Original assessment tasks 1 · repeated fraction
Find 4 × 4/6 by thinking of 4 equal fractional groups.
Singapore Math 5A · Independent learning
Chapter 5 — Review
Review and retrieve learning across the chapter. Write reasons and label units.
Original assessment tasks
Original assessment tasks 2 · worked-error diagnosis
Error-analysis notebook: Learner notebook (REVIEW): “2 × 1/3 = 7/3. I added one fraction only once.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Find 2 × 1/3 by thinking of 2 equal fractional groups.
Original assessment tasks 3 · fraction of a set
Find 1/4 of 28 counters. Divide into 4 equal groups first.
Original assessment tasks 4 · worked-error diagnosis
Error-analysis notebook: Learner notebook (REVIEW): “3/8 of 72 = 24. 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 3/8 of 72 counters. Divide into 8 equal groups first.
Original assessment tasks 5 · fraction of a set
An art club has 20 sheets. It uses 1/5 of the original sheets for posters. How many sheets is that? State the original whole.
Original assessment tasks 6 · worked-error diagnosis
Error-analysis notebook: Learner notebook (REVIEW): “5/8 of 72 = 72/5. 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 72 sheets. It uses 5/8 of the original sheets for posters. How many sheets is that? State the original whole.
Original assessment tasks 7 · fraction product
Find 4/5 × 1/5. Explain the overlapping partitions of one rectangle.
Original assessment tasks 8 · worked-error diagnosis
Error-analysis notebook: Learner notebook (REVIEW): “3/5 × 1/6 = 23/30. I added instead of multiplying equal fractional parts.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Find 3/5 × 1/6. Explain the overlapping partitions of one rectangle.
Original assessment tasks 9 · fraction product
Find 3/5 × 1/5. Explain the overlapping partitions of one rectangle.
Original assessment tasks 10 · worked-error diagnosis
Error-analysis notebook: Learner notebook (REVIEW): “1/3 × 1/4 = 7/12. I added instead of multiplying equal fractional parts.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Find 1/3 × 1/4. Explain the overlapping partitions of one rectangle.
Original assessment tasks 11 · fraction product
Find 3/5 × 5/6. Explain the overlapping partitions of one rectangle.
Original assessment tasks 12 · worked-error diagnosis
Error-analysis notebook: Learner notebook (REVIEW): “4/5 × 2/5 = 6/5. I added instead of multiplying equal fractional parts.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Find 4/5 × 2/5. Explain the overlapping partitions of one rectangle.
Original assessment tasks 13 · mixed-number product
Calculate 3 2/5 × 1 2/5. Estimate before multiplying.
Original assessment tasks 14 · worked-error diagnosis
Error-analysis notebook: Learner notebook (REVIEW): “13/4 × 11/4 = 6. I added instead of multiplying equal fractional parts.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Calculate 3 1/4 × 2 3/4. Estimate before multiplying.
Original assessment tasks 15 · changing whole
A workshop starts with 63 tiles. It uses 2/3 of its original tiles on a wall. It then uses 2/3 of the remaining tiles on a table. How many tiles go on the table?
Original assessment tasks 16 · worked-error diagnosis
Error-analysis notebook: Learner notebook (REVIEW): “After using 2/5 of 160, I take 3/4 of 160 again, not of the remaining 96.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: A workshop starts with 160 tiles. It uses 2/5 of its original tiles on a wall. It then uses 3/4 of the remaining tiles on a table. How many tiles go on the table?
Original assessment tasks 17 · reciprocal
Find the reciprocal of 1/4 and prove the product equals 1.
Original assessment tasks 18 · worked-error diagnosis
Error-analysis notebook: Learner notebook (REVIEW): “The reciprocal of nonzero 6/11 is 0; multiplying by 0 gives 1.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: Find the reciprocal of 6/11 and prove the product equals 1.
Additional targeted transfer tasks
Answer from first principles. Include a model where requested. These questions are distinct from taught worked examples.
Transfer and model L06 · targeted mastery: fraction
Show why 4/9 × 3/8 simplifies to 1/6 using cross-cancellation.
Scoring guidance
Calculation items: 2 points for correct mathematics and units plus 1 for valid working. Notebook diagnosis tasks: 4 points, one each for identifying a specific faulty step, explaining the repair, solving accurately, and checking units/logic. Targeted transfer tasks: 4 points with detailed anchors in private teacher keys. Equivalent exact representations accepted; reviewers must examine explanations.