Standard: 3.OA.B5 – Apply properties of operations as strategies to multiply and divide. Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property.)
Grade level: Grade 3
Subject: Mathematics
Domain: Operations & Algebraic Thinking
Teacher Overview
This standard focuses on applying properties of operations as strategies to multiply and divide. Understanding these properties helps students solve problems more efficiently and build a foundation for algebraic thinking. Students should be fluent in basic multiplication and division facts and understand the concept of equal groups and arrays.
Mastering this standard will prepare students for more complex multiplication and division problems and introduce them to algebraic thinking.
Common Misconception 1
A common misconception is that multiplication order matters, which is not true due to the commutative property. For example, 3 x 4 is the same as 4 x 3.
Intervention 1
Use visual aids like arrays and grouping objects to demonstrate that the order of multiplication does not affect the product.
Common Misconception 2
Another misconception is confusing the associative property with the commutative property. Students might think that changing the grouping of numbers is the same as changing the order.
Intervention 2
Provide practice problems that clearly illustrate the difference between the associative and commutative properties, using step-by-step solutions.
Prerequisite Knowledge
Students should understand basic multiplication and division facts, and have a grasp of addition and subtraction. They should also be familiar with the concept of equal groups and arrays.
Subsequent Knowledge
Students will develop the ability to solve more complex multiplication and division problems, understand the relationship between multiplication and division, and apply these properties to algebraic expressions.
Instructional Activities
- Create arrays to visualize multiplication problems
- Group objects to demonstrate the commutative property
- Use number lines to show the associative property
- Solve word problems involving the distributive property
