ccgps mathematics 6 th grade update webinar unit 4: one-step equations and inequalities november 8,...

CCGPS Mathematics6th Grade Update Webinar

Unit 4: One-Step Equations and InequalitiesNovember 8, 2013

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

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These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

What are update webinars?

• Update on the work of the 2013 Resource Revision Team Overall revisions Unit 4 revisions

• Addressing areas which teachers have found to be more challenging• Resources

Determine whether the two following expressions are equivalent.

Unit 3 Challenges

MCC.6.EE.4

Determine whether the two following expressions are equivalent.

Unit 3 Challenges

MCC.6.EE.4

Determine whether the two following expressions are equivalent.

Unit 3 Challenges

MCC.6.EE.4

Determine whether the two following expressions are equivalent.

Unit 3 Challenges

MCC.6.EE.4

2013 6th Grade Resource Revision Team

6TH GRADE MATH

RESOURCE REVISION TEAM

Tonya Burt-Lincoln County Middle School

Anne Miller Gay – MS Math Coach, Camden County

Beverly Harvey- Ebenezer MS, Effingham County

Janet Kennedy – Kittredge Magnet School, Dekalb County

Ashley Powell – Marietta 6th Grade Academy, Marietta City

6TH GRADE MATH

RESOURCE

REVISION TEAM

Webinar Guide

Unit 4

SMP’s, Strategies and Misconceptions – Janet Kennedy

Unit 4 Changes and Task Chart – Beverly Harvey

Points of note and Reminders– Anne Gay

UPDATE TO UNIT 3 WEBINAR Equivalent Expression with Algebra Tiles

No negative numbers in this unit

Better problem Are these two expressions equal?

3(2x+1) + 2x and 8x + 4

EQUIVALENT EXPRESSIONS? 3(2x+1) + 2x and 8x + 4

STANDARDS FOR MATHEMATICAL PRACTICE, STRATEGIES, MISCONCEPTIONS

Specific Standards for Mathematical Practice

A step was taken by the team to incorporate in each unit specific Standards for Mathematical Practice. Instead of listing the eight general SMPs repeatedly throughout the units, we chose the standards that were most relevant with terminology specific to the task.

Below are the relevant Standards for Mathematical Practice for the task: It Is On Sale.

1. Make sense of problems and persevere in solving them. Students choose the appropriate proportion to represent the given situation and solve to find the answer.

3. Construct viable arguments and critique the reasoning of others. Students construct written explanations for their work with percent.

STANDARDS FOR MATHEMATICAL PRACTICE, STRATEGIES AND MISCONCEPTIONS

Unit 4

STRATEGIES FOR TEACHING AND LEARNING-SOME KEY POINTS

Teach solving equations conceptually/ concretely before procedurally

Consider introducing negative numbers, in a situation where possible answers for an inequality could fall below zero

Consider whether or not continuous data makes sense in an inequality situation, or if the answers have to be whole numbers/Integers

Provide abundant practice translating from words to expressions AND expressions to words

MISCONCEPTIONS

STUDENT MISCONCEPTIONS Students need practice with translating

verbal expressions into expressions and equations8 less than x expression is x - 8

many students want to put 8 – x

STUDENT MISCONCEPTIONS Students do not see 5>x as many

solutions.

TEACHER MISCONCEPTION This unit does NOT include solving

inequalities

Students should be able to identify numbers that fit into the solution for an inequality.

FOR EXAMPLE Dakota has 15 boxes to pack cans for

donated for Red Ribbon Week. She can fit 24 cans into each box. She is wondering if she needs to get more boxes.

Does she have enough boxes to pack 400 cans?

350 cans?

2415

x

ANOTHER EXAMPLE Is 5 a solution to this inequality?

Is 20 a solution? 84x

TASK CHART FOR UNIT 4

Task Task Type Content Addressed Standards

TASKS LEFT AS IS Set It Up Building Toothpicks Fruit Punch Picturing Proportions Making Sense of graphs Analyzing Tables Culminating Task: Want Ads

CHANGES TO TASKS TASK - When is it Not Equal

Deleted solving inequalities

Added inequalities that fit standard

NEW TASKS It is on Sale The Catering Job Converting Measures (metrics)

IT IS ON SALE Added to address MCC.6.RP3 Real work percent problems

THE CATERING JOB Added to address MCC.6.RP3b Solving unit rate problems

CONVERTING MEASURES Should be “measures” not “metrics”

Added to address MCC.6.RP3d Using ratio reasoning to convert

measurement units

TAPE DIAGRAMSUse of tape diagrams (sometimes called Singapore Strips) is important in this unit. If teachers are unfamiliar with tape diagrams, some good resources are http://learnzillion.com/lessons/589-solve-ratio-problems-using-a-tape-diagram http://www.risd.k12.nm.us/instruction/singaporemathbook.cfm http://www.mathplayground.com/ThinkingBlocks/thinking_blocks_modeling%20_tool.html

VOCABULARY Four additional key vocabulary terms were

added:

Dependent variable Independent variable Solution Substitution

There are three links to glossaries/ dictionaries suggested in the Frameworks to aid students in understanding mathematics terms.

