CCGPS Mathematics Unit-by-Unit Grade Level Webinar Coordinate Algebra & Accelerated Coordinate Algebra/Analytic Geometry A Unit 1: Relationships Between Quantities May 10, 2012 Session will be begin at 4:00 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.

CCGPS Mathematics Unit-by-Unit Grade Level Webinar Coordinate Algebra / Accelerated Coordinate Algebra/Analytic Geometry A Unit 1: Relationships Between Quantities May 10, 2012 James Pratt – Brooke Kline – Secondary Mathematics Specialists

Welcome! Thank you for taking the time to join us in this discussion of Unit 1. At the end of today’s session you should have at least 3 takeaways:  the big idea of Unit 1  something to think about…some food for thought  how might I approach this unit next fall?  what is my conceptual understanding of the material in this unit?  a list of resources and support available for CCGPS mathematics

Welcome! For today’s session:  read the standards  read the unit  downloaded and saved the documents from this session Ask questions and share resources/ideas for the common good.

Welcome! Please provide feedback at the end of today’s session.  Feedback helps us become better teachers, and it helps you to reflect upon your learning.  Feedback helps us as we develop the remaining unit-by-unit webinars.  Please visit to provide us with your feedback, ask questions, and share your ideas and resources. After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. James Pratt – Brooke Kline – Secondary Mathematics Specialists

Clearing up confusion This webinar focuses on CCGPS content specific to one grade level and one unit within that grade. For information about CCGPS across a single grade span, please access the list of recorded GPB sessions on Georgiastandards.org. For information about the Standards for Mathematical Practice, please access the list of recorded Blackboard sessions from Fall 2011 on GeorgiaStandards.org. CCGPS is taught and assessed from and beyond. PARCC assessments begin in A list of resources will be provided at the end of this webinar and this list has also been included in your document downloads.

Activate your Brain Represent the total number of calories in p peanuts and c chips if each peanut has 6 calories and each chip has 12 calories.

Activate your Brain What does the coefficient of the term with the variable p represent? What does the term with the variable c represent?

Examples of Structure of Expressions A company uses two different-sized trucks to deliver sand. The first truck can transport x cubic yards, and the second y cubic yards. The first truck makes S trips to a job site, while the second makes T trips. What do the following expressions represent in practical terms? 1. S+T2. x+y3. xS+yT

Examples of Structure of Expressions S+T=the total number of trips both trucks make to a job site

Examples of Structure of Expressions S+T=the total number of trips both trucks make to a job site x+y=the total amount of sand that both trucks can transport together

Examples of Structure of Expressions S+T=the total number of trips both trucks make to a job site x+y=the total amount of sand that both trucks can transport together xS=the total amount of sand being delivered to a job site by the first truck yT=the total amount of sand being delivered to a job site by the second truck

Examples of Structure of Expressions S+T=the total number of trips both trucks make to a job site x+y=the total amount of sand that both trucks can transport together xS+yT=the total amount of sand (in cubic yards) being delivered to a job site by both trucks.

What’s the big idea? Enduring Understandings Essential Questions Key Standards Overview

What’s the big idea? Number and Quantity - Quantities  Reason quantitatively and use units to solve problems. Algebra – Seeing Structure in Expressions  Interpret the structure of expressions. Algebra – Creating Equations  Create equations that describe numbers or relationships.

What’s the big idea? Developing an understanding of representing relationships between quantities

Navigating a Unit Table of Contents  Overview  Standards  Enduring Understandings  Essential Questions  Selected Terms and Symbols  Classroom Routines  Strategies for Teaching and Learning  Evidence of Learning  Tasks

Navigating a Unit What’s New? Concepts and Skills to Maintain Strategies for Teaching and Learning Evidence of Learning

Navigating a Unit What’s New? Task Table  Task Type  Grouping Strategy  Task Description

Navigating a Unit What’s New? Classroom Routines  SMP’s (analyzing, estimating, reasoning, describing patterns, defending, discussing, peer feedback, contentious discourse, answering, etc.)  Collaborative skills (How collaborative are your collaborative activities?)  Productive Struggle  Classroom technology, materials…how to use materials in a productive manner.  Journaling/Notebook  Development of own understanding  The regular use of routines is important to the development of students’ number sense, flexibility, fluency, collaborative skills and communication.

Navigating a Unit Classroom Routines What might all of this look like in the classroom?  Also check out:  Inside Mathematics : Mathematical Community of Learners - mathematics/classroom-teachers/157-teachers-reflect-mathematics- teaching-practices mathematics/classroom-teachers/157-teachers-reflect-mathematics- teaching-practices  Edutopia.org - Chris Optiz  video video 

Coherence and Focus – Unit 1 What are students coming with?

Coherence and Focus – Unit 1 What foundation is being built? Where does this understanding lead students?

Coherence and Focus – Unit 1 View across grade bands K-8 th  Operations with rational numbers, expressions and equations. 10 th -12 th  Everything!

Examples & Explanations The Penny Pattern Create a pattern using pennies To create each additional stage, place more pennies extending out from the six that surround the center penny.

Examples & Explanations The Penny Pattern Write an algebraic model that expresses the relationship between the stage number, n, and the number of pennies required to make the design, p.

Examples & Explanations The Penny Pattern video

Examples & Explanations The Penny Pattern p = 1 + 6n

Examples & Explanations Fold a piece of paper in half and determine the number of sections the paper has after you have made the fold. Continue in the same manner until it becomes too hard to fold the paper. Determine a mathematical model that represents the data. Number of FoldsNumber of Sections

Assessment How could it look? Examples of how balanced assessments can be assembled.  The target audience for these example assessments are: 1.teachers who have already started to work on their student’s mathematical practice skills 2.designers of future CCSSM-aligned assessments

Assessment How could it look?

Resource List The following list is provided as a sample of available resources and is for informational purposes only. It is your responsibility to investigate them to determine their value and appropriateness for your district. GaDOE does not endorse or recommend the purchase of or use of any particular resource.

Resources Common Core Resources  SEDL videos - or  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Arizona DOE -  Ohio DOE - ID= ID=1704  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards - talks/index.htmlhttp://serpmedia.org/daro- talks/index.html Books  Van DeWalle’s “Elementary and Middle School Mathematics, Teaching Developmentally” - College Level Text

Resources Professional Learning Resources  Inside Mathematics-  Annenberg Learner -  Edutopia –  Teaching Channel - Assessment Resources  MARS -  MAP -  PARCC -

As you start your day tomorrow… Who dares to teach must never cease to learn ~ John Cotton Dana

Thank You! Please visit to provide us with your feedback, ask questions, and share your ideas and resources! Please visit to join the 9-12 Mathematics listserve. Brooke Kline Program Specialist (6‐12) James Pratt Program Specialist (6-12) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.