Just like in addition and subtraction, students need a variety of ways to solve for number sentences involving multiplication and division without relying on rote memorization. Students should employ a variety of solution methods that demonstrate their understanding of the meaning of multiplication. These methods include the use of the commutative property of multiplication, the associative property of multiplication, and the distributive property of multiplication over addition. Because these properties do not apply directly to division, a division problem needs to be thought of in terms of multiplication.
Understanding the Standard:
- Students should have a variety of opportunities to work with number sentences that are missing one of the whole numbers.
- Continued work with multiplication and division fact families will aid students in finding solutions much faster.
- Students should learn how to solve problems using the following strategies:
- Example: If 6 x 4 = 24 is known, then 4 x 6 is also known (commutative property of multiplication).
- Example: 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).
- Example: 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 porperty of multiplication).
Questions to Focus Instruction:
- Can students fluently multiply and divide one digit numbers?
- Can students make a set of multiplication and division fact families?
- Are students able to use a picture or diagram to help them solve for a missing portion of a multiplication or division number sentence?
Students are able to fluently multiply and divide.
At Grade Level:
Students are able to fluently move between multiplication and division number sentences and use a variety of strategies for solving problems.
1Students need not use formal terms for these properties.