1. Connecting Academics & Parents
Academic seminars to sharpen skills and build understanding in MATHEMATICS:
4th grade Division Strategies
TRAINING MATERIALS NEEDED:
Prepared sets of “Playing for Partial Quotients” playing cards
RESOURCES FOR PARTICPANT PACKETS:
Powerpoint
Full page learning progression
Area model for partial products video problem
Playing for partial quotients directions, recording sheet and playing cards
CRITICAL POINT:
The purpose of this slide is to welcome parents and share that this session is about how to help their child have a better understanding of the 4th grade standard on division strategies.
STEP-BY-STEP DIRECTIONS:
Welcome Parents and Guardians to the training.
Share that this training is about how they can help their child better understand the 4TH grade standard on division strategies.
Explain that they will be engaged in some activities that will help them better understand the standard and help them support their child with developing their understanding.
The training will also include some purposeful practice tasks that they can do at home.
Only spend about 2 minutes on this slide.

2. What’s Erik’s Error?
Erick is getting caught up in the “steps” for long division, and he is not thinking about the value of the digits or checking to see if his answer is reasonable.
CRITICAL POINT:
Engage parents with a task in which they analyze common student misconceptions with the standard algorithm for long division to give them a purpose for understanding the importance of connecting division to place value.
STEP-BY-STEP DIRECTIONS:
1. Share with participants that this slide is a sample of work from a 4th grader, Erik.
2. Explain that Erik keeps making the same “mistake” when using long division.
3. Give parents time to think on their own about what Erik’s misconception is.
4. Give participants another minute or so to share their thinking with a partner.
5. Have participants share out.
6. Click for animation to come in with an explanation of the misconception.

3. What’s Amy’s Error?
Amy did not take away enough groups of 6, and she was so busy going through the “steps” that she didn’t realize that her difference was greater than her divisor.
CRITICAL POINT:
Continuation of activity from previous slide. Engage parents with a task in which they analyze common student misconceptions with the standard algorithm for division to give them a purpose for understanding the importance of connecting division to place value.
STEP-BY-STEP DIRECTIONS:
Share with participants that this slide is a sample of work from a 4th grader, Amy.
Explain that Amy is also struggling when trying to apply long division. She keeps making an error, but his error is different from Erik’s.
Give parents time to think on their own about what Amy’s misconception is.
Give participants another minute or so to share their thinking with a partner.
Have participants share out.
Click for animation to come in with an explanation of the misconception.

4. Mathematics Florida Standards Focus
Grade 4
MAFS.4.NBT.2.6 Find whole number quotients and remainders with up to four digit dividends and one digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
CRITICAL POINT:
Expose parents to the portion of the 4th grade division standard that this training will focus on.
STEP-BY-STEP DIRECTIONS:
Share with parents that the misconceptions they just looked at are very common with students who have been rushed to the traditional algorithm (long division) and have not been given adequate time to develop a meaningful understanding through experiences with more conceptually based strategies.
Give parents time to read the standard.
Explain that, while the traditional algorithm (aka long division) is a part of the standard, this workshop will focus on those strategies connected to place value and the distributive property and the illustration of those strategies through arrays/ the area model. These strategies give meaning to the connection between place value and division and help prevent misconceptions similar to those we looked at earlier.

5. Learning Progression: Partial Quotients
CRITICAL POINT:
This slide shows how learning about division progresses from earlier grades to future grades.
STEP-BY-STEP DIRECTIONS:
Give parents time to look at the learning progression. They have a full page version in their packet that might be easier to look at.
Ask parents what they notice about the progression of learning from 3rd grade to 4th, and then how the standard changes in 5th grade.
Clarify to help parents see that 4th grade students will apply their experiences from 3rd grade with fluency in basic multiplication and division facts, understanding of the inverse relationship between multiplication and division, and multiplying whole numbers by multiples of ten to develop and use strategies based in place value and the properties of operations to divide multi-digit whole numbers by one-digit divisors in 4th grade and 2-digit divisors in 5th.
If needed, clarify that we established in earlier conversations that we do not want to rush to that traditional long division algorithm. 4th grade is really focused on those strategies that will deepen students’ conceptual understanding to prevent common errors/misconceptions with the traditional algorithm.
Copyright 2009

6. 3rd Grade Multiplication & Division Strategies
CRITICAL POINT:
The purpose of this slide is to give parents a glimpse and brief description of the background knowledge that 4th grade students have from their work in 3rd grade with multiplication and division.
STEP-BY-STEP DIRECTIONS:
Share that this slide gives parents a brief glimpse into some of the background knowledge that a 4th grader would have to draw upon as they make sense of strategies for division of large dividends..
Give parents time to look at the strategies for the two operations.
Ask parents to compare the strategies for the two operations.
Help parents to see that they both include pictures with equal groups, they both include number lines, arrays, the distributive property (breaking apart numbers) and repeated addition for multiplication, and repeated subtraction for division. Multiplication facts are also shown as a strategy for solving for quotients.
Explain to parents that students in 3rd grade develop the understanding that multiplication and division are inverse, or opposite, operations. Multiplication is repeated addition of equal groups, while division is separating a total amount into equal groups.
Remind parents they will want to keep the inverse relationship between multiplication and division and these foundational strategies in mind as they make sense of division strategies for dividing larger dividends.

