Find 3 × 8.
Incorrect answer: 11
The factors describe groups, not the total. Also, multiplication by zero gives zero, while multiplication by one leaves the number unchanged.
Adding the factors instead of multiplying
Multiplication counts equal groups. One additional group contributes the group size, not just one.
The correction
24
Three groups of eight: 8 + 8 + 8 = 24.
- Identify the number of equal groups and the number in each group.
- Represent them with repeated addition or an array.
- Use a known fact to find a nearby fact rather than counting every item again.
Try the reasoning in another example
Use 5 × 6 to find 6 × 6.
- Five groups of six make 30.
- One more group adds 6.
Answer: 36
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
The short check below reuses the first example as a retrieval question and adds a second question. It checks this method; it does not establish a grade level.
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