1. Divide & Conquer Joe Zavada: K-6 CCSS Instructional Coach
Elk Grove Unified School District
Welcoming and introduction and logistics

2.  A little humor 

3. Challenges to Division
One of the challenges my students encounter when dividing is_______________.
Teacher Quotes:
“kids come to us…..relying completely on rote processes without having a clue as to how to diagnose or dissect the problems...”
“Kids just always struggle with 2 digit divisors.  Plain and simple.  Especially with decomposition and especially with decimals.”
“It seems that a lot of the students (and their parents) think they can only do division with the standard algorithm…When I try to teach them how to use a model or partial quotients, they are resistant.”
( 2 min ) We are all here because we have students in our classrooms that struggle with the fundamentals of division. Whether it’s when they are first being introduced to the concept or when they are sixth grade are expected to master using the algorithm with double digit divisors. I would like you to take a min. and think about the challenges your students face when working with division. With a partner, each one of you will have 30 sec. to share the following sentence frame: One of the challenges my students encounter when dividing is ________.
( 3 min ) When I began thinking about the session and how it was going to be structured, it’s content, what I was going to focus on, I sent out a survey to teachers at a few sites in my region and asked them what challenges their students, parents, and even they face when working with division. I received quite a few responses that showed me that there is a real concern out there that students are struggling just to master the basic fundamental of division. I wanted to share a few of those responses with you. Your challenges could be, and may be, different from the ones on the board. Read the following quotes.

4. Objectives for Today
Connect how learning in prior grade levels supports the foundation of division
Understand the progression of division across grade levels
Investigate a variety of strategies for division
Review objectives for the workshop
We will look at the development of division from 3rd grade through 6th and what foundational skills the students need to be successful.
We will investigate a variety of strategies that students use to help them develop those foundational skills and what strategies will give you and your students the biggest bang for your buck.
We will then do some math ourselves and practice those strategies.

5. Progression of Division

6. Division progression Fourth Grade Base ten blocks Arrays Area models
Kindergarten
Addition and subtraction strategies
Fourth Grade
Base ten blocks
Arrays
Area models
Repeated subtraction
Partial quotients
First Grade
Addition and subtraction strategies
Base ten blocks
Second Grade
Repeated addition (building block for multiplication)
Base ten blocks
Equal groups
Arrays
Fifth Grade
Base ten blocks
Arrays
Area models
Repeated subtraction
Partial quotients
Building foundation for mathematics in K … see how strategies build each year. As math concepts increase in difficulty students an rely on strategies they understood previously to help them understand the more difficult math concepts.
Students that are struggling in 5th/6th grade reference strategies taught and practiced prior to help students be successful with grade level math
Third Grade
Repeated addition (building block for multiplication)
Base ten blocks
Equal groups
Arrays
Area models
Sixth Grade
Algorithm

7. Table Talk
How does offering multiple strategies help students build the skills they need to deeply understand division, and ultimately conquer the concept of division? Offering multiple strategies help students deepen their understanding of division by_______________.

8. Area Model
So let’s take a look at modeling. Here are some examples of how modeling is represented in the framework and in Go Math. These are examples from 4th and 5th grade. (give a brief description of each example focusing on the progression of the strategy from one grade level to the next)
The 4th grade framework shows modeling represented by an area model
modeling represented by using counters and dividing them up into equal groups.
Modeling represented with base ten blocks is used in 4th grade and can continue into 5th
Modeling with a quick picture is also used in both 4th and 5th grades. 4th grade with one digit divisors, and 5th grade with two digit divisors.

9. Example 10 5 1 5 3
-140 84
- 70 14
- 14 4
- 20 10
+10 12 14
5 + 3 8

10. Partner Practice
Use an area model to solve the following division problems:
168 ÷ 14
104 ÷ 13
TABLE TALK: How will using area models help students deepen their understanding of division?

11. Partial Quotient
Repeated subtraction is a strategy that is directly taught in 4th grade, but can still be utilized in 5th and 6th for students who are struggling with the fundamental skills of division. (give a brief)
Finally, let’s take a look a the strategy of partial quotient. Here are some examples of how partial quotient is represented in the framework and in Go Math. These are examples from 4th and 5th grade. (give a brief description of each example focusing on the progression of the strategy from one grade level to the next)
The 4th and 5th grade frameworks show partial quotient represented by an area model with the student keeping track of how much is left. When the student records how much is left to divide, this represents the strategy of partial quotient.
Partial quotient is used to show that the student can subtract by multiples of the divisor and to find the quotient they add up the numbers multiplied to the divisor. This strategy can also be used with double digit divisors.

12. Example
4 32
x 4 12
x 4 8
x x x

13. Partner Practice
364 ÷ ÷ 28
TABLE TALK: How will using the partial quotient strategy help students deepen their understanding of division?
Participants will be given 5 min to work independently and use the strategy of partial quotient to solve the problems. After 5 min. bring the group back together and ask them to have a discussion with their neighbor/group on how they used this strategy.

14. Connection to algorithm

15. Practice modeling

16. Objectives for Today
Connect how learning in prior grade levels supports the foundation of division
Understand the progression of division across grade levels
Investigate a variety of strategies for division
Review objectives for the day

17. Commitment to new learning
Be prepared to share a response to one of the following sentence frames:
One implication for instruction I see is _________.
One way I see today’s information impacting my students is ___________.
Share with a partner. 30 seconds to share your sentence frame.

18. Thank you!! Joe Zavada CCSS Instructional Coach K-6
Elk Grove Unified School District