Explore · fraction of a set
Find 3/4 of 24 counters. Divide into 4 equal groups first.
Singapore Math 5A · Independent learning
Multiplying a Whole Number by a Fraction
Learning target: Find a fraction of a whole-number quantity by dividing into equal groups first.
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.
Find 1/4 of 20 counters.
Understand the idea
Find a fraction of a whole-number quantity by dividing into equal groups first.
A fraction of a whole-number set is found by partitioning the entire set into denominator-many equal groups, then taking numerator-many groups. Label the original whole before any calculation so the divisor is never confused with the numerator.
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: Dividing by numerator rather than denominator.
Model to study: Equal-part bar model with counted items.
Worked examples
Worked examples 1 · fraction of a set
Find 5/6 of 18 counters. Divide into 6 equal groups first.
Solution: 15 counters
Why: The whole is 18. One 6-th is 3; 5 parts are 5×3=15.
Worked examples 2 · fraction of a set
Find 3/4 of 28 counters. Divide into 4 equal groups first.
Solution: 21 counters
Why: The whole is 28. One 4-th is 7; 3 parts are 3×7=21.
Worked examples 3 · fraction of a set
Find 1/4 of 32 counters. Divide into 4 equal groups first.
Solution: 8 counters
Why: The whole is 32. One 4-th is 8; 1 parts are 1×8=8.
Check understanding
Check understanding 1 · fraction of a set
Find 2/8 of 24 counters. Divide into 8 equal groups first.
Check understanding 2 · fraction of a set
Find 3/4 of 16 counters. Divide into 4 equal groups first.
Guided practice
Guided practice 1 · fraction of a set
Find 2/5 of 35 counters. Divide into 5 equal groups first.
Guided practice 2 · fraction of a set
Find 2/5 of 45 counters. Divide into 5 equal groups first.
Guided practice 3 · fraction of a set
Find 5/8 of 24 counters. Divide into 8 equal groups first.
Independent practice
Independent practice 1 · fraction of a set
Find 2/3 of 24 counters. Divide into 3 equal groups first.
Independent practice 2 · fraction of a set
Find 1/8 of 32 counters. Divide into 8 equal groups first.
Independent practice 3 · fraction of a set
Find 2/4 of 24 counters. Divide into 4 equal groups first.
Independent practice 4 · fraction of a set
Find 1/3 of 18 counters. Divide into 3 equal groups first.
Independent practice 5 · fraction of a set
Find 3/5 of 15 counters. Divide into 5 equal groups first.
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “3/4 of 36 = 12. I divided by the numerator, not the denominator.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Find 3/4 of 36 counters. Divide into 4 equal groups first.
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). Find 1/4 of 12 counters. Divide into 4 equal groups first.
Exit check
Exit check 1 · fraction of a set
Find 2/4 of 16 counters. Divide into 4 equal groups first.
Exit check 2 · fraction of a set
Find 1/3 of 27 counters. Divide into 3 equal groups first.
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.