CCGPS Mathematics Unit-by-Unit Grade Level Webinar 8 th Grade Unit 4: Functions October 2, 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 8 th Grade Unit 4: Functions October 4, 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 This webinar focuses on CCGPS content specific to Unit 4, 8 th 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 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.
Expectations and clearing up confusion 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 to share your feedback.. After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. James Pratt – Brooke Kline – Secondary Mathematics Specialists
Misconception?
Welcome! For today’s session have you: 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?
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 The function machine takes an input, does something to this input according to some rule and returns a unique output. Adapted from Illustrative Mathematics: 8.F Function Rules
Misconceptions It is important to realize that inevitably students will develop misconceptions… Askew and Wiliam 1995; Leinwand, 2010; NCTM, 1995; Shulman, 1996
Misconception Functions and Graphs: Rhode Island Department of Education, 2007
Misconception Functions and Graphs: Rhode Island Department of Education, 2007
Misconceptions Therefore it is important to have strategies for identifying, remedying, as well as for avoiding misconceptions. Leinwand, 2010; Swan 2001; NBPTS, 1998; NCTM, 1995; Shulman, 1986;
Importance of Dealing with Misconceptions 1) Teaching is more effective when misconceptions are identified, challenged, and ameliorated. 2) Pupils face internal cognitive distress when some external idea, process, or rule conflicts with their existing mental schema. 3) Research evidence suggests that the resolutions of these cognitive conflicts through discussion leads to effective learning.
Some principles to consider Encourage learners to explore misconceptions through discussion. Focus discussion on known difficulties and challenging questions. Encourage a variety of viewpoints and interpretations to emerge. Ask questions that create a tension or ‘cognitive conflict' that needs to be resolved. Provide meaningful feedback. Provide opportunities for developing new ideas and concepts, and for consolidation.
Activate your Brain The function machine takes an input, does something to this input according to some rule and returns a unique output.
Activate your Brain The function machine takes an input, does something to this input according to some rule and returns a unique output. heremathfunctionrule
Activate your Brain The function machine takes an input, does something to this input according to some rule and returns a unique output. heremathfunctionrule
What’s the big idea? Overview Key Standards Enduring Understandings Essential Questions Strategies for Teaching & Learning
What’s the big idea? Unit 4: Functions Functions Define, evaluate, and compare functions. New Content
What’s the big idea? Develop a deep understanding of the concept of a function.
What’s the big idea? Standards for Mathematical Practice Education Week’s Blog > EdTech Researcher – Justin Reich Dan Meyer Blog – Dan Meyer MTT2K Grand Prize Winning Video – What if Khan Academy was Made in Japan? khan_academy_was_made_in_japan_mtt2k_grand_prize.html?utm_ source=twitterfeed&utm_medium=twitter khan_academy_was_made_in_japan_mtt2k_grand_prize.html?utm_ source=twitterfeed&utm_medium=twitter
What’s the big idea? Standards for Mathematical Practice Education Week Webinar – Math Practices and the Common Core
Basic Understandings for Teachers Teacher Misconception : As long as students are getting the correct answers, the students are understanding the material.
Questions that arose
Coherence and Focus – Unit 3 Education Week Webinar – Jason Zimba, lead writer of the CCSM
Coherence and Focus – Unit 4 What 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 4 View across grade bands K-7 th Determining unknowns Determine a pattern that follows a given rule Graphing on the coordinate plane Ratio and proportions 9 th -12 th Linear and Exponential functions Polynomial functions Trigonometric functions
Misconception A function is a graph. The vertical line test is how you identify a function. A graph is a picture.
Examples & Explanations Is the Dewey Decimal System that is used in some libraries to categorize books a function?
Examples & Explanations Is the Dewey Decimal System that is used in some libraries to categorize books a function?
Examples & Explanations Is the Dewey Decimal System that is used in some libraries to categorize books a function? 500 Science and Mathematics Book on Probability Book on Biology
Examples & Explanations Is the Dewey Decimal System that is used in some libraries to categorize books a function? 500 Science and Mathematics Book on Probability Book on Biology 510 Mathematics Book on Algebra Book on Probability
Examples & Explanations Is the Dewey Decimal System that is used in some libraries to categorize books a function? 500 Science and Mathematics Book on Probability Book on Biology 510 Mathematics Book on Algebra Book on Probability 512 Algebra Book on Algebra by Smith Book on Algebra by Jones
Examples & Explanations Given below is a table that gives the populations of foxes and rabbits in a national park over a 12 month period. Note that each value of t corresponds to the beginning of the month. Adapted from Illustrative Mathematics: 8.F.1 Foxes and Rabbits
Examples & Explanations Given below is a table that gives the populations of foxes and rabbits in a national park over a 12 month period. Note that each value of t corresponds to the beginning of the month. According to the data in the table, is F a function of R ?
