CCGPS MathematicsUnit-by-Unit Grade Level Webinar

8th GradeUnit 4: Functions

October 2, 2012

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CCGPS MathematicsUnit-by-Unit Grade Level Webinar

8th GradeUnit 4: Functions

October 4, 2012

James Pratt – jpratt@doe.k12.ga.usBrooke Kline – bkline@doe.k12.ga.usSecondary 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, 8th 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.

http://ccgpsmathematics6-8.wikispaces.com/

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 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.

James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usSecondary 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.

here math function rule

Activate your Brain The function machine takes an input, does something to this

input according to some rule and returns a unique output.

here math function rule

2 1 3 2

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 PracticeEducation Week’s Blog > EdTech Researcher – Justin ReichDan Meyer Blog – Dan MeyerMTT2K Grand Prize Winning Video – What if Khan Academy was Made in Japan?

•http://blogs.edweek.org/edweek/edtechresearcher/2012/08/what_if_khan_academy_was_made_in_japan_mtt2k_grand_prize.html?utm_source=twitterfeed&utm_medium=twitter

•http://www.youtube.com/watch?v=CHoXRvGTtAQ

What’s the big idea?Standards for Mathematical Practice

Education Week Webinar – Math Practices and the Common Core

Basic Understandings for TeachersTeacher 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 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-7th Determining unknownsDetermine a pattern that follows a given ruleGraphing on the coordinate planeRatio and proportions

• 9th-12th Linear and Exponential functionsPolynomial functionsTrigonometric functions

MisconceptionA function is a graph.

The vertical line test is how you identify a function.

A graph is a picture.

Examples & ExplanationsIs the Dewey Decimal System that is used in some libraries to categorize books a function?

Examples & ExplanationsIs the Dewey Decimal System that is used in some libraries to categorize books a function?

Examples & ExplanationsIs the Dewey Decimal System that is used in some libraries to categorize books a function?

500Science and Mathematics

Book on Probability

Book on Biology

Examples & ExplanationsIs the Dewey Decimal System that is used in some libraries to categorize books a function?

500Science and Mathematics

Book on Probability

Book on Biology

510Mathematics

Book on Algebra

Book on Probability

Examples & ExplanationsIs the Dewey Decimal System that is used in some libraries to categorize books a function?

500Science and Mathematics

Book on Probability

Book on Biology

510Mathematics

Book on Algebra

Book on Probability

512 Algebra

Book on Algebra by

Smith

Book on Algebra by

Jones

Examples & ExplanationsGiven 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 & ExplanationsGiven 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 & ExplanationsGiven 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 & ExplanationsGiven 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? NoIs R a function of F?

Examples & ExplanationsGiven 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? NoIs R a function of F? No

Examples & ExplanationsGiven 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? NoIs R a function of F? NoAre either R or F functions of t?

Examples & ExplanationsGiven 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? NoIs R a function of F? NoAre either R or F functions of t? Yes

Examples & ExplanationsSam 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 & ExplanationsSam 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 & ExplanationsIf 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 & ExplanationsIf 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 & ExplanationsIf 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 & ExplanationsIf 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 & ExplanationsIf 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.

AssessmentHow might it look?

• Mathematics Assessment Project - http://map.mathshell.org/materials/tests.php

• Illustrative Mathematics - http://illustrativemathematics.org/

• Dana Center’s CCSS Toolbox: PARCC Prototype Project - http://www.ccsstoolbox.org/

• PARCC - http://www.parcconline.org/• Online Assessment System - http://www.gadoe.org/Curriculum-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.

http://ccgpsmathematics6-8.wikispaces.com/

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 - 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

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

• Assessment Resources MAP - http://www.map.mathshell.org.uk/materials/index.php CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/ PARCC - http://www.parcconline.org/parcc-states

• BlogsDan Meyer – http://blog.mrmeyer.com/Timon Piccini – http://mrpiccmath.weebly.com/3-acts.htmlDan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/

Resources• Dana Center’s CCSS Toolbox - PARCC Prototyping Project

http://www.ccsstoolbox.com/

Resources• Dan Meyer’s Three-Act Math Tasks

https://docs.google.com/spreadsheet/lv?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE

ResourcesLearnzillion.com

• Review• Common Mistakes• Core Lesson• Guided Practice• Extension Activities• Quick Quiz

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.aspxto join the 6-8 Mathematics email listserve.

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.