CCGPS Mathematics6th Grade Update Webinar

Unit 3: ExpressionsOctober 11, 2013

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

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What are update webinars?

• Update on the work of the 2013 Resource Revision Team Overall revisions Unit 3 revisions

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

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

Comprehensive Course GuideTonya Burt

Unit 3

SMP’s, Strategies and Misconceptions – Janet Kennedy

Unit 3 changes – Beverly Harvey

FALs for Unit 3 (General information for FALs along with specific information on the one FAL in this unit). – Anne Gay

6th Grade Comprehensive Course Overview

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 6th Grade Math

Direct Link to Page

Select the Comprehensive Course Guide

Flipbooks

Bold words will provide access to the Common Core Flipbooks

The Flipbooks offer clarification Very Large File (slow loading)

Direct link to Flipbook

Content Domain Flipbook Resources

Active links to standard resources

Other Sections of Interest

• Unit Descriptions• Webinar Information• Assessment Resources and

Instructional Support Resources

• Internet Resources• Curriculum Map

Correction to Unit 1 Teachers Edition

STRATEGIES FOR TEACHING AND LEARNING Computation with fractions is best understood when it builds upon the familiar understandings of whole numbers and is paired with visual representations. Solve a simpler problem with whole numbers, and then use the same steps to solve a fraction divided by a fraction. Looking at the problem through the lens of “How many groups?” or “How many in each group?” helps visualize what is being sought. For example: 312 means “How many groups of three would make 12?” Or, “How many in

each of 3 groups would make 12?” Thus 4

1

2

7 can be solved the same way. “How many groups

of 4

1 make

2

7?” Or, ”How many objects in a group when

2

7fills

4

1?”

The highlighted statement below seems a little confusing. A better way to say this is: “ How many one-fourths equal 7/2?” We hope this clears this up.

TasksUnit 3

Standards for Mathematical Practice, Strategies Misconceptions

Unit 3

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: Exponents .

3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding the equivalence of expressions and the use of variable expressions to represent real-world situations.

6. Attend to precision. Students use the mathematical language with relation to exponents.

7. Look for and make use of structure. Students use the table to organize and compare base, exponent, exponential forms, standard from, and value.

Standards for Mathematical Practice, Strategies and Misconceptions

Unit 3

Standards for Mathematical Practice, Strategies and Misconceptions

Unit 3

MISCONCEPTIONS

1. The mnemonic PEMDAS can mislead students into thinking that addition must comes before subtraction and multiplication must come before division.

2. Students fail to see juxtaposition (side by side) as indicating multiplication. For example, evaluating 3x as 35 when x = 5 instead of 3 times 5 = 15. Also, students may rewrite 8 – 2a as 6a.

3. Students also miss the understood “1” in front of a lone variable like a or x or p. For example, not realizing that 4a + a is 5a.

4. Many of the misconceptions when dealing with expressions stem from the misunderstanding/reading of the expression. For example, knowing the operations that are being referenced with notation like x3, 4x, 3(x + 2y) is critical. The fact that x3 means (x)(x)(x) which is x times x times x, not 3x or 3 times x; 4x means 4 times x or x + x + x + x, not forty-something.

Task Changes

Unit 3

Tasks - unchanged Rules for Exponents Conjectures about Properties Are we Equal?

Writing Expressions Added to address EE.2a

Update Tasks Writing and Evaluating Expressions

Added some items

Culminating Task: Sweet Tooth Chocolate Shop Reworked to be more relevant

Exponents Removed prime factor tree

FALSFormative Assessment Lessons

• Developed by the MARS, Shell Center

• To Inform Instruction• 2/3 into a unit• Preferably not graded

2 Types of FALs Specific to Unit 3

Called “Classroom Challenges” in the new revision by Shell. GaDOE will continue to refer to this type of informing activity as Formative Assessment Lessons

Concept Development FALs Problem Solving FALS

Unit 3 contains 6th Grade’s first Concept Development FAL

Concept Development FALs Intended to assess and develop

understanding of fundamental concepts Feedback given after collaborative task

but before post-assessment Students may be grouped based on

common misconceptions from pre-assessment

Laws of Arithmetic http://map.mathshell.org.uk/

materials/download.php?fileid=1358

6th Grade FAL in Unit 3

Laws of Arithmetic Addresses 6EE and 6G (uses area model, which

students should be familiar with) SMPs: 1, 5, 7 Pre-assessment

about 2 days before the task (15 minutes: Expressions and Areas)

Students shouldn’t worry if they can’t do everything on the pre-assessment

80-minute lesson Some whole class examples, then cards of

expressions and area models to match 15 minute Post-assessment

Expressions and Areas (revisited)

Laws of Arithmetic Following the pre-assessment, the

teacher should note problems seen in student work.

There is also a page of “Common Issues” included to provide commonly found misconceptions and problems you might see. Use these, add to them, whatever helps diagnose and address YOUR students’ needs.

FALs are accessible at the MAP website http://map.mathshell.org.uk/materials/index.php

Training is Available The Mathematics Specialists at the

RESAS offer training in using the FALS, Short Cycle Tasks, and other resources from the

Mathematics Design Collaborative.

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.

The students in Mr. Nolan’s class are writing expressions for the perimeter of a rectangle of side length and width .• Sam: • Joanna: • Kiyo: • Erica:

Which of the expressions are correct and how might the students have been thinking about finding the perimeter of the rectangle?

Unit 3 Challenges

Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

The students in Mr. Nolan’s class are writing expressions for the perimeter of a rectangle of side length and width .• Sam:

Correct, uses the sum of the lengthand width then doubles.

Unit 3 Challenges

Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

The students in Mr. Nolan’s class are writing expressions for the perimeter of a rectangle of side length and width .• Joanna:

Correct, adds all the way around the perimeter

Unit 3 Challenges

Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

The students in Mr. Nolan’s class are writing expressions for the perimeter of a rectangle of side length and width .• Kiyo:

Incorrect, does not use the widthtwice.

Unit 3 Challenges

Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

The students in Mr. Nolan’s class are writing expressions for the perimeter of a rectangle of side length and width .• Erica:

Correct, recognizes that there are two widths and two lengths

Unit 3 Challenges

Adapted from Illustrative Mathematics 6.EE Rectangle Perimeter 2

Determine whether the two following expressions are equivalent.

Unit 3 Challenges

MCC.6.EE.4

Determine whether the two following expressions are equivalent.

Several ways to determine whether the expressions are equivalent.

Unit 3 Challenges

MCC.6.EE.4

Determine whether the two following expressions are equivalent.

Several ways to determine whether the expressions are equivalent.• Rewrite one expression to make it look like the other.• Substitute values• Use of manipulatives

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

Determine whether the two following expressions are equivalent.

Unit 3 Challenges

MCC.6.EE.4

• 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/

• 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

http://robertkaplinsky.com/

Mathematical Understanding?

http://robertkaplinsky.com/what-does-it-mean-to-understand-mathematics

/

http://robertkaplinsky.com/what-does-it-mean-to-understand-mathematics

/

• Procedural skill and fluency

• Conceptual understanding

• The ability to apply mathematics

Mathematical Understanding?

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.