ccgps mathematics 6 th grade update webinar unit 5: area and volume december 13, 2013 james pratt...
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CCGPS Mathematics6th Grade Update Webinar
Unit 5: Area and VolumeDecember 13, 2013
James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usSecondary Mathematics Specialists
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These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
What are update webinars?
• Update on the work of the 2013 Resource Revision Team Overall revisions Unit 5 revisions
• Addressing areas which teachers have found to be more challenging• Resources
2013 6th Grade Resource Revision Team
6th Grade Math Resource Revision Team
Tonya Burt- Lincoln County Middle School
Anne Miller Gay – MS Math Coach, Camden County
Beverly Harvey- Ebenezer MS, Effingham County
Janet Kennedy – Kittredge Magnet School, Dekalb County
Ashley Powell – Marietta 6th Grade Academy, Marietta City
Unit 5 Area and VolumeWebinar Guide
SMP’s, Strategies and Misconceptions
Unit 5 Changes
Teacher Notes and FALs for Unit 5
UNIT 5
Standards for Mathematical Practice, Strategies and Misconceptions
Specific Standards for Mathematical Practice
Below are the relevant Standards for Mathematical Practice for the task: Volume and Cubes.
STANDARDS FOR MATHEMATICAL PRACTICE1. Make sense of problems and persevere in solving them. Students will solve problems by finding the volume of rectangular prisms with fractional edges. 2. Reason abstractly and quantitatively Students will use their understanding of the volume to find the number of cubes that will fit inside a rectangular prism. Students will be able to see and justify the reasoning packing a rectangular prism to find volume.6. Attend to precision. Students will use appropriate measurement units (square units and cubic units) and correct terminology to justify reasonable solutions.7. Look for and make use of structure. Students will understand the relationship between the structure of a three-dimensional shape and its volume formula.8. Look for and express regularity in repeated reasoning. Students use properties of figures and properties of operations to connect formulas to volume.
UNIT 5
Standards for Mathematical Practice, Strategies and Misconceptions
UNIT 5
Standards for Mathematical Practice, Strategies and Misconceptions
MISCONCEPTIONS
1. Students may believe the orientation of the figure changes the type of figure. They struggle with recognizing common figures in different orientation. For example students may think that “square” rotated 45 degrees is no longer a square and instead is called a “diamond.” This impacts students’ ability to decompose composite figures and to appropriately apply formulas for area. Providing multiple orientations of objects within classroom examples and work is essential for students to overcome this misconception.
2. Students may have trouble identifying the height of triangles and parallelograms. They confuse the height with always being a side length. Height is the altitude and must perpendicular to the base (form a right angle). 3. The height of a triangle can be one of the sides of the right angle in a right triangle. The height is an interior segment in an acute triangle, and it is an exterior segment (the base needs to be extended) in an obtuse triangle. See the screen shots below from the GeoGebra web site for examples of each of these types of triangles.
Unit 5 Changes
TASKS Kept the Same:
Who put the Tang in Tangram?
What's My Area?
King Arthur's New Table
How many Ways?
Unit 5 Changes
TASKS Changed:
Packing Our Goods
Boxing Bracelets
Culminating Task
Unit 5 Changes
TASKS ADDED:
Rectangle Wrap-around
Finding Surface Area
Volume and Cubes
Unit 5 Changes
Packing Our Goods
Unit 5 Changes
Finding Surface Area
Unit 5 Changes
Volume and Cubes
Unit 5 Changes
2 short cycle tasks Candle Box Smoothie Box
Unit 5 Changes
1 FAL Designing Candy Cartons
Vocabulary Changes
Added vocabulary Composing Decomposing Dimension
Trapezoid – using the inclusive definition: A quadrilateral with AT LEAST one pair of parallel sides
http://www.illustrativemathematics.org/illustrations/1505
Points for Teachers
What is a “special quadrilateral”?
Students need to find the area of trapezoids and rhombi by decomposing figures, not by formulas
Use the formula sheet for the CRCT provided on the GaDOE website
http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Documents/CRCT%20Mathematics%20Formula%20Sheet%20Revised2013.pdf
Surface area is found by breaking down the shapes, NOT by using the formulas
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Find the area that is shaded in each figure in at least two different ways.
