Partial Products Multiplication Worksheets, Set Out in Columns

Pick a sheet type, from two partial products to six, press Make a new sheet for new problems, then Print.

Sheet type

Problems

Answer key

12 problems. 2-digit × 1-digit, two partial products. Sheet 4IDJQ0, with its answer key.

2-digit × 1-digit, two partial products

Name Date Score / 12

Multiply with partial products: write the product of each pair of parts, then add them up.

Sheet 4IDJQ0 · Made at homeroomtools.com

Answer key. 2-digit × 1-digit, two partial products

1.48
2.792
3.171
4.54
5.276
6.216
7.294
8.156
9.66
10.534
11.114
12.150

Sheet 4IDJQ0 · Made at homeroomtools.com

Next step Print more 2-digit × 1-digit sheets Warm up with a times tables sheet

How it works

These partial products multiplication worksheets stack each problem over a rule, with room for each partial product and the total. Sheets run from 47 × 6 on two lines to 243 × 36 on six. The key shows every line.

Read the full guide

How the partial products method works

Split each number by place value, multiply every part by every part, write each product on its own line, and add once at the end. For 67 × 48 that is four lines: 2,400, 480, 280 and 56, total 3,216. Nothing is carried while multiplying.

Where partial products sit in the standards

Texas names the method: 3.4(G) and 4.4(D) both list partial products among the strategies, next to the standard algorithm. The Common Core never uses the words: 4.NBT.5 asks for strategies based on place value and the properties of operations, and 5.NBT.5 asks for the standard algorithm a year later. The two sheets under Bridge to the standard algorithm cover that move.

A partial product multiplication worksheet needs space. Set Problems to 9 for four lines and 6 for six lines.
Have pupils say each line as a place value product, 60 times 40, not 6 times 4, so no zero is dropped.
When a total is wrong, check the lines first: a wrong line is a multiplication slip, right lines with a wrong total an addition slip.

Questions and answers

Is partial products the same as the area model?

The arithmetic is identical and the layout differs. The area model writes the four products of 67 × 48 in four boxes. Partial products writes the same four numbers on four lines under the stacked problem. For the box layout, use the area model worksheets.

Which partial product goes on the first line?

Either order gives the same total. Most sheets here start with the largest product, 60 × 40 = 2,400, which gives an estimate at once. The sheet Ones first, to match the standard algorithm starts from 8 × 7 = 56.

When should pupils move on to the standard algorithm?

When four lines come easily and the place values are right every time. Then print Two partial products, one per multiplier digit: 67 × 8 = 536 and 67 × 40 = 2,680 are the two rows of the standard algorithm.

All 13 sheet types

One-digit multiplier 4

2-digit × 1-digit, two partial products 47 × 6 is worked as 40 × 6 = 240 and 7 × 6 = 42, then 240 + 42 = 282. Each problem is stacked over a rule, with room below for the two partial products and the total. The page opens on this sheet.
3-digit × 1-digit with a zero digit 405 × 7 = 2,800 + 35 = 2,835. The 0 in the tens place gives no product, so the answer key lists only the lines that are not zero: 400 × 7 and 5 × 7.
3-digit × 1-digit, three partial products 352 × 4 = 1,200 + 200 + 8 = 1,408. Three lines, one for each digit of the top number: hundreds, tens, ones. No carrying happens until the final addition, which is the point of the method.
4-digit × 1-digit, four partial products 1,352 × 6 = 6,000 + 1,800 + 300 + 12 = 8,112. Four digits by one digit is the largest one-digit-multiplier size that Texas 4.4(D) and Common Core 4.NBT.5 set for grade 4.

Show all 13 sheet types (9 more)

Two-digit multiplier 4

2-digit × 2-digit, four partial products 67 × 48 = 2,400 + 480 + 280 + 56 = 3,216. The four lines are tens × tens, tens × ones, ones × tens and ones × ones. Print 9 to a page: four lines and a total need more room than a fact.
2-digit × multiple of 10 36 × 40 = 1,200 + 240 = 1,440. Only two lines, because the ones digit of the multiplier is 0. Both lines are a basic fact with zeros attached: 3 × 4 and 6 × 4.
2-digit × teen number 23 × 14 = 200 + 80 + 30 + 12 = 322. A multiplier from 11 to 19 keeps two of the four lines easy, because they are × 10. A good first sheet for four lines.
3-digit × 2-digit, six partial products 243 × 36 = 6,000 + 1,200 + 1,200 + 240 + 90 + 18 = 8,748. Six lines is where the method starts to feel long, and both standards documents move on at this size: Texas 5.3(B) and Common Core 5.NBT.5 ask for the standard algorithm.

Scaffolds and warm-ups 3

Labeled lines Each line is labeled with its own small problem, so 47 × 6 prints '40 × 6' and '7 × 6' beside the lines. The pupil only multiplies and adds. Use it for the first lesson, then move to the unlabeled sheets.
Labeled lines, 2-digit × 2-digit The four labels for 34 × 52 read 30 × 50, 30 × 2, 4 × 50 and 4 × 2, and the lines fill in as 1,500, 60, 200 and 8 for a total of 1,768. The labels show where each of the four products comes from before pupils have to find them alone.
Tens × tens and tens × ones warm-up 60 × 40 = 2,400, 60 × 8 = 480 and 7 × 40 = 280: the products that fill the lines, practiced bare. 30 to a page, written across, as a starter before a four-line sheet.

Bridge to the standard algorithm 2

Ones first, to match the standard algorithm The same four lines from the bottom up: 7 × 8 = 56, 60 × 8 = 480, 7 × 40 = 280 and 60 × 40 = 2,400, and 56 + 480 + 280 + 2,400 = 3,216. Addition does not mind the order, and starting with the ones follows the direction of the standard algorithm.
Two partial products, one per multiplier digit 67 × 48 worked as 67 × 8 = 536 and 67 × 40 = 2,680, then 536 + 2,680 = 3,216. These two lines are the two rows of the standard algorithm, so this sheet is the step between four lines and the short form.

How this list was compiled: Sheet types, wording and worked examples are own work; every partial product and total was computed twice by script on 2026-09-18. The method was checked on 2026-09-18 against https://en.wikipedia.org/wiki/Multiplication_algorithm , which says the grid method 'is also known as the partial products algorithm', that 'its essence is the calculation of the simple multiplications separately, with all addition being left to the final gathering-up stage', and that 'the number of sub-products becomes cumbersome as the number of digits increases'. Standards facts were checked the same day against the full texts. Texas Essential Knowledge and Skills for Mathematics, 19 TAC chapter 111 subchapter A (https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111a.pdf): 3.4(G) and 4.4(D) both list partial products among the strategies, 4.4(D) sets up to a four-digit number by a one-digit number and a two-digit number by a two-digit number, and 5.3(B) asks for a three-digit number by a two-digit number with the standard algorithm. Common Core State Standards for Mathematics (national copy, https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf, read again 2026-09-20): 4.NBT.5 sets the same two sizes with 'strategies based on place value and the properties of operations', the words 'partial products' appear nowhere in the document, and 5.NBT.5 asks for the standard algorithm. Fix pass 2026-09-20: the example 1,352 × 6 = 8,112 replaced 2,714 × 3, which a sibling page also works; its four partial products and total were computed by script that day. A search of the national Common Core text for the words partial product finds nothing, which is what the guide says. Licence: own work