Multiplication•Grade 6•Vertical Format

Grade 6 Multiplication Vertical Format

Grade 6 multiplication vertical format sheet: 16 problems on multi-digit multiplication, four-digit by two-digit multiplication.

CCSSAligned to Common Core 6.NS.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

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Three different problem sets — same skill, same layout, fresh numbers.

Preview — Set A

Solve each problem. Line up the place values and show any regrouping.

1.
549
×364
2.
5467
×18
3.
168
×322
4.
9845
×14
5.
872
×782
6.
9987
×78
7.
788
×536
8.
4812
×21
9.
208
×969
10.
4069
×23
11.
293
×275
12.
8928
×16
13.
977
×518
14.
9244
×98
15.
387
×780
16.
1064
×76

Other ways to solve this

Using 549 × 364 from this sheet (Set A, problem 1). Each method below reaches the same answer, 199,836, by a different route; pick the one that makes the most sense to you.

Lattice method

Helps keep carrying tidy: every digit product gets its own box, and you only add at the end.

Step 1Write 549 across the top and 364 down the right side, one digit per box.
Step 2Multiply each pair of digits. Put the tens above the diagonal and the ones below it.
- 3 × 5 = 15 → tens 1, ones 5
- 3 × 4 = 12 → tens 1, ones 2
- 3 × 9 = 27 → tens 2, ones 7
- 6 × 5 = 30 → tens 3, ones 0
- 6 × 4 = 24 → tens 2, ones 4
- 6 × 9 = 54 → tens 5, ones 4
- 4 × 5 = 20 → tens 2, ones 0
- 4 × 4 = 16 → tens 1, ones 6
- 4 × 9 = 36 → tens 3, ones 6
Step 3Add along each diagonal, starting at the bottom right. Carry when a sum is 10 or more.
- Diagonal 1 (from the bottom right): 6 = 6
- Diagonal 2 (from the bottom right): 13 = 13: write 3, carry 1
- Diagonal 3 (from the bottom right): 17 + carry 1 = 18: write 8, carry 1
- Diagonal 4 (from the bottom right): 8 + carry 1 = 9
- Diagonal 5 (from the bottom right): 9 = 9
- Diagonal 6 (from the bottom right): 1 = 1
Step 4Read the digits down the left side and along the bottom: 1 9 9 8 3 6. So 549 × 364 = 199,836.

Step 1 of 4

Doubling and halving

Helps when you can halve and double quickly: the only hard step is one addition at the end.

Halving the left column and doubling the right. Rows with an even left value are crossed out.
Halve	Double	Keep?
364	549	cross out
182	1,098	cross out
91	2,196	keep
45	4,392	keep
22	8,784	cross out
11	17,568	keep
5	35,136	keep
2	70,272	cross out
1	140,544	keep

Step 1Put the smaller number, 364, in the left column and 549 in the right column.
Step 2Halve the left number (drop any remainder) and double the right number, row by row, until the left reaches 1.
- 364 | 549
- 182 | 1,098
- 91 | 2,196
- 45 | 4,392
- 22 | 8,784
- 11 | 17,568
- 5 | 35,136
- 2 | 70,272
- 1 | 140,544
Step 3Cross out every row with an even number on the left.
- Cross out 364 | 549
- Cross out 182 | 1,098
- Cross out 22 | 8,784
- Cross out 2 | 70,272
Step 4Add the right column of the rows that are left: 2,196 + 4,392 + 17,568 + 35,136 + 140,544 = 199,836.
Step 5So 549 × 364 = 199,836.

Step 1 of 5

Estimate first

Helps you catch place-value slips: round, estimate, then check that the exact answer is close.

Step 1Round each number to its first digit: 549 rounds to 500; 364 rounds to 400.
Step 2Estimate: 500 × 400 = 200,000.
Step 3Now work it out exactly: 549 × 364 = 199,836.
Step 4Compare: 199,836 is 164 away from the estimate of 200,000. An answer with a different number of digits from the estimate usually means a place-value slip.

Step 1 of 4

What this worksheet covers

This is a 16-problem vertical format for grade 6 multiplication, printed in black and white with the key on page two. The numbers run as high as 9,987. Problems 6 and 11, for instance, are "9987 × 78" and "293 × 275". It is written against Common Core 6.NS.3 — The Number System, grade 6.

Skills practiced

The grade 6 multiplication sequence covers multi-digit multiplication, greatest common factor, least common multiple and perfect squares; this page sits inside it. Specifically, the problems practice multi-digit multiplication and four-digit by two-digit multiplication. Concretely, the sheet tests whether a student can recall the multiplication facts quickly and accurately, without counting up to them.

About the vertical format format

Vertical format stacks the two operands over a rule with space above for regrouped digits; the 16 problems, problem 6, "9987 × 78" among them, sit four to a row. Stacked factors put the partial products in columns, which is where the place-value shift in long multiplication lives.

Set A, Set B and Set C

All three sets are produced by the site's deterministic generator from a fixed seed, so they are the same every time the site is built and the answer keys are exact. Where Set A's problem 9 is "208 × 969", Set B's is "535 × 795".

How to use this worksheet

Expect twenty minutes or so of real attention for sixteen problems. At grade 6, multiplication rewards care over speed — a rushed vertical format gets the arithmetic right and the signs or units wrong. If more than a third of the sixteen problems come back wrong, stop and step back a grade in multiplication rather than assigning Set B.

One mistake to watch for

In two-digit multiplication the second partial product is not shifted left, so 34 × 12 is answered 102 instead of 408. Problem 16 on this grade 6 vertical format page, "1064 × 76", is where to look for it.

The 1 in 12 is being treated as one, not ten.

Have the student write the placeholder zero in the ones column of the second row and say "ten times" aloud as they start it.

The full guide to teaching multiplicationTeaching multiplication from equal groups to integer exponents: the grade 2–8 progression, times-table strategies, and the errors that stall students.