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Finding Areas of Polygons
Leo’s recipe for banana bread won’t fit in his favorite pan. The batter fills the 8.5 inch by 11 inch by 1.75 inch pan to the very top, but when it bakes it spills over the side. He has another pan that is 9 inches by 9 inches by 3 inches, and from past experience he thinks he needs about an inch between the top of the batter and the rim of the pan. Should he use this pan?
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Banana Bread
Leo’s recipe for banana bread won’t fit in his favorite pan. The batter fills the 8.5 inch by 11 inch by 1.75 inch pan to the very top, but when it bakes it spills over the side. He has another pan that is 9 inches by 9 inches by 3 inches, and from past experience he thinks he needs about an inch between the top of the batter and the rim of the pan. Should he use this pan?
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Banana Bread
Leo’s recipe for banana bread won’t fit in his favorite pan. The batter fills the 8.5 inch by 11 inch by 1.75 inch pan to the very top, but when it bakes it spills over the side. He has another pan that is 9 inches by 9 inches by 3 inches, and from past experience he thinks he needs about an inch between the top of the batter and the rim of the pan. Should he use this pan?
Unit 5 Challenges
Adapted from Illustrative Mathematics 6.G Banana Bread
• GaDOE Resources Fall 2011 CCGPS Standards for Mathematical Practices Webinars - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx Spring 2012 CCGPS Mathematics Professional Learning Sessions on GPB - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx 2012 – 2013 CCGPS Mathematics Unit-by-Unit Webinar Series - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx Georgia Mathematics Teacher Forums - http://ccgpsmathematics6-8.wikispaces.com/ CCGPS Mathematics Frameworks and Comprehensive Course Overviews - https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx Mathematics Formative Assessment Lesson Videos - https://www.georgiastandards.org/Common-Core/Pages/Mathematics-Formative-Assessment-Lessons-Videos.aspx
Resources
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.
• CCGPS Resources Georgia Virtual Learning - http://www.gavirtuallearning.org/Resources.aspx SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc Illustrative Mathematics - http://www.illustrativemathematics.org/ Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/ Common Core Standards - http://www.corestandards.org/ Tools for the Common Core Standards - http://commoncoretools.me/LearnZillion - http://learnzillion.com/
• Assessment Resources Online Assessment System - http://bit.ly/OoyaK5 MAP - http://www.map.mathshell.org.uk/materials/index.php Illustrative Mathematics - http://illustrativemathematics.org/ CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/ Smarter Balanced - http://www.smarterbalanced.org/smarter-balanced-assessments/ PARCC - http://www.parcconline.org/
Resources
www.gavirtuallearning.org/Resources.aspx No password required!
Georgia Virtual Learning
Georgia Virtual Learning
Georgia Virtual Learning
Georgia Virtual Learning
Georgia Virtual Learning
Resources• Professional Learning Resources
Inside Mathematics- http://www.insidemathematics.org/ Annenberg Learner - http://www.learner.org/index.html Edutopia – http://www.edutopia.org Teaching Channel - http://www.teachingchannel.org Ontario Ministry of Education - http://bit.ly/cGZlce Achieve - http://www.achieve.org/ Expeditionary Learning: Center for Student Work - http://elschools.org/student-work
• Blogs Dan Meyer – http://blog.mrmeyer.com/ Robert Kaplinsky - http://robertkaplinsky.com/
• Books Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8
Feedbackhttp://www.surveymonkey.com/s/WZKG5G2
James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us
Thank You! Please visit http://ccgpsmathematics6-8.wikispaces.com/ to share your feedback, ask
questions, and share your ideas and resources!Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspx
to join the 6-8 Mathematics email listserve.Follow on Twitter!
Follow @GaDOEMath
Brooke KlineProgram Specialist (6‐12)
bkline@doe.k12.ga.us
James PrattProgram Specialist (6-12)
jpratt@doe.k12.ga.us
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
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