CCGPS Mathematics Unit-by-Unit Grade Level Webinar 7 th Grade Unit 4: Statistics October 4, 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.
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CCGPS Mathematics Unit-by-Unit Grade Level Webinar 7 th Grade Unit 4: Statistics October 4, 2012 Session will be begin at 8:00 am While you are waiting,
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CCGPS MathematicsUnit-by-Unit Grade Level Webinar
7th GradeUnit 4: Statistics
October 4, 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.
Expectations and clearing up confusion• This webinar focuses on CCGPS content specific to Unit 4, 7th Grade. • For information about CCGPS across a single grade span, please access the list of recorded GPB sessions on Georgiastandards.org.• For information on the Standards for Mathematical Practice, please access the list of recorded Blackboard sessions from Fall 2011 on GeorgiaStandards.org.• CCGPS is taught and assessed from 2012-2013 and beyond. • A list of resources will be provided at the end of this webinar and these documents are posted in the 6-8 wiki.
• The intent of this webinar is to bring awareness to: the types of tasks that are contained within the unit. your conceptual understanding of the mathematics in this unit. approaches to the tasks which provide deeper learning situations for your students.
We will not be working through each task during this webinar.
Welcome!• Thank you for taking the time to join us in this discussion of Unit 4.• At the end of today’s session you should have at least 3 takeaways:
the big idea of Unit 4 something to think about…some food for thought
how might I support student problem solving? what is my conceptual understanding of the material in this unit?
a list of resources and support available for CCGPS mathematics
Welcome!• Please provide feedback at the end of today’s session.
Feedback helps us become better teachers and learners.Feedback helps as we develop the remaining unit-by-unit webinars. Please visit http://ccgpsmathematics6-8.wikispaces.com/ to share your feedback..
• After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars.
read the mathematics CCGPS? read the unit and worked through the tasks in the unit? downloaded and saved the documents from this session?
• Ask questions and share resources/ideas for the common good.• Bookmark and become active in the 6-8 wiki. If you are still wondering what a wiki is, we will discuss this near the end of the session.
Misconception?
http://lovestats.wordpress.com
What do we do with mistakes and misconceptions?
• Avoid them whenever possible? "If I warn learners about the misconceptions as I teach,
they are less likely to happen. Prevention is better than cure.”
• Use them as learning opportunities?"I actively encourage learners to make mistakes and to learn from them.”
Diagnostic teaching.
Source: Swann, M : Gaining diagnostic teaching skills: helping students learn from mistakes and misconceptions, Shell Centre publications
“Traditionally, the teacher with the textbook explains and demonstrates, while the students imitate; if the student makes mistakes the teacher explains again. This procedure is not effective in preventing ... misconceptions or in removing [them].
Diagnostic teaching ..... depends on the student taking much more responsibility for their own understanding , being willing and able to articulate their own lines of thought and to discuss them in the classroom”.
Activate your Brain Jane collected some red and yellow roses. She measured the lengths of their stems, and drew the following box plots.
Which color rose would you buy for a 40 cm tall vase? Why?
Adapted from Mathematics Assessment Project
Misconceptions
It is important to realize that inevitably students will develop misconceptions…
Askew and Wiliam 1995; Leinwand, 2010; NCTM, 1995; Shulman, 1996
Misconception
Misconception
Misconceptions
Therefore it is important to have strategies for identifying, remedying, as well as for avoiding misconceptions.
What’s the big idea?• Develop an understanding of the importance of random samples to inferences.• Develop an understanding of inferences between a sample and population.• Develop an understanding of inferences between two populations. • Deepen the understanding of displaying and summarizing numerical data.
What’s the big idea?Standards for Mathematical PracticeEducation Week’s Blog > EdTech Researcher – Justin ReichDan Meyer Blog – Dan MeyerMTT2K Grand Prize Winning Video – What if Khan Academy was Made in Japan?
Education Week Webinar – Jason Zimba, lead writer of the CCSM
Coherence and Focus – Unit 4What are students coming with?What foundation is being built?
Where does this understanding lead students?
•Concepts and Skills to Maintain•Enduring Understandings•Evidence of Learning
Coherence and Focus – Unit 4View across grade bands
• K-6th Display data with bar graphs and line plotsSummarize numerical data
• 8th-12th Investigate patterns of associationFit functions to dataProbability modelsUse standard deviation
Misconception
xkcd.com
Examples & ExplanationsDevelop a system to estimate the mean area of the 48 lower states.
Adapted from Illustrative Mathematics: 7.SP Estimate the Mean State Area
Examples & ExplanationsDevelop a system to estimate the mean area of the 48 lower states.
•Select 5 states representative of the 48 states
Examples & ExplanationsDevelop a system to estimate the mean area of the 48 lower states.
•Select 5 states representative of the 48 states•Use a random number generator to select 5 states
Examples & ExplanationsDevelop a system to estimate the mean area of the 48 lower states.
•Select 5 states representative of the 48 states•Use a random number generator to select 5 states•Select 10 states representative of the 48 states
Examples & ExplanationsDevelop a system to estimate the mean area of the 48 lower states.
•Select 5 states representative of the 48 states•Use a random number generator to select 5 states•Select 10 states representative of the 48 states•Use a random number generator to select 10 states
Examples & ExplanationsDevelop a system to estimate the mean area of the 48 lower states.
•Calculate several means for each sampling type•Create dot plots for each sampling type•Compare dot plots
Examples & ExplanationsDevelop a system to estimate the mean area of the 48 lower states.
Examples & ExplanationsThe graph shows the highest average temperatures for each month of the year for one place in Washington and one place in California.
Examples & ExplanationsThe graph shows the highest average temperatures for each month of the year for one place in Washington and one place in California.
Write two statements about what is the same and what is different in the two sets of temperatures.
Examples & ExplanationsThe graph shows the highest average temperatures for each month of the year for one place in Washington and one place in California.
Write two statements about what is the same and what is different in the two sets of temperatures.
• The temperatures are cooler in Washington than in California by about 10 degrees.
• The temperatures increase and decrease though the year.• Both temperatures significantly rise around June/July.• Washington has a slow increase and temperature while California
has a steeper increase.• California has a mean of about 79 degrees and median about 80
degrees.• Washington has a mean of about 57 degrees and median about 56
Suggestions for getting started:• Read the unit and work through the tasks with your colleagues.
The only way to gain deep understanding is to work through each task.
• Make note of where, when, and what the big ideas are.• Discuss the focus and coherence of the unit.• Make note of where, when, and what the pitfalls might be. • Look for additional tools/ideas you want to use.• Determine any changes which might need to be made to make
this work for your students.• Share, ask, and collaborate on the wiki.
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.
What is a Wiki?
Resources• Common Core Resources
SEDL videos - https://www.georgiastandards.org/Common-Core/Pages/Math.aspx or http://secc.sedl.org/common_core_videos/ Illustrative Mathematics - http://www.illustrativemathematics.org/ Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/ Arizona DOE - http://www.azed.gov/standards-practices/mathematics-standards/ Ohio DOE - http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRelationID=1704Common 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://serpmedia.org/daro-talks/index.html
•BooksVan DeWalle and Lovin, Teaching Student-Centered Mathematics, 6-8