1. Agenda Multiplication—Level 2 and Level 3
Academically Productive Discourse
Mathematical Curiosity
Closing and Homework

2. Strong Start Math Project
March 2, 2017
4:30 p.m. - 7:30 p.m.

3. Learning Intention & Success Criteria
We are learning to…
deepen our understanding of how to facilitate classroom discourse that support students’ ability to communicate mathematical reasoning.
apply strategies that promote fluency with single digit multiplication and division.
We will be successful when we…
help students apply properties of operations as strategies to multiply.
identify the Four Steps Toward Productive Talk
articulate why Turn and Talk supports…
Step 1: Helping Individual Students Clarify and Share Their Own Thoughts.

4. Working Toward fluency with Multiplication Facts

5. 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

6. Level 2: Skip Counting
What numbers are easy to skip count by?
Twos, Fours, Threes, 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

7. Counting Around the Classroom
Gives students practice with counting many different numbers and fosters numerical reasoning.
Focus is on:
Becoming familiar with multiplication patterns
Relating factors to multiplication
Developing number sense about multiplication and division relationships.
Count by 7s or count by 15s (melissa)

8. 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

9. 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.

10. Level 2 Thinking: 5 by 4 Array8 12 16 20
= 20

11. Level 2 Thinking: 4 by 5 Array10 15 20
= 20

12. Standards Interpretation Guide Grade 2 Geometry Progressions
2.OA.4
2.G.2
Share your work from the interpretation guide with a partner and what you highlighted on pp of the Geometry Progressions Document.
What message do these standards send to Grade 2 teachers as their children work with arrays?

13. Grade 2 Cluster Statements
2.OA.4
We can make a reference to the Grade 2 cluster wheel chart – bring awareness, that all. This is called the Content Overview page.
2.G.2

14. Envisions 2.0: Grade 2 Cluster Chart

15. 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.

16. 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)?

17. Where does the CCSSM develop the distributive property in Grade 3
Revisit through 3.MD.7 (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?

18. Checking In With the Progressions
Geometric Measurement Progression Grades K-5 (The fourth red tab on the document) Read and highlight: p Start with the fourth paragraph on p. 17 “ Students learn to understand and explain…”

19. 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

20. 3 x 4 and 4 x 3
Build a 3 x 4 array with your tiles.

21. Breaking Apart a 3x4 Array
What are the ways a 3 x 4 array can be decomposed?
Decompose one factor
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?

22. 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.

23. 6 x 8

24. 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)

25. Discourse in the Classroom

26. Mathematical Shifts
Focus
Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the Standards.
Coherence
Teachers carefully connect the learning within and across the grades so that students can build new understandings on foundations built in previous grades
Deep Understanding
Students deeply understand and can operate easily within a math concept before moving on. They learn more than tricks to get the right answer. Their learning is built on conceptual understanding.
When teachers commit themselves to teaching for understanding, classroom discourse and discussion are key elements in the overall picture.
- Classroom Discussions in Math, p. xv

27. What Constitutes Effective Mathematics Discourse?
Mathematical discourse includes the purposeful exchange of ideas through classroom discussions, as well as through other forms of verbal, visual, and written communication. Principles to Action (NCTM, 2014, p. 29)

28. 5 Reasons to Use Talk in Mathematics
Talk can reveal understanding and misunderstanding. Talk supports robust learning by boosting memory. Talk supports deeper reasoning. Talk supports language development. Talk supports developmental social skills.

29. Step 1: Helping individual students to clarify their own thoughts.
4 Steps Toward Productive Discussions p Classroom Discussions in Math
Step 1: Helping individual students to clarify their own thoughts.
Step 2: Helping students to orient to others thinking.
Step 3: Helping students deepen their reasoning
Step 4: Helping students to engage with the reasoning of others.
Chapin, S., O’Connor. C, Anderson, N. (2013) Classroom Discussions in Math.
Solutions, Sausalito, CA

30. Step 1: Helping individual students to clarify and share their own thoughts.
Goal: To help students get better at saying what
they are thinking in ways that can be understood.
6 Moves:
Wait time
Turn and talk
Stop and Jot
Will You Share That With the Class?
Say More
So Are You Saying…?
Read p. 12 and p. 14 (Turn and Talk) to add to your
understanding of Step 1.

31. Focus Move: Turn and Talk
Use the grid on p. 51 – 52 to add to your
understanding of Turn And Talk.
✓ If the information is familiar.
★ If this is a new idea.
? If the information raises a question.

32. Sharing About Turn and Talk
As a trio…
Take turns articulating the purpose of Turn and Talk and how it supports Step 1: Helping Individual Students Clarify and Share Their Own Thoughts.
Focus your conversations around new ideas noted in the reading.
Be prepared to share out one suggestion that your group decided would be helpful for students or for teachers.

33. Turn and Talk in Action Grade 3 – How many cans of grape juice?
(1 min 38 sec)
As you watch the video clips note how Turn
and Talk was used to clarify or share thinking in
each instance.
What is the teacher’s role in the conversation?
What do the students understand about their role in Turn and Talk?
Show video clip Grade 3: How many cans of grape juice?

34. Grade 3 How many cans of grape juice?
Mrs. Foley needs to buy drinks for her daughter’s birthday
party.
She wants to buy both apple juice and grape juice.
Cans of apple juice are sold in 6 packs.
Cans of grape juice are sold in 4 packs.
Mrs. Foley needs to buy at least 26 but no more than 30 cans
of juice.
How many packs of apple juice might she buy?
How many packs of grape juice might she buy?
Show or explain your answer.

35. What did you notice? Discuss the following with your table group.
What was the teacher’s role in the conversation? (Revisit PtA Chart, p. 29)
What do the students understand about their role in Turn and Talk?
How did the Turn and Talk help students clarify and share thinking?

36. Thinking About Getting Started… Turn and Talk
Clip 1: Turn and Talk Modeling (4 min 57 sec)
How might the turn and talk modeling in this clip help Mrs. Luizzi’s students use this talk tool in productive ways?
How might you enact a similar role-play in your classroom before you attempt turn and talk?

37. Something to remember…
if we simply ask students to talk, without thinking carefully about our purposes, we may end up with irrelevant, hard-to-manage talk that serves no clear academic purpose. Sometimes this aimless talk may be pleasant; sometimes it may be unpleasant. But in either case it probably will not significantly advance student thinking and learning.
Classroom Discussions in Math
(Chapin, O’Connor, & Anderson, 2013, p. 9)

38. Learning Intention & Success Criteria
We are learning to…
deepen our understanding of how to facilitate classroom discourse that support students’ ability to communicate mathematical reasoning.
apply strategies that promote fluency with single digit multiplication and division.
We will be successful when we…
help students apply properties of operations as strategies to multiply.
identify the Four Steps Toward Productive Talk
articulate why Turn and Talk supports…
Step 1: Helping Individual Students Clarify and Share Their Own Thoughts.

39. Homework

40. Homework Due Mar 23 Reading & Respond – Multiplication and Division
Completed Portfolio
Classroom Discussions