CCSS.Math.Content.3.OA.D.9
The standard
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.
Common Core State Standards for Mathematics · Operations and Algebraic Thinking
What this standard means
Students need to spot patterns in addition and multiplication, then explain why the pattern happens. They should use facts, arrays, skip counting, and properties like commutative and distributive properties to justify their thinking, not just say, “I noticed it.”
Mastery looks like a student finding a pattern, testing it with several examples, and explaining it with numbers, words, or a model. Common sticking points are confusing a pattern with one lucky example, naming a pattern without explaining it, and using vague words like “it just goes up.”
Ways to teach it
- Have students color multiples of 3 and 6 on a hundreds chart, then write one sentence comparing the patterns they see.
- Ask, “Why is any number times 4 even?” and have students explain using an array, equal groups, or repeated addition.
- Show four multiplication facts, such as 3×4, 3×5, 3×6, 3×7, and ask students to write the next two facts and the rule.
- Connect to seating: if each table has 4 chairs, students predict chair totals for 1 to 10 tables and explain the pattern.
Plan a lesson for CCSS.Math.Content.3.OA.D.9
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Related standards
- CCSS.Math.Content.1.OA.B
Understand and apply properties of operations and the relationship between addition and subtraction.
- CCSS.Math.Content.6.EE.A
Apply and extend previous understandings of arithmetic to algebraic expressions.
- CCSS.Math.Content.3.MD.C.7
Relate area to the operations of multiplication and addition.
- CCSS.Math.Content.3.OA.D
Solve problems involving the four operations, and identify and explain patterns in arithmetic.