7. 4th Grade Partial Products Strategies
35 x 12
CRITICAL POINT:
The purpose of this slide is to give parents a glimpse and brief description of the background knowledge that 4th grade students have from their work in 4th grade partial products multiplication strategies.
STEP-BY-STEP DIRECTIONS:
Tell parents that, this slide has examples of partial products strategies that 4th grade students applied to solve multi-digit multiplication problems earlier in 4th grade.
Give parents time to look at the three different strategies.
Ask them what they notice the strategies all have in common. (Depending on whether or not the parents attended the 4th grade partial products CAP workshop, you may have to spend a little more time on this slide. Ultimately, you want parents to see that all three strategies are based on breaking apart factors into expanded form (by place value) and then using understanding of multiplying by multiples of 10 and basic facts to solve for parts of the final product.)
Tell parents to consider the previous slide with the basic multiplication and division strategies and the relationship they noticed between the strategies. Ask parents what that relationship leads them to believe about the connections between these multi digit multiplication strategies and strategies for division problems with multi-digit dividends. Parents should anticipate that they will be able to use similar strategies of breaking apart numbers (the dividend) to solve division problems (for the quotient). Parents may or may not use the precise vocabulary.
Remind parents they will want to keep the inverse relationship between multiplication and division and these partial products strategies in mind as they explore the division strategies in this workshop.

8. Precise Division Vocabulary
CRITICAL POINT:
The purpose of this slide is to share with parents some vocabulary that they may hear and want to use throughout the rest of the training.
STEP BY STEP:
Share with parents that this is vocabulary connected to division that their children will be using and that they will hear throughout this training.
Share that the dividend is the total amount that is being separated or divided up into equal groups, The divisor describes how the dividend is being divided up- it can represent the number of equal groups or the number of items in each group. The quotient is the answer to the division problem; if the divisor is the number of equal groups, the quotient represents the number of items in each group, and vice versa.
This slide is meant to be very brief.

9. Area Model for Partial Quotients
CRITICAL POINT:
The purpose of this slide is for parents to hear a teacher explain and area model for partial quotients to a student, and see a student begin to develop an understanding of the strategy.
STEP-BY-STEP DIRECTIONS:
Share with parents that they are now going to watch a brief video clip of a teacher explaining the strategy of using an “area model to find partial quotients” to a student.
Have parents turn in their packet to the full size version of the area model and question that accompanies this video. They will want to be able to look at this model while they watch the video to try and make sense of the strategy.
Click on the picture of the video on this slide. This link will open up the cpalms website. You will need to scroll down to the video and click on the image for it to start playing. Maximize the video to full screen.
4) Pause the video when it gets to the slide that says “the student worked for about two minutes….” and minimize (don’t close) the internet explorer. Come back to powerpoint and click to go to next slide.

10. CRITICAL POINT:
The purpose of this slide is to give parents time to process the video and make sense of this area model.
STEP BY STEP:
Parents have just watched and listened to the teacher and student’s discussion of the area model on this slide. Now, give parents time to turn and talk with a partner or table group to process and make sense of the model.
2) Remind parents of the foundational third grade division strategies they looked at earlier. They can look back at the slide with the anchor charts. Ask which of those strategies they think has the closest connection to this area model.
3) Facilitate discussion so that parents to see that this is like repeated subtraction, but instead of repeatedly subtracting the divisor, they are subtracting multiples of the divisor) and this breaks apart the dividend into parts (like distributive property)
4) Ask the following additional questions to help clarify the model:
Why do you think this is called an area model for “partial quotients”? (because they are solving for parts of the quotients)
Why do you think the student chose to use the partial quotient of 100 first? (because it is easy to mutliply 7 by 100 and it results is a large chunk to take away)-
What are the numbers under the box? (difference after part of the dividend has been subtracted)
What are numbers at the top? (Partial quotients)
How did student get the quotient of 127? (added partial quotients)
5) Once you feel like the parents have an understanding of the model, ask, “Why would this strategy be beneficial to a student?” ( It is a very flexible strategy; students get to use multiplication facts that they know.)