SOME REMINDERS FROM PREVIOUS UNIT UPDATE WEBINARS…

Frameworks are located on the 6-8 math section of www.georgiastandards.org

Designed to provide clarification of CCGPS Mathematics Standards

Organized to link together many sources of information pertinent to CCGPS

CCGPS ELA/MATH TAB

LEARNING VILLAGE FOR TEACHER EDITIONS

SELECT THE MATHEMATICS OPTION UNDER BROWSE CCGPS

Direct Link to Page

SELECT THE 6-8 OPTION IN THE MATHEMATICS SECTION

Direct Link to Page

SECTIONS OF INTEREST• Flipbook Access: Detailed Information

About Each Standard• Unit Descriptions: Overview • Webinar Information • Assessment Resources and

Instructional Support Resources• Internet Resources• Curriculum Map

CCGPS MATH WIKI SPACE

THINGS TO REMEMBER Use the Wiki to share information with other

teachers and to ask questions.

This is a living document. Please share anything you may have to enhance this or any unit. The Wiki is the teacher community page to share anything you have.

The DOE CCGPS tab is static, viewable for anyone. Teacher pages and any updates or additional resources, including hot links, are only available through Learning Village.

Unit 4 Challenges

http://nlvm.usu.edu/en/nav/frames_asid_201_g_3_t_2.html?open=instructions&from=topic_t_2.html

Stephanie is helping her band collect money to fund a field trip. The band decided to sell boxes of chocolate bars. Each bar sells for $1.50 and each box contains 20 bars. Beside is a partial table of monies collected for different numbers of boxes sold.

Unit 4 Challenges

Adapted from Illustrative Mathematics 6.EE Chocolate Bar Sales

Stephanie is helping her band collect money to fund a field trip. The band decided to sell boxes of chocolate bars. Each bar sells for $1.50 and each box contains 20 bars. Beside is a partial table of monies collected for different numbers of boxes sold.

Unit 4 Challenges

Adapted from Illustrative Mathematics 6.EE Chocolate Bar Sales

Write an equation an equation for the amount of money, , that will be collected if boxes of chocolate bars are sold. Which is the independent variable and which is the dependent variable?

Unit 4 Challenges

Adapted from Illustrative Mathematics 6.EE Chocolate Bar Sales

Write an equation an equation for the amount of money, , that will be collected if boxes of chocolate bars are sold. Which is the independent variable and which is the dependent variable?

dependent; independent

Unit 4 Challenges

Adapted from Illustrative Mathematics 6.EE Chocolate Bar Sales

The band collected $1530.00 from chocolate bar sales. How many boxes did they sell?

Unit 4 Challenges

Adapted from Illustrative Mathematics 6.EE Chocolate Bar Sales

The band collected $1530.00 from chocolate bar sales. How many boxes did they sell?

The band sold 51 boxes

Unit 4 Challenges

Adapted from Illustrative Mathematics 6.EE Chocolate Bar Sales

• GaDOE Resources Fall 2011 CCGPS Standards for Mathematical Practices Webinars - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx Spring 2012 CCGPS Mathematics Professional Learning Sessions on GPB - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx 2012 – 2013 CCGPS Mathematics Unit-by-Unit Webinar Series - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx Georgia Mathematics Teacher Forums - http://ccgpsmathematics6-8.wikispaces.com/ CCGPS Mathematics Frameworks and Comprehensive Course Overviews - https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx Mathematics Formative Assessment Lesson Videos - https://www.georgiastandards.org/Common-Core/Pages/Mathematics-Formative-Assessment-Lessons-Videos.aspx

Resources

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.

• CCGPS 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 LearnZillion - http://learnzillion.com/

• Assessment Resources Online Assessment System - http://bit.ly/OoyaK5 MAP - http://www.map.mathshell.org.uk/materials/index.php Illustrative Mathematics - http://illustrativemathematics.org/ CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/ Smarter Balanced - http://www.smarterbalanced.org/smarter-balanced-assessments/ PARCC - http://www.parcconline.org/

Resources

Resources

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 Ontario Ministry of Education - http://bit.ly/cGZlce Achieve - http://www.achieve.org/ Expeditionary Learning: Center for Student Work - http://elschools.org/student-work

• Blogs Dan Meyer – http://blog.mrmeyer.com/ Robert Kaplinsky - http://robertkaplinsky.com/

• Books Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8

Resources• SMP 3 – Construct viable

arguments and critique the reasoning of others Student Sample Work Feedback/Critique and Revision

Expeditionary Learning http://elschools.org/student-work/butterfly-drafts

Feedbackhttp://www.surveymonkey.com/s/WZKG5G2

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

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.aspx

to join the 6-8 Mathematics email listserve.Follow on Twitter!

Follow @GaDOEMath

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.