CCSS.Math.Content.3.OA.B.5
The standard
Apply properties of operations as strategies to multiply and divide.
Common Core State Standards for Mathematics · Operations and Algebraic Thinking
What this standard means
Students need to use multiplication properties as tools, not just name them. They should be able to switch factors, group factors in helpful ways, and break apart a factor to make a harder fact easier. They also need to connect these moves to division when they use related facts.
Mastery looks like a student explaining why 7 x 8 can be solved as 7 x 5 plus 7 x 3, or why 4 x 9 equals 9 x 4. Common trouble spots are treating properties like tricks to memorize, losing track of equal values, or breaking apart both factors at once and getting confused.
Ways to teach it
- Hands-on activity: Build 6 rows of 4 counters, rotate the array, and record both multiplication equations that match it.
- Discussion prompt: Ask, “Which is easier, 8 x 7 or 8 x 5 plus 8 x 2, and why?”
- Quick assessment: Give 9 x 6, 3 x 4 x 5, and 7 x 8, and ask students to show a property strategy for each.
- Real-world connection: Use egg cartons to show 3 groups of 12 as 3 groups of 10 plus 3 groups of 2.
Plan a lesson for CCSS.Math.Content.3.OA.B.5
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Related standards
- CCSS.Math.Content.7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- CCSS.Math.Content.7.NS.A.1d
Apply properties of operations as strategies to add and subtract rational numbers.
- CCSS.Math.Content.7.NS.A.2c
Apply properties of operations as strategies to multiply and divide rational numbers.
- CCSS.Math.Content.1.OA.B.3
Apply properties of operations as strategies to add and subtract.