Explore · fraction of a set
An art club has 12 sheets. It uses 2/3 of the original sheets for posters. How many sheets is that? State the original whole.
Singapore Math 5A · Independent learning
Word Problems — Part 1
Learning target: Model and solve contextual fraction-of-a-whole problems and explain the chosen whole.
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.
After using 1/3 of 12 apples, how many remain?
Understand the idea
Model and solve contextual fraction-of-a-whole problems and explain the chosen whole.
In a fraction-of-a-quantity word problem, the reference whole must be named explicitly. Calculate the size of one equal part first and then count the requested parts. Keep units such as sheets, tickets, or students in the answer.
Vocabulary focus: fraction of a quantity, overlapping partitions, reciprocal. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Applying a fraction to a later remainder rather than original whole.
Model to study: Labeled fractional part-whole bars.
Worked examples
Worked examples 1 · fraction of a set
An art club has 27 sheets. It uses 2/3 of the original sheets for posters. How many sheets is that? State the original whole.
Solution: 18 sheets
Why: The whole is 27. One 3-th is 9; 2 parts are 2×9=18.
Worked examples 2 · fraction of a set
An art club has 18 sheets. It uses 5/6 of the original sheets for posters. How many sheets is that? State the original whole.
Solution: 15 sheets
Why: The whole is 18. One 6-th is 3; 5 parts are 5×3=15.
Worked examples 3 · fraction of a set
An art club has 64 sheets. It uses 6/8 of the original sheets for posters. How many sheets is that? State the original whole.
Solution: 48 sheets
Why: The whole is 64. One 8-th is 8; 6 parts are 6×8=48.
Check understanding
Check understanding 1 · fraction of a set
An art club has 9 sheets. It uses 2/3 of the original sheets for posters. How many sheets is that? State the original whole.
Check understanding 2 · fraction of a set
An art club has 24 sheets. It uses 4/8 of the original sheets for posters. How many sheets is that? State the original whole.
Guided practice
Guided practice 1 · fraction of a set
An art club has 35 sheets. It uses 1/5 of the original sheets for posters. How many sheets is that? State the original whole.
Guided practice 2 · fraction of a set
An art club has 24 sheets. It uses 2/3 of the original sheets for posters. How many sheets is that? State the original whole.
Guided practice 3 · fraction of a set
An art club has 72 sheets. It uses 6/8 of the original sheets for posters. How many sheets is that? State the original whole.
Independent practice
Independent practice 1 · fraction of a set
An art club has 40 sheets. It uses 1/5 of the original sheets for posters. How many sheets is that? State the original whole.
Independent practice 2 · fraction of a set
An art club has 18 sheets. It uses 2/3 of the original sheets for posters. How many sheets is that? State the original whole.
Independent practice 3 · fraction of a set
An art club has 56 sheets. It uses 1/8 of the original sheets for posters. How many sheets is that? State the original whole.
Independent practice 4 · fraction of a set
An art club has 64 sheets. It uses 1/8 of the original sheets for posters. How many sheets is that? State the original whole.
Independent practice 5 · fraction of a set
An art club has 64 sheets. It uses 4/8 of the original sheets for posters. How many sheets is that? State the original whole.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “2/3 of 15 = 15/2. I divided by the numerator, not the denominator.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: An art club has 15 sheets. It uses 2/3 of the original sheets for posters. How many sheets is that? State the original whole.
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). An art club has 28 sheets. It uses 2/4 of the original sheets for posters. How many sheets is that? State the original whole.
Exit check
Exit check 1 · fraction of a set
An art club has 28 sheets. It uses 1/4 of the original sheets for posters. How many sheets is that? State the original whole.
Exit check 2 · fraction of a set
An art club has 15 sheets. It uses 1/3 of the original sheets for posters. How many sheets is that? State the original whole.
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.