Elementary Math Lessons: Revealing Numerical Patterns in Multiplication Tables

When I began teaching elementary multiplication times-tables, I recognized patterns which when taught, make mathematics more understandable and entertaining for young students. When presented as number games, it becomes easier for young students to remember, and much more fun for you to teach.

Memorizing is important, but understanding how multiplication works makes reasoning and remembering easier. Once the times-tables are memorized your students will have a solid background for other mathematical concepts.

Making Multiplication Poster Charts

Make one large (reusable) multiplication chart on poster board, labeled "Multiplication Tables" with black permanent marker. Add the numbers 1 - 12 across the top, and also down the left-hand side. Make grid squares using a yardstick, and have students help by filling in number-blanks across, and down for great puzzle-practice lessons.

To create a reusable-interactive chart, number and then cut-out 144 squares from scrap cardboard (same size as grid squares above). Then add adhesive-backed (stick-on) Velcro pieces to each of the poster-grid squares, and onto the back sides of hand-numbered, pre-cut squares.

The poster board practice lessons are more fun for students, similar to fitting together puzzle-game pieces, and makes it easier to correct mistakes. The addition of Velcro game-pieces makes this instructional poster reusable year-after-year.

Additional Charts or Blackboard Demonstrations

The blackboard can then be used to demonstrate different number-series patterns, if you enjoy blackboard writing. For future lessons it may be easier to create individual, reusable posters; showing numbers 0 - 4 on one poster board, numbers 5 - 8 on another, and 9 - 12 on a final board. These numbers should be listed in such a way that the multiplication patterns are highlighted, as described below.

Number Patterns 0 - 4 Poster Board

Label columns 0, 1, 2, 3, and 4, showing each number formula as it is multiplied by 0 - 12 down each column. Include an explanation of zero, as nothing but a placeholder, but show it multiplied out by every number 0 - 12 for demonstration purposes.

On the same poster show how multiplying the number 1 (by numbers 0 - 12) will always be the same number, and can also be shown using larger number examples as well. The number 2, when multiplied by numbers 0 - 12, creates the even numbers, skips odd numbers, and makes a fun reciting lesson up to the number 100.

Show the numbers 3 and 4 multiplied by 0 - 12, asking students if they notice other patterns emerging. They may notice the number 3 when multiplied out, is in each different tens-place 3 times, with different patterns revealed for the number 4.

Number Patterns 5 - 8 Poster Board

On another poster, the number 5 multiplied out by 0 - 12, can lead to a fun reciting lesson, counting by fives to 100 (or higher) - demonstrating that multiples of 5 always end in 5 or 0. Show the number 6 multiplied out by 0 - 12, and then point out that numbers 5 and 6, when multiplied by themselves, each end in the same number (and rhymes when you say it). Example: 5 times 5 equals 25, and 6 x 6 = 36.

List the numbers 7 and 8 multiplied out by 0 - 12, and have your students look for, and find repeating numerical patterns. Repetitive patterns are easier to find for the number 8, but number 7 also has distinct patterns emerge when multiplied beyond the number 12.

Number Patterns 9 - 12 Poster Board

On a final poster board show the number 9 multiplied out by 0 - 12 (my favorite) because the numerical digits reverse half way through the series. Numbers 10 and 11 when multiplied out by 0 - 12, are just plain fun, adding zeroes, or doubling digits. Finally the number 12 when multiplied by 0 - 12, although more difficult, also has some fun patterns for your students to discover.

It's easy to interchange numbers using the stick-on/pull-apart squares from the "Multiplication Table" poster to use with other math charts. These number squares can also be transferred to prime-number charts, odd-and-even number posters, and integer-number lines for future classroom lessons.