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Identify patterns in multiplication tables

Multiplication-table patterns are regular relationships among products in familiar tables, including how products change when one factor increases by one, the special roles of 0, 1, 2, 5, and 10, and the equivalence of related facts through commutativity. These patterns support deriving unknown facts from known facts and interpreting tables as arrays or equal groups; the focus is on factors and products within 100, not variable-based generalizations or larger-number rules.

Detailed Explanation: Identify patterns in multiplication tables

A multiplication table has patterns you can use to find an unknown fact.

  • If one factor increases by 11, the product increases by the other factor.
  • Multiplying by 11 keeps a number the same, and multiplying by 00 gives 00.
  • Factors can switch places without changing the product: (6×7=7×6)(6 \times 7 = 7 \times 6).

Example: Find (6×7)(6 \times 7).

  1. Start with a fact you know:
6×5=30 6 \times 5 = 30

  1. The second factor changes from 55 to 77. That is an increase of 22.

  2. Each new group has 66, so add two groups of 66:

30+6+6=42 30 + 6 + 6 = 42
  1. Therefore,
6×7=42 6 \times 7 = 42

You can check the related fact because the factors can switch places:

7×6=427 \times 6 = 42

Learn by doing: Identify patterns in multiplication tables

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