1. Framed by the Distributive Property
Seeing the BIG Picture!
Framed by the Distributive Property
We are looking at how the big ideas in the common core are developed across grade levels. As leaders of mathematics, it’s important for you to be able to make connections across grade levels. One of the big ideas that we are focusing on is properties. Today we are specifically looking at the distributive property and how it extends across grade levels. Arrays are important in 3rd grade and is an activity, but how does multiplication build in other grade levels.
Beth Schefelker
Bridget Schock
Connie Laughlin
Hank Kepner
Kevin McLeod
November 16, 2012

2. 17 x 32 Time to Think… Find the product (creatively?)
Look For Strategies – Chart out individual strategies from the audience. Surface an open array model. Make connections to the partial products that are present.
Make connections to “the” standard algorithm – identify where the partial products connect.
Partial products of 300, 210, 20, 14
(20x32)-(3x32)
(17x30)+(17x2)

3. Time to Think…
So what is the Distributive Property anyway? We can do it, but can we define it? Turn and talk…can you and a neighbor come up with a clear definition of the Distributive Property.
Distributive property is unlike any other properties because it involves two operations, addition and multiplication.
Distributive property is addition over multiplication.
Make the connection between the strategies and the notation…leading to the formal notation of (a+b) x (c+d).

4. Learning Intention & Success Criteria
Learning Intention: We are learning to deepen our understanding of the application of the distributive property. Success Criteria: We will be successful when we can articulate the development of the distributive property as it expands across grade levels.

5. Progressing through Multiplication
Read the following standards at your table:
2.OA.4
3.OA.5
4.NBT.5
5.NBT.5
Use the following questions to guide the discussion at the table. Be prepared to share out.
How does the idea of multiplication grow across grade levels?
How does the work in each grade level build toward an understanding and use of the distributive property to justify strategies?
40 minutes
Use note taking guide
Development and use of distributive property
Early years – numerical and visual
Don’t want to be rushed this time…but would like to address going from concrete to representational to abstract

6. 12 x 6 ¾ Does anything change? Find the product (creatively?)
Turn and talk on each product.
The number system changes
Structure and Repeated Reasoning is what allows students to use the distributive property in an abstract form.

7. The Power of the Distributive Property
Read… Use Fractions To Develop Algebraic Thinking What message is this article sending about the Distributive Property?
Turn and talk on each product.
The number system changes
Structure and Repeated Reasoning is what allows students to use the distributive property in an abstract form.

8. Extending the Progression Study
Read the following standards at your table:
6.EE.3
6.NS.4
7.NS.2
7.EE.1 and 2
Use the following questions to guide the discussion at the table. Be prepared to share out.
How does the previous work done in grades 2-5 with distributive property extend in the middle grades?
How do student expectations about the use of the distributive property change?
30 minutes
Make into a handout including
Development of the use of distributive property
Middle years – Symbolic and abstract
Don’t want to be rushed this time…but would like to address going from concrete to representational to abstract

9. Math Practice Standards
Where were Math Practice Standards 7 “Look for and make use of structure.” and 8, “Look for and express regularity in repeated reasoning.” evident in today’s session on multiplication?
10 minutes
How does the repeated reasoning and structure evolve from the standards?

10. Learning Intention & Success Criteria
Learning Intention: We are learning to deepen our understanding of the application of the distributive property. Success Criteria: We will be successful when we can articulate the development of the distributive property as it expands across grade levels.

11. Reflections
As a teacher of mathematics, how has your understanding of the importance of the distributive property grown? As a leader of mathematics in the district, how will your understanding of the distributive property support your work with teachers?
10 minutes

12. Professional Practice
How is the understanding of the distributive property developed in your textbook materials?