Multiplication Table Patterns: Fill In and Explain
Print 3rd grade multiplication table pattern worksheets: fill in a row and column of a 10 × 10 table, then explain even rows, symmetry and more. 12 versions.
Worksheet version 1 of 12. The answer key matches the current version.
Fill in the whole 5 row and the whole 8 column (shaded), then the other empty boxes. Use the finished table to answer the pattern questions. Explain why, not just what.
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 10 | ||
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 18 | 20 | |
| 3 | 3 | 6 | 12 | 18 | 21 | 30 | ||||
| 4 | 4 | 8 | 16 | 20 | 24 | 28 | 36 | 40 | ||
| 5 | ||||||||||
| 6 | 12 | 18 | 24 | 30 | 36 | 42 | 54 | 60 | ||
| 7 | 7 | 28 | 35 | 42 | 49 | 63 | 70 | |||
| 8 | 8 | 16 | 32 | 40 | 48 | 56 | 72 | 80 | ||
| 9 | 9 | 18 | 27 | 36 | 45 | 63 | 81 | 90 | ||
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 90 | 100 |
- a) Which products in the 3 row are odd?
- b) Add the digits of each product in the 9 row (9, 18, 27 … 90). What do you notice?
- c) Add the 4 row and the 5 row, column by column. Which row do you get?
- d) Why is every product in the 8 row even?
- e) How many times does 18 appear in the table? Write the facts.
- f) Why does every product in the 10 row end in 0?
About this worksheet
A multiplication table is full of patterns, and explaining them is how students turn memorized facts into understanding. Each product in a row is the one before plus the row number, because one more group is added. The table is symmetric across the diagonal, because 3 × 7 and 7 × 3 are the same product. Every product in an even row is even, and the 5 row ends in 5 and 0 in turn.
Each version blanks a different row and column plus ten other boxes, so students build the facts first and then look for patterns in a table they finished themselves. The six questions come from eleven kinds: even rows, the 5 row, swapping the factors, the step along a row, doubling rows, adding two rows, the digits of the 9 row, how often a product appears, odd products, the square numbers on the diagonal and the 10 row. The answer key fills in the table and gives a sample explanation for every question.
Practice aligned to CCSS 3.OA.D.9.
Need a full table to look at? Print the multiplication table printable. Before this: odd and even numbers and equal groups and sharing. Also useful: unknown factors and fact families and two-step word problems. More practice: multiplication worksheets and 3rd grade math worksheets.
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