Same Math › Grades 4–5 › Partial products
What are partial products?
Partial products multiplies each part of one number by each part of the other, writes every answer on its own line, then adds them up. Nothing is carried, so every step is visible.
- Multiply part by part, usually starting with the ones: 4 × 3, then 4 × 20.
- One line per product. The small note says where each line came from.
- Add the lines: 12 + 80 + 30 + 200 = 322
Why schools teach it
It's the bridge to the stacked method
Each line is one box from the area model. In the stacked method most of us learned, those four lines get squeezed into two by carrying, and carrying is where kids lose track of what they're doing.
Writing every partial product out keeps place value in plain sight: 4 × 20 is written as 80, not as an 8 in the tens column. Once that's solid, the stacked method in 5th grade is just a shorter way to write the same thing.
At the kitchen table
What to say, and what to skip
Say this
Which two parts are you multiplying now?
Is that 4 × 2 or 4 × 20?
Dropping the zero is the most common slip.Can you match each line to a box in the area model?
If the class used boxes first, this connects the two.How many lines should there be?
2-digit × 2-digit makes four lines, unless a digit is zero.
Skip this
You can combine those lines and carry.
That's the standard method, expected in 5th grade. Showing it early mixes the two up.Why so many steps?
The steps are the point. Each one shows a place-value idea.- Insisting on a different order.Any order gives the right answer. Use the order the class uses.
See it in action
How a 4th grader solves 47 × 6
Multiply the ones
6 × 7 = 42Multiply the tens, keeping the zero
6 × 40 = 240Add the partial products
42 + 240 = 282
Compare this with the stacked method: "6 × 7 is 42, write 2, carry 4." Partial products writes the 42 in full.
Free practice sheet
Make a partial products sheet
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Parents also ask
Is this the same as the area model?
Same math, different picture. The area model draws boxes; partial products lists the box answers in a column.
Does the order matter?
No. Many classes start with the ones so it lines up with the stacked method later.
When do kids switch to the regular method?
The standards expect the standard stacked method by 5th grade. Partial products usually comes first in 4th.
Does it work for bigger numbers?
Yes. 3-digit × 2-digit makes six lines. It gets long, which is one reason the shorter method follows.