the books remaining.
Independent practice 5 · multistep expression
4 shelves each hold 10 novels and 2 reference books. Then 3 books are removed from each shelf. Write one expression for the books remaining.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “I erased grouping from 3×(28+5−3) and wrote 3 × 28 + 5 − 3 = 86. I claimed parentheses do not change the answer.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: 3 shelves each hold 28 novels and 5 reference books. Then 3 books are removed from each shelf. Write one expression for the books remaining.
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). 6 shelves each hold 11 novels and 4 reference books. Then 5 books are removed from each shelf. Write one expression for the books remaining.
Exit check
Exit check 1 · multistep expression
6 shelves each hold 18 novels and 5 reference books. Then 5 books are removed from each shelf. Write one expression for the books remaining.
Exit check 2 · multistep expression
6 shelves each hold 8 novels and 7 reference books. Then 3 books are removed from each shelf. Write one expression for the books remaining.
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.