CCGPS Mathematics Unit-by-Unit Grade Level Webinar 6 th Grade Unit 7: Rational Explorations: Numbers and their Opposites February 26, 2013 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 6 th Grade Unit 7: Rational Explorations: Numbers and their Opposites February 26, 2013 James Pratt – Brooke Kline – Secondary Mathematics Specialists These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Expectations and clearing up confusion Intent and focus of Unit 7 webinar. Framework tasks. GPB sessions on Georgiastandards.org. Standards for Mathematical Practice. Resources. CCGPS is taught and assessed from and beyond.

CCGPS Mathematics Sequence for Implementation

CCGPS Mathematics Resources for Implementation

The big idea of Unit 7 Incorporating SMPs into rational number tasks Resources Welcome!

MCC6.G.4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures… Question: The standard states to find the surface area of 3-d shapes made up of triangles and rectangles, but the frameworks appear to only address prisms. Are pyramids included in this standard? We have noticed other states including them with this standard and wanted to make sure. Wiki/ Questions – Unit 5

MCC6.G.1: Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes;  Question: For 6th grade math G.1, it states "other triangles". There are lots of these. Are we supposed to teach all other triangles, too, or are there particular ones? Wiki/ Questions – Unit 5

MCC6.SP.5d: Summarize numerical data sets in relation to their context, such as by: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement Question: Is this standard asking about sampling at all? I see a lot of items aligned to that standard asking sampling questions. For example, given a question to research, which would give most accurate results, surveying people at school, surveying people at the grocery, surveying people around town, surveying every second house in the neighborhood? Wiki/ Questions – Unit 6

MCC6.G.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate… Question: I have a question about Unit 5 standards, is there supposed to be a MCC6.G.3? It is listed on Learnzillion as drawing polygons in the coordinate plane with given vertices, but the standard is not listed in the frameworks. Wiki/ Questions – Unit 7

Question: I have a question about the placement of the rational number standards. Can we teach them earlier in the year in order to help students with solving the one-step equations? Wiki/ Questions – Unit 7

As part of the continuing implementation of CCGPS, the current CCGPS mathematics frameworks and units are being reviewed, revised, and augmented. The Georgia Department of Education is seeking qualified math educators to become part of the 2013 CCGPS Mathematics Resource Revision Team which will assist in this critical process. The scope of the CCGPS Mathematics Resource Revision Team work will include, but is not limited to: evaluating newly submitted tasks assessing the need for additional tasks assessing the order of current units and tasks editing of current units and tasks creating additional tasks to address gaps, if necessary 2013 Resource Revision Team

All work will be completed collaboratively with support structures provided by the Georgia Department of Education Mathematics Team. All work is to be completed at the Georgia Department of Education, June 3rd-June 6, and June 10-13, Team members will be compensated for contracted work in the amount of $2000 and travel expenses will be reimbursed. If you are interested in becoming a part of the CCGPS Mathematics Resource Revision Team, please respond to the appropriate Georgia Department of Education contact below by March 1, In your response, please indicate grade level interest, why you would like to be part of this team, related experience, and the contact information for two references Resource Revision Team Grades 6-High School Brooke Kline Mathematics Program Lead Specialist Grades 6-High School James Pratt Secondary Mathematics Program Specialist

As part of the continuing implementation of CCGPS in the year , the current GADOE mathematics frameworks and units are being reviewed, revised, and augmented. We are offering an opportunity for educators to assist in this critical process. The challenge: Create a career-based mathematics task using guidelines provided to supplement and/or address gaps in the existing CCGPS frameworks units. If your task is selected for addition to a unit, you will receive a $200 honorarium per task. All work is to be original using support structures provided by the Georgia Department of Education Mathematics Team. If you are interested in participating in this challenge, please view the task creation guidelines at and get started! Task submission period begins now and closes May 1, We look forward to seeing your tasks. Career-Based Mathematics Task Challenge

As part of the continuing implementation of CCGPS in the year , the current GADOE mathematics units are being augmented. We would like your assistance with this critical process. Student work samples are a vital component of the frameworks which only you can provide. If you have been using the GADOE frameworks and have student work which you would be willing to share, please send it our way. We will remove any identifiers, and include selected student work samples in the revised frameworks which are slated to be released July 1, If your student work sample is selected for inclusion we will notify you of its placement in the units via . Request for Student Sample Work

