CCGPS Mathematics Unit-by-Unit Grade Level Webinar 7 th Grade Unit 1: Operations with Rational Numbers May 3, 2012 Session will be begin at 4:30 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 7 th Grade Unit 1: Operations with Rational Numbers May 3, 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 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.

Activate your Brain Use a model, diagram, or manipulative to perform the following operations…try not to rely upon your algorithm! 3 – (-2) 6 + (-2) (-2) x (-4) (-10) ÷ (-5)

Models for Teaching Operations of Integers Addition/Subtraction  Charged Particle or Two- Color Counter Model  Stack or Row Model  Hot Air Balloon Model  Number Line Model Multiplication/Division  Charged Particle or Two- Color Counter Model  Number Line Model

Models for Teaching Operations of Integers Division using a Number Line Model

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

What’s the big idea? Developing deep understanding and fluency with operations of rational numbers.

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-6 th  Operations with whole numbers and fractions.  Numbers and their opposites. 8 th -12 th  Everything!

Examples & Explanations 3 – (-2)

Examples & Explanations 3 – (-2) + = 0

Examples & Explanations 3 – (-2) + = 0

Examples & Explanations 3 – (-2) + = 0 Remove two negative chips.

Examples & Explanations 3 – (-2) + = 0 Remove two negative chips …but I do not have two negative chips to remove!

Examples & Explanations 3 – (-2) + = 0

Examples & Explanations 3 – (-2) + = 0 You can now remove two negative chips!

Examples & Explanations 3 – (-2) + = 0

Examples & Explanations 3 – (-2) + = 0 Which leaves you with five positive chips!

Examples & Explanations 3 – (-2) + = 0 Which leaves you with five positive chips! 3 – (-2) =

Examples & Explanations -2 x (-4)

Examples & Explanations -2 x (-4) Facing east or to the right = positive Facing west or to the left = negative Walking forward = positive = Walking backward = negative =

Examples & Explanations -2 x (-4) Facing east or to the right = positive Facing west or to the left = negative Walking forward = positive = Walking backward = negative = Facing to the left (because of -2), I step backwards 4 units (because of -4) twice. 048

Examples & Explanations -2 x (-4) Facing east or to the right = positive Facing west or to the left = negative Walking forward = positive = Walking backward = negative = This leaves me at 8! -2 x (-4) = 8 084

Examples & Explanations Multiplication using a Number Line Model

Examples & Explanations Making sense of division… Partitive Division – If the number of groups is known and you are trying to find the number in each group. (learner.org) Ex: You have six dollars and you want to divide it equally among 3 groups. Quotative Division – If the number in each group is known and you are trying to find the number of groups. (learner.org) Ex: You have six dollars and you want to give 3 dollars to each group. 6 ÷ 3 (Partitive) = = 2 (in each of the 3 groups) 6 ÷ 3 (Quotative) = = 2 (groups of 3)

Examples & Explanations Making sense of division… -6 ÷ 3 (Partitive)

Examples & Explanations Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups)

Examples & Explanations Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups) -6 ÷ -3 (Quotative)

Examples & Explanations Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups) -6 ÷ -3 (Quotative) = = 2 (groups of -3’s)

Examples & Explanations Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups) -6 ÷ -3 (Quotative) = = 2 (groups of -3’s) 6 ÷ -3

Examples & Explanations Making sense of division… -6 ÷ 3 (Partitive) = = -2 (in each of the 3 groups) -6 ÷ -3 (Quotative) = = 2 (groups of -3’s) 6 ÷ -3 I’m stuck because I can’t make -3 groups (partitive) nor can I determine how many -3’s are in 6 (quotative)!

Examples & Explanations Making sense of division… 6 ÷ -3 How many sets of -3 will make 6?

Examples & Explanations Making sense of division… 6 ÷ -3 How many sets of -3 will make 6? Remove one set of -3.

Examples & Explanations Making sense of division… 6 ÷ -3 How many sets of -3 will make 6? Remove a second set of -3.

Examples & Explanations Making sense of division… 6 ÷ -3 How many sets of -3 will make 6? 2 sets of -3 were removed to make 6 or -2 sets (removing 2 sets) of -3 were used to make 6. 6 ÷ -3 = -2

Examples & Explanations Division using a Number Line Model

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 6-8 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.