How many multiplication facts are there from 0 to 12?

One hundred sixty-nine cells in the grid, ninety-one distinct facts after commutativity, and roughly fifty that have to be memorized rather than derived from a rule.

Is it better to drill one table or a mixed sheet?

One table while the recall is being built, mixed once it is. A single-table sheet lets a child use the pattern; a mixed sheet checks whether the fact survives being asked out of order.

Which multiplication fact is missed most often?

7 × 8 = 56, with 6 × 7 = 42 close behind. Both sit in the middle of the table with no digit rule and no neighbouring anchor.

Multiplication Timed Test — Printable and On-Screen (1, 2 or 5 Minutes)

Multiplication · Multiplication · 20 problems · 1 minute NameDateScore

1 5 × 11
2 9 × 2
3 7 × 7
4 5 × 0
5 2 × 2
6 1 × 8
7 10 × 12
8 10 × 7
9 2 × 0
10 5 × 9
11 1 × 2
12 2 × 4
13 7 × 3
14 11 × 11
15 11 × 10
16 11 × 11
17 2 × 1
18 8 × 3
19 5 × 5
20 5 × 6

Answer key · Multiplication · Multiplication · 20 problems NameDate

1 5 × 11 55
2 9 × 2 18
3 7 × 7 49
4 5 × 0 0
5 2 × 2 4
6 1 × 8 8
7 10 × 12 120
8 10 × 7 70
9 2 × 0 0
10 5 × 9 45
11 1 × 2 2
12 2 × 4 8
13 7 × 3 21
14 11 × 11 121
15 11 × 10 110
16 11 × 11 121
17 2 × 1 2
18 8 × 3 24
19 5 × 5 25
20 5 × 6 30

Thirteen tables, and three of them are rules

The 0–12 multiplication grid has 169 cells, 91 of them distinct once you notice that 7 × 8 and 8 × 7 are one fact. Of those 91, the 0s, 1s and 10s are rules rather than things to memorize, and the 2s, 5s and 11s have patterns visible enough to be nearly free. What is left is roughly fifty facts that have to be known outright.

That is why single-table sheets matter more here than in any other operation. The tables are not equally hard, and a mixed sheet averages over the difference. A 7s sheet and a 5s sheet from the same child will differ by a factor a mixed sheet never shows.

Every multiplication fact from 0 to 12

Every multiplication fact from 0 to 12. Row times column gives the cell.
×	1	2	3	4	5	6	7	8	9	10	11	12
0 ×	0	0	0	0	0	0	0	0	0	0	0	0
1 ×	1	2	3	4	5	6	7	8	9	10	11	12
2 ×	2	4	6	8	10	12	14	16	18	20	22	24
3 ×	3	6	9	12	15	18	21	24	27	30	33	36
4 ×	4	8	12	16	20	24	28	32	36	40	44	48
5 ×	5	10	15	20	25	30	35	40	45	50	55	60
6 ×	6	12	18	24	30	36	42	48	54	60	66	72
7 ×	7	14	21	28	35	42	49	56	63	70	77	84
8 ×	8	16	24	32	40	48	56	64	72	80	88	96
9 ×	9	18	27	36	45	54	63	72	81	90	99	108
10 ×	10	20	30	40	50	60	70	80	90	100	110	120
11 ×	11	22	33	44	55	66	77	88	99	110	121	132
12 ×	12	24	36	48	60	72	84	96	108	120	132	144

Row times column gives the cell. The diagonal is the squares; everything above it repeats below it. The dense region in the lower right — the 6s through 9s crossed with each other — is about a dozen facts and it accounts for most of what comes back wrong.

The dozen facts in the middle of the table

Teachers report the same short list year after year: 7 × 8, 6 × 7, 8 × 7, 7 × 9, 6 × 8. None has a digit rule, none sits next to an anchor fact, and all of them are large enough that a wrong answer is not obviously wrong. A child can be solid on eleven tables and lose a timed sheet on these five facts alone.

The doubling chain is the way through. 8 × 7 is 7 doubled three times, 4 × 7 is doubled twice, 6 × 7 is 3 × 7 doubled. A child who is fast on the 2s and 3s can derive most of the hard middle, which is slower than recall but far faster than counting up. Recall arrives after that, from repetition.

The order the tables are usually taught

The conventional order is 2s, 10s, 5s, then 3s and 4s, then 6s through 9s, then 11s and 12s, and it is conventional because it front-loads the tables with visible patterns. Each of those ranges has its own sheet here, so a week can drill exactly the one that is not yet automatic.

The 9s are worth taking out of order: the digit-sum rule makes them checkable, so a child can catch their own mistakes without an answer key. The 12s are worth leaving until last, not because they are conceptually harder but because they are large enough that a slip is expensive. Mixed sheets and the full 0–12 range belong after a table has already been drilled on its own.

Thirteen sheets for multiplication

Each of these is its own sheet with its own fact table and its own trouble spots. The single ranges hold one operand steady; 0–12 and mixed draw from the whole set.

Three that come up

How many multiplication facts are there from 0 to 12?: One hundred sixty-nine cells in the grid, ninety-one distinct facts after commutativity, and roughly fifty that have to be memorized rather than derived from a rule.
Is it better to drill one table or a mixed sheet?: One table while the recall is being built, mixed once it is. A single-table sheet lets a child use the pattern; a mixed sheet checks whether the fact survives being asked out of order.
Which multiplication fact is missed most often?: 7 × 8 = 56, with 6 × 7 = 42 close behind. Both sit in the middle of the table with no digit rule and no neighbouring anchor.

What the standards and the critics actually say

Common Core State Standards for Mathematics (PDF), page 23 — 3.OA.C.7 “By the end of Grade 3, know from memory all products of two one-digit numbers.” thecorestandards.org — CCSSI_Math Standards.pdf

NCTM — Procedural Fluency in Mathematics (position statement) “Timed tests do not assess fluency and can negatively affect students, and thus should be avoided.” nctm.org — Procedural Fluency in Mathematics

youcubed — Fluency Without Fear “For about one third of students the onset of timed testing is the beginning of math anxiety.” youcubed.org — Fluency Without Fear