11. Can you use an area model to solve 792÷6?
CRITICAL POINT:
The purpose of this slide is to give parents the opportunity to apply the area model to solve for partial quotients.
STEP BY STEP:
1) Have parents apply the area model strategy to the problem on the slide. This is the same problem that the student will complete when you show the rest of the video.
2) Give parents 2 minutes to solve using the area model; this is the same amount of time that the student uses in the video. 3) Have parents close their powerpoint, so they don’t look see solutions in the powerpoint. They can look at the model that was on the previous slide to use as an example.
4) Do not have discussion about the problem or parents’ solutions and strategies at this point.

12. CRITICAL POINT:
Parents will watch as a student explains how they applied the area model and analyze the students’ work.
STEP BY STEP:
Tell parents that they are now going to see the student from the video apply the area model to the same problem they just solved.
Have parents turn to this slide in their powerpoint, so they can clearly see the student’s work as he explains his thinking.
3) In order to continue the video, you will need to minimize this powerpoint and re-maximize internet explorer. Click on the video so it continues to play.
4) After the video maximize the powerpoint again, and resume slideshow mode.
4) Facilitate a discussion to debrief on the video and support parents in understanding the strategy:
Why did the student say he used the partial quotient of 100? (because he knew 600 was close to 792)
What made student switch from using partial quotient of 7 to 11? (he realized he would be able to subtract a larger number from 108 to get the problem completed more efficiently)
How did student find final quotient of 132? (he added his partial quotients)

13. Which is correct? CRITICAL POINT:
The purpose of this slide is to make sure parents see that the flexibility of using partial quotients makes division problems like this accessible to varying levels of students.
STEP BY STEP:
This slide shows the work from student in the video and another student’s response to the same question.
Give parents time to analyze the two models.
Point out that the two models are different but they got the same quotient. Ask parents, “Who was correct?” (both) “How is this possible?” (they used different partial quotients to break apart the dividend)
Clarify that this is a huge benefit to using this strategy, because students are able to use those facts that they know the best so they can most efficiently solve the problem.
Ask parents if any of them used different partial quotients, if any did, have them share the way they broke apart the dividend, and ask them why they chose to use the partial quotients that they did.
Give parents time to ask any clarifying questions about the strategy. (You may find it beneficial to view the two tutorials that are on the “Online Resources Slide – slide 17” prior to delivering the workshop ,so that you feel prepared to answer questions from parents.)

14. Written Record for Partial Quotients
What connections do you see?
CRITICAL POINT:
This slide will help parents make connections between the area model for partial quotients, and the written record strategies.
STEP BY STEP:
1) Give parents time to compare the area model to the two examples of the written record for recording partial quotients.
2) Have parents turn and talk about any connections they see between the two ways of recording partial quotients and the area model.
3) Parents should see that the partial quotients are recorded to the right of the one record and on top of the other record. 4) Click to highlight the student’s “list of multiples/think box/I know box…” .
5) Ask parents why they think the student did that. Parents should see student was recording those facts/multiples of the divisor that they knew really well that could help them efficiently solve the problem.

15. How could we represent these partial quotients strategies as an expression?
(600÷6)+(120÷6)+(60÷6)+(12÷6)
CRITICAL POINT:
Parents will see the connection between partial products and expressions modeling the distributive property.
STEP BY STEP:
Ask parents to try and represent the partial products strategy for this problem as an expression.
Give time for parents to work. Look to see if any parent records the correct expression of (600÷6)+(120÷6)+(60÷6)+(12÷6). Do not give too much time for this.
Click for the expression to come up on the slide. Explain to parents that this expression represents the distributive property.
Ask parents how this expression matches the two partial products strategies. They should see that the dividend has been broken up into the addends of 600,120, 60 and 12. Each of those is then divided by the divisor of 6. The partial quotient for each of those problems is then added to give the total quotient.

16. Try It and Take it Home! DO TRY THIS AT HOME!
Warning: Implementing this engaging activity will result in an increase in motivation and long-lasting learning.
CRITICAL POINT:
Parents will now apply the strategies they learned at the workshop while they play the game “Playing for Partial Quotients” .
STEP BY STEP:
Pass out the prepared decks of division problem cards for the game to pairs of parents.
Have parents turn in their packet to the directions for the game.
Give parents time to read the directions. They have two copies of the recording sheets in their packets, so they can use one while they play today, and they will have a blank copy for them to use when they play with their child at home.
Clarify the directions for the game if needed, and give parents time to play. It is important that there by enough time left for parents to play the game, because this is when they will practice using both the area model and the written record for partial quotients.
While parents are playing, monitor to help support them if needed while they apply the partial quotients strategies.

17. Online Resources
Video tutorials to help parents build their understanding of partial quotients: -
Online division game for students: –
CRITICAL POINT:
Share with parents some online games, practice, and instructional videos that could help reinforce this standard.
STEP-BY-STEP DIRECTIONS:
If there is time and you have internet access, visit some of these websites.
Address any additional questions parents may have.
Thank parents for coming.