CCGPS MathematicsUnit-by-Unit Grade Level Webinar

6th GradeUnit 4: One Step Equations and Inequalities

September 25, 2012

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CCGPS MathematicsUnit-by-Unit Grade Level Webinar

6th Grade Unit 4: One Step Equations and Inequalities

September 25, 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, 6th 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 A towns’ total allocation for firefighter’s wages and

benefits in a new budget is $600,000. If wages are calculated at $40,000 per firefighter and benefits at

$20,000 per firefighter, write an equation whose solution is the number of firefighters the town can

employ if they spend their whole budget. Solve the equation.

Adapted from Illustrative Mathematics: 6.EE Firefighter Allocation

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.

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 A towns’ total allocation for firefighter’s wages and

benefits in a new budget is $600,000. If wages are calculated at $40,000 per firefighter and benefits at

$20,000 per firefighter, write an equation whose solution is the number of firefighters the town can

employ if they spend their whole budget. Solve the equation.

Adapted from Illustrative Mathematics: 6.EE Firefighter Allocation

MisconceptionIf f represents the maximum number of firemen that

could be employed then f = 15.5

MisconceptionIf f represents the maximum number of firemen that

could be employed then f = 15.5

There can only be one f in an equation, therefore600,000 + 20,000 = 40,000f

620,000 = 40,000f15.5 = f

Misconception If f represents the maximum number of firemen that

could be employed, then600,000 = 40,000f + 20,000f.

f = 7

Misconception If f represents the maximum number of firemen that

could be employed, then600,000 = 40,000f + 20,000f.

f = 7

f = 7 because f is the 7th letter of the alphabet!

What’s the big idea?

• Overview • Key Standards• Enduring Understandings• Essential Questions• Strategies for Teaching & Learning

What’s the big idea?

• Develop a conceptual understanding of solving simple equations using properties of equality.• Develop a conceptual understanding of inequalities.• Deepen understanding of operating with variables.

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.

Phil Daro on “Answer Getting” - http://www.serpmedia.org/daro-talks/index.html

What’s the big idea?Expressions and Equations• Reason about and solve one-variable equations and

inequalities.• Represent and analyze quantitative relationships between

dependent and independent variables.Ratio and Proportional Relationships• Understand ratio concepts and use ratio reasoning to solve

problems.

New Content• Solve and graph inequalities – came from 8th grade

Questions that arose•Solving Inequalities•Cross Multiply

Coherence and Focus – Unit 4

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-5th Operations with rational numbersWriting expressionsEvaluating expressions

• 7th-12th Solving multi-step linear equations and inequalitiesSolving polynomial and exponential functionsWorking with systems of equations

Misconceptions

x + 1 = 7 and y + 1 = 7 are different equations.

You can’t do p + q = 10 because there isn’t an answer.

If y stands for yards and f stands for feet, then y = 3f.

Adapted from Project Mathematics Update

Examples & Explanations

Steve had $10 when he purchased a bottle of water for $1.50 and a

magazine. When he left the store, the cashier gave him $5.25 in

change.

Create a picture of this situation that tells whether you are adding or

subtracting.Adapted from Learn Zillion

Examples & Explanations

Let m = cost of magazine

m $1.50 $5.25

$10

+ +

Adapted from Learn Zillion

Examples & Explanations

Write an equation to represent the situation.

Steve had $10 when he purchased a bottle of water for $1.50 and a

magazine. When he left the store, the cashier gave him $5.25 in change.

m + 1.50 + 5.25 = 10m + 6.75 = 10

Adapted from Learn Zillion

Examples & Explanations

Sierra walks her dog Pepper twice a day. Her evening walk is two and a half times as far as her morning walk.

At the end of the week she tells her mom, “I walked Pepper for 30 miles this week!”

How long is her morning walk?

Adapted from Illustrative Mathematics: 6.EE Morning Walk

Examples & Explanations

Examples & Explanations

Examples & Explanations

Examples & Explanations

www 5.35.2

Examples & Explanations

www 5.35.2

Examples & Explanations

www 5.35.2

ww 5.24)5.3(7

Examples & Explanations

www 5.35.2

ww 5.24)5.3(7

miles 30

Examples & Explanations

www 5.35.2

ww 5.24)5.3(7

miles 30

305.24 w

Examples & Explanations

www 5.35.2

ww 5.24)5.3(7

miles 30

305.24 w

2.15.24/30 w

Examples & ExplanationsA theme park has a log ride that can hold 12 people. They also have a weight limit of 1500 lbs per log for safety reasons. If the average adult weight 150 lbs, the average child weights 100 lbs and the log itself weighs 200, the ride can operate safely if the inequality

is satisfied. There are several groups of children of differing numbers waiting to ride. Group one has 4 children, group two has 3 children, group three has 9 children while group four 6 children.

If 4 adults are already seated in the log, which groups of children can safely ride with them?

Adapted from Illustrative Mathematics: 6.EE Log Ride

1500200100150 CA

Examples & ExplanationsFor group 1:

1500200)4(100)4(150 ?

Examples & ExplanationsFor group 1:

1500200)4(100)4(150 ?

15001200

Examples & ExplanationsFor group 1: Yes

1500200)4(100)4(150 ?

15001200

Examples & ExplanationsFor group 1: Yes

For group 2:

1500200)3(100)4(150 ?

Examples & ExplanationsFor group 1: Yes

For group 2:

1500200)3(100)4(150 ?

15001100

Examples & ExplanationsFor group 1: Yes

For group 2: Yes

1500200)3(100)4(150 ?

15001100

Examples & ExplanationsFor group 1: Yes

For group 2: Yes

For group 3:

1500200)9(100)4(150 ?

Examples & ExplanationsFor group 1: Yes

For group 2: Yes

For group 3:

1500200)9(100)4(150 ?

15001700

Examples & ExplanationsFor group 1: Yes

For group 2: Yes

For group 3: No

1500200)9(100)4(150 ?

15001700

Examples & ExplanationsFor group 1: Yes

For group 2: Yes

For group 3: No

For group 4:

1500200)6(100)4(150 ?

Examples & ExplanationsFor group 1: Yes

For group 2: Yes

For group 3: No

For group 4:

1500200)6(100)4(150 ?

15001400

Examples & ExplanationsFor group 1: Yes

For group 2: Yes

For group 3: No

For group 4: Yes

1500200)6(100)4(150 ?

15001400

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.