Connect Standard Multiplication to Place Values
Multiply by the ones digit and then by the tens value.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For 236×42, the ones-row product is 472 and the tens-row product is 9440.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
A standard multiplication algorithm records partial products by the multiplier’s places. An entry in a tens row represents tens times the multiplicand. Add the full-valued partial products, using exchanges when column sums reach ten. The compact layout is useful only when its place meanings stay correct.
Multiply by the ones digit and then by the tens value. Align those products according to their values and add. Use a nearby estimate and a decomposed equation to check that the standard layout represents the same sum.
Write the multiplier’s full tens value before generating its row. A misplaced tens row can make a plausible-looking product ten times too small. Label each partial-product row by the actual multiplier place value.
- Label each partial-product row by the actual multiplier place value.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Multiply by the ones digit and then by the tens value.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
For 236×42, the ones-row product is 472 and the tens-row product is 9440. Add them to get 9912. An estimate 240×40=9600 has the right scale. The tens digit four means forty, so its row is not merely 944. Write the multiplier’s full tens value before generating its row. A misplaced tens row can make a plausible-looking product ten times too small. Label each partial-product row by the actual multiplier place value.
Check your reasoning
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Helpful tips
- Write the multiplier’s full tens value before generating its row.
- A misplaced tens row can make a plausible-looking product ten times too small.
See the answer and explanation
6848
Add correctly aligned ones and tens partial products. The result is 6848.
Take it further
Find 408×37. Expected: 12,240+2,856=15,096.
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