CCGPS Mathematics Unit-by-Unit Grade Level Webinar 6 th Grade Unit 5: Area and Volume October 23, 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 6 th Grade Unit 5: Area and Volume October 23, 2012 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

My Favorite No

Wiki/ Questions Unit Overview: Decipher and draw views of rectangular and triangular prisms from a variety of perspectives  Question: This was something we did last year, but I'm not getting this from these standards??

Unit Overview: Recognize and construct nets for rectangular and triangular prism  Question: I can see this a little, but finding the surface area of it is much different than labeling the nets-- we can do this one, but ? MCC.6.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. Wiki/ Questions

Unit Overview: Determine the surface area of rectangular and triangular prisms by substituting given values for their dimensions into the correct formulas  Question: They do not list the formula and they do not say to use a formula in this standard ---We did surface area using a formula last year, we don't want to go beyond the standard and make it any harder than we have to. It's hard enough as it is for sure. Wiki/ Questions

Unit Overview: Measure and compute volume with fractional edge length using cubic units of measure.  Question: Do they mean measure with unit cubes or centimeters---This whole standard is confusing. Wiki/ Questions

Task: Packing Our Goods

Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn is 80 feet, the width is 50 feet, and the height is 30 feet. The paint costs $28 per gallon, and each gallon covers 420 square feet. How much will it cost Alexis to paint the barn? Adapted from Illustrative Mathematics 6.G Painting a Barn

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

What’s the big idea? Deepen understanding of volume of rectangular prisms. Develop the understanding of area of polygons by composing into rectangles or decomposing into triangles. Develop the understanding of nets to determine surface area of three- dimensional figures. Standard 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-5 th  Identify geometric figures  Calculate area of rectangles  Determine volume of rectangular prisms using whole number sides. 7 th -12 th  Determine the area of circles  Solve problems using area, surface area, and volume

Examples & Explanations Which students, if any, have identified a base and its corresponding height? Which ones have not? Explain what is incorrect. Mark Adapted from Illustrative Mathematics 6.G.1 Base and Height

Examples & Explanations Which students, if any, have identified a base and its corresponding height? Which ones have not? Explain what is incorrect. Mark Adapted from Illustrative Mathematics 6.G.1 Base and Height

Examples & Explanations Which students, if any, have identified a base and its corresponding height? Which ones have not? Explain what is incorrect. Kiki Adapted from Illustrative Mathematics 6.G.1 Base and Height

Examples & Explanations Which students, if any, have identified a base and its corresponding height? Which ones have not? Explain what is incorrect. Kiki Adapted from Illustrative Mathematics 6.G.1 Base and Height

Examples & Explanations Compare the areas of the following triangles made on a geoboard. Adapted from Illustrative Mathematics 6.G.1 Same Base and Height

Examples & Explanations Compare the areas of the following triangles made on a geoboard. Adapted from Illustrative Mathematics 6.G.1 Same Base and Height

Examples & Explanations Compare the areas of the following triangles made on a geoboard. Adapted from Illustrative Mathematics 6.G.1 Same Base and Height

Examples & Explanations Compare the areas of the following triangles made on a geoboard. Adapted from Illustrative Mathematics 6.G.1 Same Base and Height

Examples & Explanations Compare the areas of the following triangles made on a geoboard. Adapted from Illustrative Mathematics 6.G.1 Same Base and Height

Examples & Explanations Compare the areas of the following triangles made on a geoboard. Adapted from Illustrative Mathematics 6.G.1 Same Base and Height

Examples & Explanations Three students drew the figures below showing the base b and its corresponding height h in their triangles. Which students, if any, have identified a base and its corresponding height? Which ones have not? Explain what is incorrect. Adapted from Illustrative Mathematics 6.G.1 Base and Height

Examples & Explanations Amy wants to build a cube with 3 cm sides using 1 cm cubes. How many cubes does she need? Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations Amy wants to build a cube with 3 cm sides using 1 cm cubes. How many cubes does she need? Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations Amy wants to build a cube with 3 cm sides using 1 cm cubes. How many cubes does she need? Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations Amy has a fish tank shaped like a rectangular prism that is 20 cm by 20 cm by 16cm. If she only fills the tank ¾ of the way, what will be the volume of water in the tank? Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations Amy has a fish tank shaped like a rectangular prism that is 20 cm by 20 cm by 16cm. If she only fills the tank ¾ of the way, what will be the volume of water in the tank? Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations Amy has a fish tank shaped like a rectangular prism that is 20 cm by 20 cm by 16cm. If she only fills the tank ¾ of the way, what will be the volume of water in the tank? Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations Amy has a fish tank shaped like a rectangular prism that is 20 cm by 20 cm by 16cm. If she only fills the tank ¾ of the way, what will be the volume of water in the tank? Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations Amy has a fish tank shaped like a rectangular prism that is 20 cm by 20 cm by 16cm. If she only fills the tank ¾ of the way, what will be the volume of water in the tank? Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations A rectangular tank is 40 cm wide and 50 cm long. It can hold up to 129 ½ l of water when full. If Amy fills 2/3 of the tank as shown, find the height of the water in centimeters. Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations A rectangular tank is 40 cm wide and 50 cm long. It can hold up to 129 ½ l of water when full. If Amy fills 2/3 of the tank as shown, find the height of the water in centimeters. Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations A rectangular tank is 40 cm wide and 50 cm long. It can hold up to 129 ½ l of water when full. If Amy fills 2/3 of the tank as shown, find the height of the water in centimeters. Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Examples & Explanations A rectangular tank is 40 cm wide and 50 cm long. It can hold up to 129 ½ l of water when full. If Amy fills 2/3 of the tank as shown, find the height of the water in centimeters. Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression

Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn is 80 feet, the width is 50 feet, and the height is 30 feet. The paint costs $28 per gallon, and each gallon covers 420 square feet. How much will it cost Alexis to paint the barn?

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 - Blogs  Dan Meyer –  Timon Piccini –  Dan Anderson –

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

Resources Learnzillion.com ~Thank you! Thank you! Thank you! This webinar was great, and the site has great resources that I can use tomorrow! I just shared it with everyone at my school! It is like going to a Common Core Conference and receiving all the materials for every session and having them in one place! I love it! ~I watch so many math videos for our common core lessons and I am speechless, how awesome all these small video clips are. ~Thanks for this. I attended the webinar last week and really like this site. I'm planning on having a PL session at school on Thursday.

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.