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.
Transcript
CCGPS MathematicsUnit-by-Unit Grade Level Webinar
6th GradeUnit 5: Area and Volume
October 23, 2012
Session will be begin at 8:00 amWhile 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.
• Intent and focus of Unit 5 webinar.• Framework tasks.• GPB sessions on Georgiastandards.org.• Standards for Mathematical Practice. • Resources. • http://ccgpsmathematics6-8.wikispaces.com/• CCGPS is taught and assessed from 2012-2013 and beyond.
Wiki/Email 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/Email 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/Email 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/Email Questions
in
in
in
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?
Activate your Brain
Adapted from Illustrative Mathematics 6.G Painting a Barn
Mathematical CommunicationThe 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 CommunicationMathematical 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 CommunicationWhen teacher talk dominates whole-class discussion, students tend to rely on teachers tobe 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
ImitativeBad Math?
Passive/receptive Bad Math?
Minimal student explanations, comparisons
Bad Math?
Passive Active
Transmission Challenging
Research - CommunicationResearch 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 tasks2. Justification of solutions3. Students questioning one
another4. Use of wait time5. Use of guidelines for Math Talk
Coherence and Focus• K-5th
Identify geometric figuresCalculate area of rectanglesDetermine volume of rectangular prisms using whole number sides.
• 7th-12th Determine the area of circlesSolve 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
2
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A
2
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21
A
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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
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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
2793
933
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
lwhV
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
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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
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)16(2020 43
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lwhV
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
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lwhV
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. )10001( 3cml
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. )10001( 3cml
Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression
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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. )10001( 3cml
Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression
cmcmcm
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cml
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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. )10001( 3cml
Adapted from Illustrative Mathematics 6.G.2 Computing Volume Progression
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•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?
Activate your Brain
•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.
Activate your Brain
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 - 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/Phil Daro talks about the Common Core Mathematics Standards - http://bit.ly/URwOFT
~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.
