CCGPS Mathematics Unit-by-Unit Grade Level Webinar 7 th Grade Unit 5: Geometry January 23, 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 7 th Grade Unit 5: Geometry January 23, 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 5 webinar. Framework tasks. GPB sessions on Georgiastandards.org. Standards for Mathematical Practice. Resources. CCGPS is taught and assessed from and beyond.

The big idea of Unit 5 The importance of mathematical communication  How can I help my students become more effective mathematical communicators?  What does research say about communication? Resources Welcome!

Feedback James Pratt – Brooke Kline – Secondary Mathematics Specialists

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MCC7.G.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.  Question: Does MCC7.G.1 include similar figures? Similar figures is not listed in the vocabulary for the unit, but it is found in the Coach books for this standard. I'm not sure exactly what I'm supposed to teach for this standard? Wiki/ Questions – Unit cm 4.5 cm 3 cm 1.5 cm Unit Scale: ¼ cm = 1 meter

MCC7.RP.2: Recognize and represent proportional relationships between quantities. MCC7.RP.2c: Represent proportional relationships by equations. For example, if the total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed at t = pn.  Question: Only direct relationships are mentioned in the standards. Should I be teaching them about indirect as well? Wiki/ Questions – Unit 3

MCC7.G.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.  Question: Does the 7 th grade teacher need to teach geometric constructions as they did under GPS? Wiki/ Questions – Unit 5

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, 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

Find the area of a circle with radius of 15 cm.

Mathematical Communication The development of students’ mathematical communication shifts in precision and sophistication throughout the primary, junior and intermediate grades, yet the underlying characteristics remain applicable across all grades. CBS Mathematics

Mathematical Communication Mathematical communication is an essential process for learning mathematics because through communication, students reflect upon, clarify and expand their ideas and understanding of mathematical relationships and mathematical arguments. Ontario Ministry of Education

Mathematical Communication Developing effective mathematical communication Categories of mathematical communication Organizing students to think, talk, and write Updating the three-part problem-solving lesson Tips for getting started

Mathematical Communication “Because mathematics is so often conveyed in symbols, oral and written, communication about mathematical ideas is not always recognized as an important part of mathematics education. Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so.” Cobb, Wood, & Yackel

Mathematical Communication “The role of the teacher during whole-class discussion is to develop and to build on the personal and collective sense- making of students rather than to simply sanction particular approaches as being correct or demonstrate procedures for solving predictable tasks.” Stein, Engle, Smith, & Hughes

Mathematical Communication When teacher talk dominates whole-class discussion, students tend to rely on teachers to be the expert, rather than learning that they can work out their own solutions and learn from other students. CBS Mathematics

Parent Communication Explanation of need for change in mathematics Description of 3 major changes in mathematics What your child will be learning in Grade 7 Partnering with your child’s teacher Grade level examples Helping your child learn outside of school Additional resources

What’s the big idea? Unit 5: Geometry New Content Derive formulas for circumference and area of a circle – came from 5 th grade Complementary and supplementary angles and angles formed from intersecting lines – came from 8 th grade Solve real-life and mathematical problems involving area, surface area, and volume – came from 6 th grade

What’s the big idea? Deepen understanding of area, volume, and surface area. Develop the understanding of area and circumference of circles. Informally develop understanding of properties of 2-D and 3-D figures. Standards for Mathematical Practice

 Passive/receptive

 Minimal student explanations, comparisons

Research - Communication Research tells us that student interaction – through classroom discussion and other forms of interactive participation – is foundational to deep understanding and related student achievement. But implementing discussion in the mathematics classroom has been found to be challenging. Dr. Catherine D. Bruce

Research - Communication The value of student interaction Challenges the teachers face in engaging students The teacher’s role Five strategies for encouraging high- quality student interaction 1.The use of rich math tasks 2.Justification of solutions 3.Students questioning one another 4.Use of wait time 5.Use of guidelines for Math Talk

Coherence and Focus K-6 th  Identify geometric figures  Determine volume of rectangular prisms  Calculate area of polygons by composing into rectangles or decomposing into triangles  Use nets to determine surface area of three-dimensional figures 8 th -12 th  Solve problems using area, surface area, and volume  Geometric constructions and proofs

Examples & Explanations The sum of the two marked vertical angles equals 55° what is the value of x ?

Examples & Explanations

What are the possible values of x ?

Examples & Explanations

Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter, rounding to the nearest millimeter, at 50 mm. As a percentage, how large is the possible error in Juan’s measurement for the area of the circle? Adapted from Illustrative Mathematics 7.G, RP Measuring the area of a circle

Examples & Explanations Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter, rounding to the nearest millimeter, at 50 mm. As a percentage, how large is the possible error in Juan’s measurement for the area of the circle? Adapted from Illustrative Mathematics 7.G, RP Measuring the area of a circle

Examples & Explanations Adapted from Illustrative Mathematics 7.G, RP Measuring the area of a circle Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter, rounding to the nearest millimeter, at 50 mm. As a percentage, how large is the possible error in Juan’s measurement for the area of the circle?

Examples & Explanations Adapted from Illustrative Mathematics 7.G, RP Measuring the area of a circle Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter, rounding to the nearest millimeter, at 50 mm. As a percentage, how large is the possible error in Juan’s measurement for the area of the circle?

Examples & Explanations Adapted from Illustrative Mathematics 7.G, RP Measuring the area of a circle Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter, rounding to the nearest millimeter, at 50 mm. As a percentage, how large is the possible error in Juan’s measurement for the area of the circle?

Examples & Explanations Adapted from Illustrative Mathematics 7.G, RP Measuring the area of a circle Juan wants to know the cross-sectional area of a circular pipe. He measures the diameter, rounding to the nearest millimeter, at 50 mm. As a percentage, how large is the possible error in Juan’s measurement for the area of the circle?

Examples & Explanations The figure is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point. Each small circle has a radius of 5 cm. Calculate the area of the shaded part of the figure. Adapted from Illustrative Mathematics 7.G Eight Circles

Examples & Explanations The figure is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point. Each small circle has a radius of 5 cm. Calculate the area of the shaded part of the figure. Adapted from Illustrative Mathematics 7.G Eight Circles The area of the shaded area is one-sixth of the difference of the area of the big circle and the combined area of the small circles

Examples & Explanations Adapted from Illustrative Mathematics 7.G Eight Circles The area of the shaded area is one- sixth of the difference of the area of the big circle and the combined area of the small circles 555

Examples & Explanations Adapted from Illustrative Mathematics 7.G Eight Circles 555

Examples & Explanations Adapted from Illustrative Mathematics 7.G Eight Circles 555

Examples & Explanations Adapted from Illustrative Mathematics 7.G Eight Circles 555

Find the area of a circle with radius of 15 cm.

Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so. The role of the teacher during whole-class discussion is to develop and the build on the personal and collective sense-making of students. …learning that they can work out their own solutions and learn from other students.

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 - 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 -  Capacity Building Series: Communication in the Mathematics Classroom -  What Works? Research into Practice -  Council of the Great City Schools - Blogs  Dan Meyer –  Timon Piccini –  Dan Anderson –

Resources Learnzillion.com Review Common Mistakes Core Lesson Guided Practice Extension Activities Quick Quiz

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.