1. ALGEBRA SESSION Session 4: Range of Learners

2. 12 x 3 Array  Using the same picture, show 6 x 6 and prove that array also has the same value  How did your representation change?  What mathematical "rule" or property did you apply?  How would this help students struggling with computational fluency?

3. Students in action  Video 1 and Video 2

4. Computational Fluency  Major focus in elementary grades  Obstacle to success and confidence in math  Students see each problem as a separate endeavor (trying to remember the "right steps" to follow rather than building on what they already know)

5. CCSS Connections  Our goal: students learn computation strategies deriving from the operations' properties and the structure of the base ten system.  Where do you see evidence of this goal across grade level standards?  Where is it that we expect kids to master these ideas within the CCSS specifically?  Stay in OA even though NBT would also be relevant

6. Karly (p. 69-70)  What does she understand?  What does she need to work on?

7. Karly (pg. 71)  What has changed?  What property is she using when she talks about dispersing the 9 into 3 bags of 3?  4 x 9 = 4 x (3 x 3)  What does this tell us about her progress?  What are the teacher's next steps?

8. Quick vs. Efficient  What is the difference? Work as a table to come up with an explanation.  Many times with struggling learners teachers what to give them quick strategies for success  Quick: non transferrable, procedural  Efficient - you can reuse you work, long range planning, investment, working smarter, not harder  Analogy - math center vs. copies of recording sheets  Fad diet vs. changing of eating habits. Long term effects!

9. Reflecting on Work  The equivalent of "Night Writes" - when I was doing this work, I was thinking about...  Show Me - exciting for kids  Is it different than "checking your work?"  Brainstorm some sentence starters students can use when expressing their ideas about strategies

10. Sharing Homework  Sharing Protocol - 1 minute explanation, questions, rebuttal  Talking chips - get rid of chips  At the end of your discussion, please highlight the work of your team

11. HW Share Out  Recognizing each other's work  Comparing what we saw at different schools  How will we share our work? Everyone? Small groups? Jigsaw?