Examples & Explanations Given below is a table that gives the populations of foxes and rabbits in a national park over a 12 month period. Note that each value of t corresponds to the beginning of the month. According to the data in the table, is F a function of R ? No
Examples & Explanations Given below is a table that gives the populations of foxes and rabbits in a national park over a 12 month period. Note that each value of t corresponds to the beginning of the month. According to the data in the table, is F a function of R ? No Is R a function of F ?
Examples & Explanations Given below is a table that gives the populations of foxes and rabbits in a national park over a 12 month period. Note that each value of t corresponds to the beginning of the month. According to the data in the table, is F a function of R ? No Is R a function of F ? No
Examples & Explanations Given below is a table that gives the populations of foxes and rabbits in a national park over a 12 month period. Note that each value of t corresponds to the beginning of the month. According to the data in the table, is F a function of R ? No Is R a function of F ? No Are either R or F functions of t ?
Examples & Explanations Given below is a table that gives the populations of foxes and rabbits in a national park over a 12 month period. Note that each value of t corresponds to the beginning of the month. According to the data in the table, is F a function of R ? No Is R a function of F ? No Are either R or F functions of t ? Yes
Examples & Explanations Sam wants to take his MP3 player and his video game player on a car trip. An hour before they plane to leave, he realized that he forgot to charge the batteries last night. At that point, he plugged in both devices so they can charge as long as possible before they leave. Sam knows that his MP3 player has 40% of its battery life left and that the battery charges by an additional 12% every 15 minutes. His video game player is new, so Same doesn’t know how fast it is charging but he recorded the battery charge for the first 30 minutes after he plugged it in. Adapted from Illustrative Mathematics: 8.F.2 Battery Charging
Examples & Explanations Sam knows that his MP3 player has 40% of its battery life left and that the battery charges by an additional 12% every 15 minutes. His video game player is new, so Same doesn’t know how fast it is charging but he recorded the battery charge for the first 30 minutes after he plugged it in. If Sam’s family leaves after an hour of charging, what percent of the battery will be charged for each of the two devices?
Examples & Explanations If Sam’s family leaves after an hour of charging, what percent of the battery will be charged for each of the two devices? We can extend the chart for the video game player:
Examples & Explanations If Sam’s family leaves after an hour of charging, what percent of the battery will be charged for each of the two devices? We can extend the chart for the video game player:
Examples & Explanations If Sam’s family leaves after an hour of charging, what percent of the battery will be charged for each of the two devices? We can extend the chart for the video game player: And create a similar chart for the MP3 player:
Examples & Explanations If Sam’s family leaves after an hour of charging, what percent of the battery will be charged for each of the two devices? We can extend the chart for the video game player: And create a similar chart for the MP3 player:
Examples & Explanations If Sam’s family leaves after an hour of charging, what percent of the battery will be charged for each of the two devices? We can extend the chart for the video game player: And create a similar chart for the MP3 player: Therefore the video game player battery will be 92% charged and the MP3 player battery will be 88% charged.
Assessment How might it look? Mathematics Assessment Project - Illustrative Mathematics Dana Center’s CCSS Toolbox: PARCC Prototype Project PARCC - Online Assessment System - Instruction-and-Assessment/Assessment/Pages/OAS.aspx Instruction-and-Assessment/Assessment/Pages/OAS.aspx
Assessment
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.
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.
What is a Wiki?
Resources Common Core Resources SEDL videos - or Illustrative Mathematics - Dana Center's CCSS Toolbox - Arizona DOE - Ohio DOE - ationID= ationID=1704 Common Core Standards - Tools for the Common Core Standards - Phil Daro talks about the Common Core Mathematics Standards Books Van DeWalle and Lovin, Teaching Student-Centered Mathematics, 6-8
Resources Professional Learning Resources Inside Mathematics- Annenberg Learner - Edutopia – Teaching Channel - Assessment Resources MAP - CCSS Toolbox: PARCC Prototyping Project - PARCC - Blogs Dan Meyer – Timon Piccini – Dan Anderson –
Resources Dana Center’s CCSS Toolbox - PARCC Prototyping Project
Resources Dan Meyer’s Three-Act Math Tasks M2YWxWYVM1UWowTEE M2YWxWYVM1UWowTEE
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. 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.