CCGPS Mathematics Unit-by-Unit Grade Level Webinar First Grade Unit 5: Operations and Algebraic Thinking November 28, 2012 Session will be begin at 3:15 pm While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

Please provide feedback at the end of today’s session.  Feedback helps us all to become better teachers and learners.  Feedback helps as we develop the remaining unit-by-unit webinars.  Please visit to share your feedback. After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. Turtle Gunn Toms– Elementary Mathematics Specialist

CCGPS Mathematics Unit-by-Unit Grade Level Webinar First Grade Unit 5: Operations and Algebraic Thinking November 28, 2012 Turtle Toms– Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Welcome! Thank you for taking the time to join us in this discussion of Unit 5. At the end of today’s session you should have at least 3 takeaways:  What the research says about developing understanding.  Ideas to support student and teacher understanding.  Content specific to Unit 5.

The intent of this webinar is to bring awareness to:  the development of foundational algebraic thinking.  the mathematics of addition and subtraction.  the underlying structure of a task. We will view task structure by looking at a performance task for Unit 5 during this webinar.

What’s Unit 5 all about? Strategies for addition and subtraction Commutative property as a strategy Associative property as a strategy Identification and analysis of structure in addition and subtraction Organizing information

What should students bring from Kindergarten? Understanding of quantity Fluency adding and subtracting within 5 Decomposition of quantities to 10 Understanding of ten and some more (teen numbers) Strategies for addition and subtraction Ability to represent computations numerically Use of the 8 Standards for Mathematical Practice

Here’s the skinny- The short version is happening right now. The long version is here: content/uploads/2011/05/ccss_progression_cc_oa_k5 _2011_05_302.pdf

What’s Unit 5 all about? Strategies for addition and subtraction - Pages 14 and 15

What’s Unit 5 all about? Strategies for addition and subtraction - Pages 14 and 15

What’s Unit 5 all about? Strategies for addition and subtraction – cphttp:// cp Watch this.

What’s Unit 5 all about? Commutative property as a strategy

What’s Unit 5 all about? Associative property

What’s Unit 5 all about? Identification and analysis of structure in addition and subtraction

What’s Unit 5 all about? How to get to these ideas? Tasks Journaling Number talks- /09/number-talks.html /09/number-talks.html

What’s Unit 5 all about? Organizing information

A quick word about Key Words: other-case-against-key-words.html other-case-against-key-words.html

Visual Representations A major task for any student engaged in problem solving is to translate the quantitative information in a problem into a symbolic equation (an arithmetic/algebraic statement) necessary for solving the problem. Students who learn to visually represent the mathematical information in problems prior to writing an equation are more effective at problem solving. What Works Clearing House

Visual Representations Visual representations help students solve problems by linking the relationships between quantities in the problem with the mathematical operations needed to solve the problem. Visual representations include tables, graphs, number lines, and diagrams such as strip diagrams, percent bars, and schematic diagrams. What Works Clearing House

Visual Representations Recommendations by WWC to assist students in their development and use of visual representations: Select visual representations that are appropriate for students and the problems they are solving. Use think-alouds and discussions to teach students how to represent problems visually. Show students how to convert the visually represented information into mathematical notation. What Works Clearing House

What’s Unit 5 all about? Visual models- Yep. I think we get this now.

Performance Task: Atlanta Zoo

Atlanta Zoo What’s the goal of this task? What might you add? How might you increase student choice/entry points?

Performance Task: Atlanta Zoo How can you structure the task so that it works for your classroom? Intro task- start with task and create a rubric. Edit task if necessary to better fit your students. Students work independently while you circulate and ask questions, take notes Set benchmarks along the way to keep students moving forward, help kids to organize their workflow

Performance Task: Atlanta Zoo Refer students back to rubric all along the way to help kids to organize their thinking and improve their work. Choose strategically which student ideas offer opportunities for “mid-stream minilessons”. Question more than you answer. Listen more than you talk. If you are recording your thinking, you are modeling your expectation for them.

Rubric How might a rubric be made by your students? Different criteria- you can choose! Standards (for sure) Organization Clarity Student behavior

Rubric Sample

Interested? and-management/rubrics/4586.html and-management/rubrics/4586.html epaper/rubrics.htm epaper/rubrics.htm rubrics.html rubrics.html most-rubrics most-rubrics

Effective Feedback Sharing thinking ture=plcp ture=plcp

Other task/assessment options math?resume=0 Quick and effective, making ten. math?resume=0 elementary-math-hungary?fd=1 27 minutes of goodness. elementary-math-hungary?fd=1 Pinterest boards- this is ridiculous! +core+math +core+math

Horizontal and vertical connections Strategies apply everywhere, in multiple contexts Integration of content areas ensures connections and relational thinking Multiple steps builds understanding and deeper thinking Work the culminating task collaboratively with colleagues so you know where your kids need to go, and what they might have difficulty with

Culmination of the unit, not the grade.

Food for thought: “ I’ve learned a lot from watching good teachers. The most important thing I’ve learned: adopt the mantra “ Just the answer isn’t good enough.” I watched teachers transform passive students into thinkers because of this simple idea. This expectation, that a teacher sets at any point in the year, opens up doors to all of the SMP’s (not every one every day – but many every day). In those classes, because “ just the answer isn’t good enough,” kids made sense of the mathematics they were doing, reasoned to justify that their answer was correct, critiqued their work and others’, used tools and made models of the mathematics that was happening, used some measure of precision as they explained their thinking, and sometimes found structure (even a few teachers found this) in their own repeated reasoning.” From a math coach friend…

Thank You! Please visit to provide us with your feedback! Turtle Gunn Toms Program Specialist (K-5) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Join the listserve! Follow on Twitter! (yep, I’m tweeting math resources in a very informal manner)