The nines are the most pattern-rich table in the grid, which makes them a pleasure to teach. Up to 9 x 10 the digits of every answer add to nine, the tens digit is always one less than the number you multiplied by, and the units digits count down from nine as the tens count up. There is also the finger method, which works and which children remember for years. These sheets are ordered first so the patterns are visible on the page, then mixed so the facts get stored rather than reconstructed.
Ordered sheets running 9 x 1 to 9 x 12, mixed-order recall pages, and missing-number rows in both directions. Ordered pages are laid out so the answers line up vertically and the digit pattern is easy to spot. Division facts from the same table appear later in the set. One worksheet per US Letter page, black and white.
Hold both hands up with ten fingers showing. To find 9 x 4, fold down the fourth finger from the left. Three fingers stand to its left and six to its right, giving 36. It works for 9 x 1 through 9 x 10 and is one of the few classroom tricks that is genuinely reliable.
Do the digits of every multiple of 9 add to 9?
For the first ten they do — 18, 27, 36 and so on all give 9. Beyond that the digits sum to a multiple of nine rather than nine exactly: 99 gives 18, and 18 gives 9 when you add again. So the test for divisibility by nine is that the digit sum is itself a multiple of nine.
What is the one-less pattern?
The tens digit of the answer is one less than the number you multiplied by, and the units digit makes it up to nine. For 9 x 7: one less than 7 is 6, and 6 plus 3 makes 9, so the answer is 63. It holds from 9 x 1 to 9 x 10.
Does the pattern break down after 9 x 10?
The one-less rule stops working at 9 x 11 and 9 x 12, which give 99 and 108. Those two are usually learned as separate facts, and it is worth flagging the break rather than letting a child discover it in a test.