Understanding Patterns of Multiplication

Primary Standards:

MAFS.3.OA.2.5: Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

MAFS.3.OA.4.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Connecting Standards:

MAFS.3.OA.3.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 • 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Content Knowledge:

The ability to recognize mathematical patterns is one of the most important characteristics of a successful math student.  Identifying and explaining patterns leads students to develop the ability to make generalizations, which is the foundation for mathematical reasoning.  In this Unit, students will focus on identifying and describing arithmetic patterns, such as with products on a multiplication chart.  Students should also use patterns to describe how the properties of multiplication work and continuously ask questions such as “How do you know?” and “Does this always work?”

The goals of standard OA.2.5 are less about naming properties and definitions, and more about understanding how these properties work, and how they can be used to efficiently multiply.  It is not the goal of this Unit that students master an understanding of these properties (Commutative, Associative, and Distributive Properties of multiplication), but simply an introduction to discovering how they can strategically be used to make finding products efficient.  Through investigations with concrete manipulatives and drawings, students will discover and understand these critical properties, and be able to apply them in further Units throughout the year.


GCG 1 – Learning Goal: As a mathematician, I can Model and apply the commutative property of multiplication MAFS.3.OA.2.5

  • Step 1: Use models to explain what happens when the order of the factors changes in a multiplication situation/equation
  • Step 2: Apply the commutative property as an efficient strategy when multiplying

GCG 2 – Learning Goal: As a mathematician, I can Model and apply the associative property of multiplication MAFS.3.OA.2.5

  • Step 1: Model and investigate finding the product when multiplying three factors (the order of multiplying does not affect the product)
  • Step 2: Justify and apply the associative property as an efficient strategy when multiplying

GCG 3 – Learning Goal: As a mathematician, I can Identify and explain patterns in the multiplication and addition table MAFS.3.OA.4.9

  • Step 1: Look for, identify and explain patterns in an addition table and hundreds chart
  • Step 2: Look for, identify and explain patterns in a multiplication chart
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