CCGPS Mathematics Unit-by-Unit Grade Level Webinar Coordinate Algebra & Accelerated Coordinate Algebra/Analytic Geometry A Unit 2: Reasoning with Equations and Inequalities August 2, 2012 Session will be begin at 8:00 am 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 2: Reasoning with Equations and Inequalities August 2, 2012 James Pratt – Brooke Kline – Secondary Mathematics Specialists 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 2. At the end of today’s session you should have at least 3 takeaways:  the big idea of Unit 2  something to think about…some food for thought  how might I support student problem solving?  what is my conceptual understanding of the material in this unit?  a list of resources and support available for CCGPS mathematics

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 share your feedback, ask questions, and share your ideas and resources. If you are wondering what a wiki is, we will discuss this near the end of this session. After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. James Pratt – Brooke Kline – Secondary Mathematics Specialists

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

Expectations and clearing up confusion This webinar focuses on CCGPS content specific to Unit 2, Coordinate Algebra and Accelerated Coordinate Algebra/Analytic Geometry A. For information about CCGPS across a single grade span, please access the list of recorded GPB sessions on Georgiastandards.org. For information on 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. A list of resources will be provided at the end of this webinar and these documents are posted in the 9-10 wiki.

Expectations and clearing up confusion The intent of this webinar is to bring awareness to:  the types of tasks that are contained within the unit.  your conceptual understanding of the mathematics in this unit.  approaches to the tasks which provide deeper learning situations for your students. We will not be working through each task during this webinar.

Activate your Brain Two cyclists start at the same corner and ride in opposite directions. One cyclist rides twice as fast as the other. In 3 hours, they are 81 miles apart. Find the rate of each cyclist.

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Strategies to Improve Students’ Mathematical Problem Solving Skills 1.Prepare problems and use them in whole-class instruction. 2.Assist students in monitoring and reflecting on the problem-solving process. 3.Teach students how to use visual representations. 4.Expose students to multiple problem-solving strategies. 5.Help students recognize and articulate mathematical concepts and notation. What Works Clearing House

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

Examples of visual representations and linear equations

What’s the big idea? Enduring Understandings Essential Questions Strategies for Teaching and Learning Key Standards Overview

What’s the big idea? Developing a deeper understanding and fluency in writing and solving linear equations and inequalities. Developing a deeper understanding in solving systems of equations and interpreting their solutions.

What’s the big idea? Standards for Mathematical Practice Classroom Routines What might all of this look like in the classroom?   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 -    Teaching Channel –

Coherence and Focus – Unit 2 What are students coming with?

Coherence and Focus – Unit 2 What foundation is being built? Where does this understanding lead students?

Coherence and Focus – Unit 2 View across grade bands K-8 th  Operations with rational numbers and algebraic thinking  Proportional reasoning, expressions, equations and inequalities  Linear functions & models, and solving linear systems 10 th -12 th  Linear functions  Transformations  Solving various functions

Examples & Explanations Jaden has a prepaid phone plan that charges 15 cents for each text sent and 10 cents per minute for calls. If Jaden wants to send 21 texts and only has $6, how many minutes can he talk? Will this use all of his money? If not, will how much money will he have left? Justify your answer. Adapted from CCGPS Frameworks

Examples & Explanations NumberCostTotal Cost Text t t Calls c.1.1 c

Examples & Explanations NumberCostTotal Cost Text t t Calls c.1.1 c.15t +.1c = Cost per month

Examples & Explanations NumberCostTotal Cost Text t t Calls c.1.1 c.15t +.1c = Cost per month.15(21) +.1c ≤ 6.00

Examples & Explanations NumberCostTotal Cost Text t t Calls c.1.1 c.15t +.1c = Cost per month.15(21) +.1c ≤ c ≤ 6.00

Examples & Explanations NumberCostTotal Cost Text t t Calls c.1.1 c.15t +.1c = Cost per month.15(21) +.1c ≤ c ≤ c ≤ 2.85

Examples & Explanations NumberCostTotal Cost Text t t Calls c.1.1 c.15t +.1c = Cost per month.15(21) +.1c ≤ c ≤ c ≤ 2.85 c ≤ 28.5

Examples & Explanations NumberCostTotal Cost Text t t Calls c.1.1 c.15t +.1c = Cost per month.15(21) +.1c ≤ c ≤ c ≤ 2.85 c ≤ 28.5 Jaden could talk for 28 minutes since most phone companies charge for whole minutes and would have 5 cents left.

