CCGPS Mathematics Unit-by-Unit Grade Level Webinar 8 th Grade Unit 3: Geometric Applications of...

CCGPS MathematicsUnit-by-Unit Grade Level Webinar

8th GradeUnit 3: Geometric Applications of Exponents

September 4, 2012

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CCGPS MathematicsUnit-by-Unit Grade Level Webinar

8th GradeUnit 3: Geometric Applications of Exponents

September 4, 2012

James Pratt – [email protected] Kline – [email protected] Mathematics Specialists

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

mailto:[email protected]


Expectations and clearing up confusion• This webinar focuses on CCGPS content specific to Unit 3, 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 3.• At the end of today’s session you should have at least 3 takeaways:

the big idea of Unit 3 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 – [email protected] Brooke Kline – [email protected] Mathematics Specialists




Misconception?

Richard Benson: The Very Best Totally Wrong Answers

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.

Activate your Brain Use the Pythagorean Theorem to find the length of

orange line segment inside the cube.

5 in



5 in

• Do you like this question?

• Does this question require students to reveal their understanding of when to apply the Pythagorean Theorem to determine lengths in 3-D figures?

• Could you improve this question in order to assist in revealing student misconceptions with the Pythagorean Theorem and 3-D figures?

Misconceptions

It is important to realize that inevitably students will develop misconceptions…

Askew and Wiliam 1995; Leinwand, 2010; NCTM, 1995; Shulman, 1996

Misconception – Invented Rule?


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;



5 in

Activate your Brain

How do you find the length of the orange line segment inside of the cube?

Adapted from Learnzillion.com 8.G.7 & 8.EE.2

5 in

Activate your Brain



5 in

5 in

5 in

5 in

Activate your Brain



5 in

5 in

5 in

5 in

leg2 + leg2 = hypotenuse2

52 + 52 = x2

25 + 25 = x2

50 = x2

Activate your Brain



5 in

5 in

5 in

7.1 in

5 in


52 + 52 = x2

25 + 25 = x2

50 = x2

=7.1 = x

Activate your Brain




5 in

7.1 in

x

Activate your Brain




5 in

7.1 in

x

52 + 7.12 = x2

25 + 50.4 = x2

75.4 = x2

Activate your Brain




5 in

7.1 in

x

52 + 7.12 = x2

25 + 50.4 = x2

75.4 = x2

8.68… = x

8.7 = x

=

Activate your Brain Learnzillion.com

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

What’s the big idea?

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

What’s the big idea?• Deepen understanding with evaluating square roots and cube roots. • Develop deep understanding with using square root and cube root symbols to represent solutions of simple quadratic and cubic equations.•Develop deep understanding with applications of the Pythagorean Theorem.•Deepen understanding with volume. • Develop deep understanding with using and applying the volume formulas for a cone, cylinder and sphere.

What’s the big idea?Standards for Mathematical Practice

Education Week Webinar – Bristol CT School District

What’s the big idea?Standards for Mathematical Practice

Education Week Webinar – Math Practices and the Common Core

Questions that arose•Converse of the Pythagorean Theorem•“Small” perfect squares and cubes•Operations with radicals

Questions that arose•Essential Questions

Questions that arose•Enduring Understandings

estimate

Questions that arose•Acting Out Task – Essential Questions

Questions that arose•Angry Bird Task – Essential Questions

Questions that arose•Angry Bird Task Extension – Distance Formula

Coherence and Focus – Unit 3

Education Week Webinar – Jason Zimba, lead writer of the CCSM

Coherence and Focus – Unit 3What are students coming with?

Coherence and Focus – Unit 3What foundation is being built?

Where does this understanding lead students?

•Enduring Understandings•Evidence of Learning

Coherence and Focus – Unit 3View across grade bands

• K-7th 3-D shapes & volumeRational/Irrational numbers, square roots & cube rootsSolving Equations

• 9th-12th Distance FormulaSolving quadratic and cubic equationsTrigonometry

Misconception?


Examples & ExplanationsUse the right triangle with side lengths of 3 cm, 4cm, and 5 cm to

explain a proof of the Pythagorean Theorem?

4 cm

3 cm 5 cm

Examples & ExplanationsHow can you explain a proof of the Pythagorean Theorem using

the diagram below?

