1. Graph Paper Jigsaw How many squares are on your paper?
Find your partner (to make 900).
Refer to Becky’s notes regarding the activity. Use one grid page to do the activity (i.e. pre-cut for your teachers). Then give complete handout (grid & directions) to the teachers for their reference.

2. Extending beyond 100

3. Phase 6
Extending Multiplication and Division to Multi-digit Factors and Beyond 100

4. *Utilize the ten-plus structure!*
Build IT!
Using two colors of unifix cubes, build three trains that are thirteen cubes long.
*Utilize the ten-plus structure!*

5. 13 x 3
Break 13 into groups of 13 = 3 groups of 10 and 3 groups of 3 = = 39
Bring out here how absolutely critical it is that students are comfortable with multiples of 10!!! (Addition, Subtraction & PV knowledge are CRITICAL foundations!!!)

6. 13 x 3 Record snap cube model on graph paper.
Use color coding and label each part.
Transition to showing on graph paper (and then on open arrays) without first building the model

7. What VISUALS and/or MATERIALS show 12 x 14?
let’s think about 12 x 14
What VISUALS and/or MATERIALS show 12 x 14?
See VDW page 180 for some ideas
How can those visuals help us to solve?
Which models extend easily for larger numbers?
Encourage teachers to make drawings and/or get out materials. Refer them to VDW for ideas. Try to have at least 2-3 from each teacher. May share with document camera or have everyone put their drawings on a wall (lay out materials on a table) and then gallery walk???
Van de Wall is missing the number line model… see if you can prompt at least some of your teachers to give that a try!
The following slides are my personal examples. If helpful, you are welcome to show them. But skip them if your teachers have this covered!

8. Set Model
12 groups of 10 = 120
12 groups of 4 = 48
= 168

9. Array
= 168

10. Unifix Cubes
= 168

11. 12 x 14 – graph paper array
= 168

12. 12 x 14 – Open array
= 168

13. 12 x 14 Linear

14. Visual models Figure 11.6 and 11.7 – page 182 in VDW
Use visuals (e.g., graph paper arrays, open arrays, open number line) to show the partitioning and compensation strategies in 11.6 & 11.7
Use a partition and/or compensation strategy to solve: 19 x 5, 220 x 7.
Record your strategy!
Van de Walle book
Recommend wrapping up this activity by 11:00 so that Multiplication beyond 100 can be completed by lunch time.

15. Jot down some ways to solve
Getting Bigger!
Jot down some ways to solve
43 x 51
Consider having participants work independently to solve with a strategy/drawing method, then collect ideas. Following slides are hidden but show possible solutions.
After recording the arrays and/or open number line(s), ask what foundations and understanding of PV a student would need to make sense of this. In particular, consider what it takes to understand that 10 x 50 = 500, or 3x50 = 150 etc.

16. Multiplication and Division of whole numbers
Fluency Standards for
Multiplication and Division of whole numbers
3.OA.7
Multiply & Divide within 100
Strategies based on meaning and properties of operations (i.e. associative and commutative)
Inverse relationship of multiplication and division
By end of year, know one digit by one digit multiplication facts
4 – Critical Domain 1
Multi-digit Multiplication
Strategies based on place value and properties of operations
Supported by suitable representations
Also developing understanding of multi-digit division
5.NBT.5
Fluently multiply multi-digit numbers
Standard algorithm for multiplication
6.NS.2
Fluently divide multi-digit numbers
Standard algorithm for division
Just thought it might be helpful to remind teachers of the fluency expected at each grade level. Revisit the expectations of when kids should use strategies vs algorithms. I know most of our teachers understand this progression & distinction. You might frame this as … how about the teachers in your building… do they see these progression. Next two slides give specific standards.. They are the “fluency” standards but show the emphasis of using strategies BEFORE expecting fluency the following year.

17. Connecting to the Standards
4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Emphasize that supporting students in these strategies IS in the standards!!!

18. Partial Products http://www.showme.com/sh/?h=FvwxRrM
Omit if not time…. Or skip up to the 12 x 14 part…
We’re going to transition here to algorithms - starting with this introduction to partial products.
In this video, the student uses a snap cube “area model” to explain partial products. Probably a bit redundant in terms of content of the pD, but it’s very quick and I think it’s neat that (1) a student is doing the explanation and (2) the focus on using color coding of unifix cubes.