Examples & Explanations Jose had 4 times as many trading cards as Phillipe. After Jose gave away 50 cards to his little brother and Phillipe gave 5 cards to his friend for his birthday, they each had an equal amount of cards. Write a system to describe the situation. Adapted from Arizona Department of Education

Examples & Explanations Start: Phillipe Jose

Examples & Explanations Start: Phillipe Jose

Examples & Explanations Start: Phillipe Jose J = 4P

Examples & Explanations Start: Phillipe Jose Finish: Phillipe Jose 50 5 J = 4P

Examples & Explanations Start: Phillipe Jose Finish: Phillipe Jose 50 5 J = 4P P – 5 = J – 50

Examples & Explanations Start: Phillipe Jose Finish: Phillipe Jose 50 5 J = 4P P – 5 = J – 50

Examples & Explanations Fishing Adventures rents small fishing boats to tourists for day long fishing trips. Each boat can hold at most eight people. Additionally, each boat can only carry 1200 pounds of people and gear for safety reasons. Assume on average an adult weighs 150 pounds and a child weighs 75 pounds. Also assume each group will require 200 pounds of gear plus 10 pounds of gear per person. Can a group of 5 adults and 3 children safely rent a boat? Adapted from Illustrative Mathematics – A.REI.12 Fishing Adventures 3

Examples & Explanations

a + c ≤ 8 ( ) a + ( ) c ≤ 1200

Examples & Explanations a + c ≤ a + 85 c ≤ 1200

Examples & Explanations a + c ≤ a + 85 c ≤ 1000

Examples & Explanations a + c ≤ a + 85 c ≤ 1000 adults children

Examples & Explanations a + c ≤ a + 85 c ≤ 1000 Does the point (3,5) lie in the shaded area? adults children

Examples & Explanations a + c ≤ a + 85 c ≤ 1000 Does the point (3,5) lie in the shaded area? adults children

Assessment How might it look? Mathematics Assessment Project  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 Illustrative Mathematics Online Assessment System - Instruction-and-Assessment/Assessment/Pages/OAS.aspx Instruction-and-Assessment/Assessment/Pages/OAS.aspx

Assessment How might it look?

Assessment How might it look? Try thinking about assessment in this way: The chef preparing and tasting the soup in the kitchen is engaged in formative assessment. The person eating the soup in the restaurant is engaged in summative assessment. You are the chef. Adjust constantly with the end in mind.

Suggestions for getting started: Read the unit and work through the tasks with your colleagues. What are the big mathematical ideas of the unit? Discuss the focus and coherence of the unit. Discuss where students are going and where students will end up. What do you notice? What do you wonder? What do you need? Share your thoughts and questions on the wiki.

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.

What is a Wiki?

Resources Common Core Resources  SEDL videos - or  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Arizona DOE -  Ohio DOE - ationID= ationID=1704  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards Books  Van DeWalle and Lovin, Teaching Student-Centered Mathematics, 6-8

Resources Professional Learning Resources  Inside Mathematics-  Annenberg Learner -  Edutopia –  Teaching Channel - Assessment Resources  MAP -  PARCC - Start of School- Parents  ( how to support your school and teacher )

As you start your day tomorrow… think about the use of visual representations in the classroom. Dan Meyer – Timon Piccini – Dan Anderson –

Thank You! Please visit to share 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.