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.)

[divider] [/divider] Students are able to… 

[divider] [/divider] Students are able to…because teachers:

  • Present students with a variety of multiplication examples using concrete representations including equal group and array models. Ask questions that lead them to conclude that the order of the factors does not affect the product.
  • Provide students with opportunities to explore the identity element for multiplication. (Students only need to recognize that when multiplying a number by one, the product is the number).
  • Provide examples of models of the associative property for students to explore that will help them discover strategies for making multiplication of several factors easier.
  • Introduce the distributive property by having students build a multiplication array for 6×7 using square tiles. Write the equation for this array.  Ask them to divide the array into 2 pieces along a horizontal or vertical line.

[divider] [/divider] Questions to ask students:

• Ask students if the order of the factors in a multiplication equation effects the product and to prove why or why not.

• Sample answer/s that indicate understanding: “The order of the factors does not change the product. I can make a 3 x 2 array, which is 6. Then I can turn that array so that it is a 2 x 3 array, and I still have a product of 6.”
• Sample answer/s that indicates partial understanding or a misconception: “It depends on what the factors are.”

• Ask students why it is helpful to know that the grouping of factors will not change the product when they are trying to find the product of 3 or more factors.

• Sample answer/s that indicate understanding: “I can decide which numbers I want to multiply first, so that I can use the facts I know. If I was trying to solve 5 x 7 x 2, I could multiply the 5 x 2 to get 10, because that is easy to multiply by 7 and get the product of 70.”
• Sample answer/s that indicates partial understanding or a misconception: “You have to multiply the factors in order.” Or “You can’t find the product of more than 2 factors.”

• Ask students to explain how breaking apart a factor can be used to find a product.

• Sample answer/s that indicate understanding: “If I have a problem I don’t know, like 6 x 7, I can break apart one of the factors and use facts I do know. I could break apart the 7 into 2 and 5, and then just find 6 x 2 and 6 x 5 and add the products together.”
• Sample answer/s that indicates partial understanding or a misconception: “If I am trying to find a product, like 6 x 7, I know that 3 x2 is 6, so I can find 3 x 7 and 3 x 2 and add those products back together.”

[divider] [/divider] FSA Notes:

Cognitive Complexity Level: 2 – Basic Application of Skills and Concepts

Achievement Level Descriptors:

2- applies commutative property of multiplication

3- applies commutative,  associative, and distributive properties of operations as strategies to multiply and divide

4- determines an appropriate strategy or multiple strategies for a given situation

5- determines the error in the steps of a distributive property strategy

Assessment Limits:

All values in items may not exceed whole number multiplication facts of 10 x 10 or the related division facts.

Items may contain no more than two properties in an equation (e.g., a × (b + c) = (a × b) + (c × a)).

[divider] [/divider] Additional Resources:

Additional in depth content knowledge

 

Blog Posts:

Understanding the Associative Property of Multiplication

Modeling the Distributive Property of Multiplication

Learn Zillion Videos:

Solve Multiplication Problems Using the Associative Property

Solve Multiplication Problems Using the Distributive Property

[divider] [/divider] Sample Formative Assessment Tasks:

[divider] [/divider] Resources/Tasks to Help Your Child at Home:

Use everyday items (cereal, toys, pennies, etc.) to make equal groups of arrays, and have your child write an expression that matches the model. Then, have them change the way the objects are grouped and find other expressions that would have the same product.

Ask, “How are 5 bags of 4 apples in each bag is similar to and different from 4 bags of 5 apples each?”

LearnZillion Video: Understand the Commutative Property by Naming Arrays https://goo.gl/hGHnjP

LearnZillion Video: Solve Multiplication Problems using the Associative Property https://goo.gl/6ZFj5r

LearnZillion Video: Understand the Distributive Property of Multiplication by Breaking Apart Numbers https://goo.gl/nU8pHh