Submission guidelines : Attach the work sample(s) to an in any format. Whatever works for you, works for us. Indicate the grade level, unit, and task in the body of your , and on the work sample in the upper left corner. You may cover any student/school identifiers if you wish, and we will do the same if any remain. Send the with student work attached to the appropriate team member below. To be considered for inclusion, work samples must be submitted by May 17, We look forward to seeing your students’ work. Request for Student Sample Work Grades 6-High School Brooke Kline Mathematics Program Lead Specialist Grades 6-High School James Pratt Elementary Mathematics Program Specialist

On the same winter morning, the temperature is -28° F in Anchorage, Alaska and 65° F in Miami, Florida. How many degrees warmer was it in Miami than in Anchorage on that morning? Adapted from Illustrative Mathematics 6.NS It’s Warmer in Miami

On the same winter morning, the temperature is -28° F in Anchorage, Alaska and 65° F in Miami, Florida. How many degrees warmer was it in Miami than in Anchorage on that morning? Adapted from Illustrative Mathematics 6.NS It’s Warmer in Miami

On the same winter morning, the temperature is -28° F in Anchorage, Alaska and 65° F in Miami, Florida. How many degrees warmer was it in Miami than in Anchorage on that morning? Adapted from Illustrative Mathematics 6.NS It’s Warmer in Miami

Achieve: Math Works

What’s the big idea? Develop understanding of the system of rational numbers. Develop understanding of absolute value. Standards for Mathematical Practice.

What’s the big idea? Unit 7: Rational Explorations New Content Introduction to Integers (Plotting points in all four quadrants) – came from 7 th grade

Coherence and Focus K-5 th  Whole numbers and fractions 7 th -12 th  Operations with rational numbers  Everything!

How many degrees warmer was it in Miami than in Anchorage on that morning? Adapted from Illustrative Mathematics 6.NS It’s Warmer in Miami

How many degrees warmer was it in Miami than in Anchorage on that morning? Adapted from Illustrative Mathematics 6.NS It’s Warmer in Miami

How many degrees warmer was it in Miami than in Anchorage on that morning? It is 93° F warmer in Miami. Adapted from Illustrative Mathematics 6.NS It’s Warmer in Miami

How many degrees warmer was it in Miami than in Anchorage on that morning? Adapted from Illustrative Mathematics 6.NS It’s Warmer in Miami

How many degrees warmer was it in Miami than in Anchorage on that morning? Adapted from Illustrative Mathematics 6.NS It’s Warmer in Miami

How many degrees warmer was it in Miami than in Anchorage on that morning? Adapted from Illustrative Mathematics 6.NS It’s Warmer in Miami

Examples & Explanations A flea is jumping around on the number line. If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far from zero is he? Adapted from Illustrative Mathematics 6.NS Jumping Flea

Examples & Explanations A flea is jumping around on the number line. If he starts at 1 and jumps 3 units to the left, then where is he on the number line? How far from zero is he? Adapted from Illustrative Mathematics 6.NS Jumping Flea

Examples & Explanations A flea is jumping around on the number line. If he starts at 0 and jumps 5 units away, where might he have landed? Adapted from Illustrative Mathematics 6.NS Jumping Flea

Examples & Explanations A flea is jumping around on the number line. If the flea jumps 2 units and lands at zero, where might he have started? Adapted from Illustrative Mathematics 6.NS Jumping Flea

Examples & Explanations A flea is jumping around on the number line. The absolute value of a number is the distance it is from zero. The absolute value of the flea’s location is 4 and he is to the left of zero. Where is he on the number line? Adapted from Illustrative Mathematics 6.NS Jumping Flea

Examples & Explanations Adapted from Illustrative Mathematics 6.NS Fractions on the Number Line 0 1

Examples & Explanations Adapted from Illustrative Mathematics 6.NS Fractions on the Number Line 0 1

Examples & Explanations Adapted from Illustrative Mathematics 6.NS Fractions on the Number Line 0 1

Examples & Explanations The lowest temperature ever recorded on earth was -89° C in Antarctica. The average temperature on Mars is about -55° C. Which is warmer, the coldest temperature on earth or the average temperature on Mars? Write an inequality to support your answer. Adapted from Illustrative Mathematics 6.Comparing Temperatures

Examples & Explanations Adapted from Illustrative Mathematics 6.Comparing Temperatures

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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.

Common Core Resources  SEDL videos - or  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards -  LearnZillion - Assessment Resources  MAP -  Illustrative Mathematics -  CCSS Toolbox: PARCC Prototyping Project -  PARCC -  Online Assessment System - Resources

Professional Learning Resources  Inside Mathematics-  Annenberg Learner -  Edutopia –  Teaching Channel -  Ontario Ministry of Education -  Achieve - Blogs  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 6-8 Mathematics listserve. Follow on Twitter! 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.