1. Strong Start Math Project
Session 7
January 26, 2017

2. Agenda Portfolio Sharing Mathematical Discourse
Multiplication Levels of Thinking
Mathematical Curiosity
Closing and Homework

3. Learning Intention & Success Criterai
We are learning to…
Identify the teacher’s role in facilitating classroom discourse.
Apply strategies that promote fluency with single digit multiplication and division.
We will be successful when we…
Describe teacher actions to facilitate discourse.
can help students apply properties of operations as strategies to multiply.

4. Portfolio Sharing

5. Portfolio Sharing of Selected Artifact
Sit with your
grade level.
No more than
4 per table.
Pick one of the two artifacts to share.
Offer an 3 minute overview of your artifacts.
Listeners will offer feedback on one of the three categories for the artifact section of the rubric.
Closure: Talk through potential ideas for remaining artifacts.
5 minutes

6. Classroom discourse

7. Homework Debrief Talk with your table group:
Share which reason for using classroom talk is most relevant to you.
Support with your example.

8. Facilitating Discourse as a High Leverage Teaching Practice
Facilitate Meaningful Mathematical Discourse
Principles to Action Read p. 29
Figure 11. Levels of Classroom Discourse (p. 32)
Read the Teacher Role column and work with your table to identify shifts from one level to the next.
Name one teacher action that could help a teacher move from one level to the next.
At the end prompt teachers to individually place themselves on the continuum and quietly set a goal for themselves.

9. Developmental levels for multiplication and division

10. Which multiplication facts might you struggle with?
List 3-4 multiplication facts that you have a hard time remembering.
Share with your group. Look for any ones that you have in common.

11. Working toward 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of the operations. By the end of Grade 3, know from memory all products of one-digit numbers.

12. Recognizing Developmental Levels in Children’s Thinking
Level 1: Direct Modeling
Level 2: Skip Counting and/or Repeated Addition
Level 3: Use Known Facts –Numerical Reasoning

13. Level 1: Direct Modeling
You can…
Use counters and make “groups of”
Draw a picture
Create an array with color tiles

14. Direct Modeling 5 x 4 means “5 groups of 4”
Draw a picture.

15. Direct Modeling 5 x 4 means “5 groups of 4”
Use counters and make “groups of.”

16. A game of circles and stars

17. Activity from Marilyn Burns: Circles and Stars
Roll the die
Draw the circles according to the number rolled
Roll the die again
Represent the number of stars in each circle.
Find the total number of stars and write a multiplication sentence and a total.

18. Activity from Marilyn Burns: Circles and Stars
2 groups of 3
2 sets of 3
3, 6
2 x 3 = 6
3 groups of 5
3 sets of 5
5, 10, 15
3 x 5 = 15

19. Teaching Multiplication Through Understanding
Developmental Levels
Level 1: Direct Modeling
Level 2: Skip Counting and/or Repeated Addition
Level 3: Use Known Facts- Numerical Reasoning

20. Level 2: Skip Counting
What numbers are easy to skip count by?
Twos, Fives, Tens
Example: 4 x 5
Say “5, 10, 15, 20.” I skip
counted by 5s four times
so 4 x 5 is 20.
Try this for 7 x 2 and 2 x 7
What is the difference between the two problems? 10 5 15 20

21. Repeated Addition 5 x 4 is the same as 4 + 4 + 4 + 4 + 4 4 4 4 4 4 4
The “groups of” model shown here can be represented by using repeated addition.
5 x 4 is the same as
Tape diagram 4 4 4 4 4 4

22. 5 x 4 Array (5 by 4 array) An array is any Arrangement of things in
rows and columns,
such as a rectangle of
square tiles.
5 rows with 4 in each row.

23. Level 2 Thinking: 5 x 4 Array8 12 16 20

24. Teaching Multiplication Through Understanding
Developmental Levels
Level 1: Direct Modeling
Level 2: Skip Counting and/or Repeated Addition
Level 3: Numerical Reasoning: Use Known Facts—Apply the associative and distributive property to compose and decompose.

25. Video and reflection question
As you watch the video, pay particular attention to the following questions:
What properties did students use and apply as they multiplied?
What evidence did you see of fluency (flexibility, accuracy, efficiency)?

26. Level 3: The Distributive Property
“Area problems where regions are partitioned by unit squares are foundational for Grade 3 OA standards because area is used as model for single-digit multiplication and division strategies (3.MD.7), in Grade 4 for multi-digit multiplication and division and in Grade 5 and Grade 6 as a model for multiplication and division of decimals and of fractions. The distributive property is central to all of these uses…” p. 25 OA Progressions

27. Where does the CCSSM develop the distributive property in Grade 3
Read through 3.MD.7c (p. 25 of the Standards)
Share what you highlighted with a neighbor.
Maybe you found this language:
“Use tiling” “concrete case”
“side lengths a and b + c
is the sum of a x b and a x c”
So what does that mean?

28. 3 X 4 and 4 x 3
Build a 3 x 4 array with your tiles.

29. Breaking Apart a 3x4 Array
What are the ways a 3 x 4 array can be broken apart?
Split rows or columns, not individual tiles
Practice your “groups of language”
3 x 4 = (3x3) + (3x1)
3 x 4 = (3x2) + (3x2)
3 x 4 = (2x4) + (1x4)
How would we record this work on graph paper?

30. Level 3: Distributive Property 6x8
Build a 6 x 8 array using tiles.
Find easier to solve facts inside of what can be a very challenging fact for some students.
Show your work with tiles and on graph paper.
Write down the number sentence that matches your easier problems. Highlight the distributive property.
Use “groups of language” as you work.
Take one of the the participants work to display and discuss.

31. 6 x 8

32. Apply the associative property and the distributive property to 12 x 7
Double a known pair
(6 x 7) + (6 x 7)
Break apart into known pairs
(10 x 7) + (2 x 7) or (12 x 3) + (12 x 4)
Use a known pair then add
(11 x 7) + (1 x 7)
Use a known pair then subtract
(12 x 10) - (12 x 3)

33. Learning Intention & Success Criterai
We are learning to…
Identify the teacher’s role in facilitating classroom discourse.
Apply strategies that promote fluency with single digit multiplication and division.
We will be successful when we…
Describe teacher actions to facilitate discourse.
can help students apply properties of operations as strategies to multiply.