9 times table worksheet

A table full of patterns

The 9s have a reputation for being hard, and then they turn out to be the easiest table once you know the tricks. There is a pattern in the digits, a hand trick, and a link to the 10s. Grade 3 asks students to notice patterns in the multiplication table, and this is the place where noticing pays off.

Every fact on this sheet includes a 9, either first or second, and the other number runs from 0 to 12. The facts are mixed up rather than in order, so a child has to recall them and cannot just count by nines.

Settings

• Fact focus. The preset is "Only the 9s" with the operation set to multiplication. Choosing "All facts in range" makes a general mixed page.
• Largest number. The preset is 12, so facts run up to 9 × 12. Lower it to 10 to stop at 9 × 10.
• Layout. Horizontal prints a row-by-row sheet; vertical stacks each fact.
• Number of problems. 10 to 100, in multiples of 5.
• Include the answer key. It lets you or the child check quickly, and the key is where the patterns below become visible.

Worked example: 9 × 7 three ways

The finger trick. Hold up ten fingers. To multiply 9 by 7, fold down the seventh finger from the left. Count the fingers to the left of the folded one: 6. Count those to the right: 3. Read them together as 63. This works for 9 × 1 through 9 × 10.

The tens-minus-one trick. 9 is one less than 10, so 9 × 7 is 10 × 7 minus one 7: 70 − 7 = 63.

The digit-sum check. Add the digits of the answer: 6 + 3 = 9. For every multiple of 9 up to 90, the digits add to 9. Try 9 × 8 = 72, and 7 + 2 = 9.

The tens digit is always one less than the number you multiplied by, so for 9 × 7 it is 6, and the ones digit makes the digits total 9.

Past 9 × 10 the digit-sum pattern still holds if you keep adding until one digit is left: 9 × 12 = 108, and 1 + 0 + 8 = 9. The finger trick does not extend, but 120 − 12 = 108 does.

Where children go wrong

• Off by one on the tens-minus trick. A child who computes 70 − 9 = 61 subtracted the wrong number. The thing to take away is the number being multiplied, which is 7.
• Folding the wrong finger. Counting from the right instead of the left reverses the digits to 36.
• Digit sum fails. If a response does not add to 9, the answer is wrong, so children can self-check without any key.
• 9 × 0. Always 0, and often missed.
• Skipping 9 × 11 and 9 × 12. These are outside the finger trick. 9 × 11 = 99 is a nice pattern of its own.

Use the answer key to mark and look for misses that pass the digit-sum check, which means a transposed pair such as 36 for 63. For a table that rewards a different strategy, see the 12 times table. If your student is ready for bigger numbers, try multiplying two-digit numbers.

Sources

1. Common Core State Standards: Grade 3 Operations and Algebraic Thinking (3.OA.D.9, identify arithmetic patterns, including patterns in the multiplication table) thecorestandards.org
2. Common Core State Standards: Grade 3 Operations and Algebraic Thinking (3.OA.C.7, fluently multiply within 100) thecorestandards.org