19. Division Make1 pile of 232 sticks.
Share the sticks equally into 4 piles
Have a pair of volunteers make the collection or start with the collection pre-made. (Consider if you want to include “super bundles of 100” in your inventory).
Ask…how might your students share out into 4 piles… get volunteers to come up and show (or describe) how they might share. (Do at least one physically)…. Record written model to match method. Examples follow. (array or number line could be used).

20. Division Make1 pile of 232 sticks.
Share the sticks equally into 4 piles
What if we wanted 8 piles… how many would be in each group?
Have a pair of volunteers make the collection or start with the collection pre-made. (Consider if you want to include “super bundles of 100” in your inventory).
Ask…how might your students share out into 4 piles… get volunteers to come up and show (or describe) how they might share. (Do at least one physically)…. Record written model to match method. Examples follow. (array or number line could be used).

21. Invented Strategies for Division
Kathy is making hair bows out of ribbon for her dance team. She has 314 inches of ribbon. Each bow takes 24 inches of ribbon. How many bows can she make?
What is answer that you know is too small?
What is an answer that you know is too big?
See how many ways you can find to solve the problem.
Ask –
What type of division (fair share (partitive) or measurement (quotative))
Does the context/type of problem affect how you approach solving it?
How do we know the answer is reasonable? What easy estimating could we do to check?
Record strategies using a linear model (see example on next slide)
How many bows can she make each bow uses 48 inches of ribbon?

22. For leader reference… do this live, engaging teacher in discussion i.e. “what do you know?” or “Is there a friendly number that might help?” or “what’s a number of bows you know you can make… why”
As a leader, you might model solving this on the quantity line…. Treat each square as 10.

23. Invented Strategies for Division
Amy is making hair bows out of ribbon for her dance team. She has 314 inches of ribbon. There are 24 girls on her team. If she wants to make 1 bow for each girl, what length ribbon can she use for each bow?
What type of division situation is this?
What division expression models this question?
314  24
Omit if low on time
The purpose of this problem is to realize that this question is written as a “fair share” situation. But we can solve the expression with either kind of thinking!!!
You might ask… how would you think about it when solving?

24. Linear models
Use your quantity line to solve or and Empty Number line to solve
49231

25. Invented Strategies for Division
James is building a patio. He has 238 paving stones. Each row of the patio uses 19 stones. How many rows can he lay?
What is answer that you know is too small?
What is an answer that you know is too big?
See how many ways you can find to solve the problem.
What might be a scaffold or an extension for this problem?
How does the context of the problem influence your thinking?
Omit if low on time
Ask –
What type of division (fair share (partitive) or measurement (quotative))
Does the context/type of problem affect how you approach solving it?

26. Visuals for illustrating division strategies
Arrays (open or graph paper)– “How many columns of this size can I make?” or “How can I share fairly into these rows”
Empty number line – “How many jumps of this size can I make?” or “How many pieces of this length can I make?”

27. Multiplication and Division of whole numbers
Fluency Standards for
Multiplication and Division of whole numbers
3.OA.7
Multiply & Divide within 100
Strategies based on meaning and properties of operations (i.e. associative and commutative)
Inverse relationship of multiplication and division
By end of year, know one digit by one digit multiplication facts
4 – Critical Domain 1
Multi-digit Multiplication
Strategies based on place value and properties of operations
Supported by suitable representations
Also developing understanding of multi-digit division
5.NBT.5
Fluently multiply multi-digit numbers
Standard algorithm for multiplication
6.NS.2
Fluently divide multi-digit numbers
Standard algorithm for division

28. Connecting to the Standards
5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.
Is solving using these non-standard ways implementing the standards?

29. Minilessons Glance through either (or both) minilessons books.
How is division developed through minilessons?

30. Division Strings Video Link
I don’t think you’ll have time for this one. But I’ve left it in the powerpoint but most likely you simply skip this slide. You can remind them that they have access to these videos on the CDs we gave them. Show what you have time for and if your teachers are engaged. Pause as needed to prompt discussion. Consider linking to Professional Noticing cycle. Or asking teachers to solve a task before we watch the students solve it.
Video Link