Adapted from Learnzillion.com 8.G.6

Examples & Explanations


4 cm

3 cm



9 cm2

16 cm2



9 cm2

16 cm2

6

66

6

1



9 cm2

16 cm2

6

66

6

1 25 cm2



9 cm2

16 cm2

6

66

6

1 25 cm2

32 + 42 = 52

9 cm2 +

16 cm2 =

25 cm2



a c

leg hypotenuse

bleg

32 + 42 = 52

9 cm2 +

16 cm2 =

25 cm2

a2 + b2 = c2

Pythagorean Theorem


Examples & ExplanationsUse the Pythagorean Theorem to determine if the triangle is a

right triangle.

Examples & ExplanationsIs it possible to determine if the triangle is a right triangle? If so,

explain how you could prove whether it is or is not a right triangle. If not possible, explain why you can not make this determination.

8.G.6, 8.G.8, & 8.EE.2


8.G.6, 8.G.8, & 8.EE.2


8.G.6, 8.G.8, & 8.EE.2

8

6


8.G.6, 8.G.8, & 8.EE.2

8

6

xx

x

x

x

x

10

100

100

6436

86

2

2

2

222


8.G.6, 8.G.8, & 8.EE.2

x

x

x

x

x

10

100

100

6436

86

2

2

2

222

8

6

x

4

4

4

10

y

z


8.G.6, 8.G.8, & 8.EE.2

x

x

x

x

x

10

100

100

6436

86

2

2

2

222

8

6

x

4

4

4

10

y

z

y

y

y

y

y

7.5

32

32

1616

44

2

2

2

222

z

z

z

z

z

8.10

116

116

10016

104

2

2

2

222


8.G.6, 8.G.8, & 8.EE.2

8

6

x

4

4

4

10

y

z

If the triangle is a right triangle, then the squares of the two shorter sides must equal the square of the longest side,

or x² + y² = z².


8.G.6, 8.G.8, & 8.EE.2

8

6

x

4

4

4

10

y

z

If the triangle is a right triangle, then the squares of the two shorter sides must equal the square of the longest side,

or x² + y² = z².

x² = 100, y² = 32, z² = 116100 + 32 ? 116

132 ≠ 116Therefore, the triangle is not a

right triangle.

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/

• Online Assessment System - http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/OAS.aspx

http://map.mathshell.org/materials/tests.php

http://illustrativemathematics.org/

http://www.ccsstoolbox.org/

http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/OAS.aspx

http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/OAS.aspx

Race to the TopAssessment Toolbox

Update Fall 2012

RT3 Assessment Initiatives

• Purpose – To support teachers in preparing the students for the

Common Core Assessment that is to occur in spring 2015– To provide assessment resources that reflect the rigor of

the CCGPS– To balance the use of formative and summative

assessments in the classroom

62

RT3 Assessment Initiatives• Development of a three-prong toolkit to support

teachers and districts and to promote student learning– A professional development opportunity that focuses on

assessment literacy– A set of benchmarks in ELA, Math, and selected grades for

Science and Social Studies– An expansive bank of formative assessment

items/tasks based on CCGPS in ELA and Math as a teacher resource

63

Formative Assessment• Conducted during instruction (lesson, unit, etc.)• Identifies student strengths and weaknesses• Helps teacher determine next steps

– Review– Differentiation– Continuation

• Supplies information to provide students with detailed feedback• Assessment for the purpose of improving achievement• LOW stakes

64

Purpose of the Formative Item Bank

The purpose of the Formative Item Bank is to provide items and tasks used to assess students’ knowledge while they are learning the curriculum. The items will provide an opportunity for students to show what they know and show teachers what students do not understand.

65

Formative Item Bank Assessments

• Aligned to CCGPS• Format aligned with Common Core Assessments• Open-ended and constructed response items as

well as multiple choice items• Holistic Rubrics• Anchor Papers• Student Exemplars• 750+ Items Available in OAS by late September

66

Formative Item Bank Availability

• All items that pass data review will be uploaded to the Georgia OAS at Level 2.

• Formative Item Bank will be ready for use by all Georgia educators mid-September, 2012.

67

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Item Types

–Multiple Choice (MC)

–Extended Response (ER)

–Scaffolded Item (SC)

Extended Response Items• Performance-based tasks• May address multiple standards, multiple domains,

and/or multiple areas of the curriculum • May allow for multiple correct responses and/or

varying methods of arriving at a correct answer• Scored through use of a rubric and associated

student exemplars

69

Mathematics Sample Item – Grade HSan extended response item

70

Example Rubric

71

Scaffolded Items• Include a sequence of items or tasks• Designed to demonstrate deeper understanding• May be multi-standard and multi-domain• May guide a student to mapping out a response to

a more extended task• Scored through use of a rubric and associated

student exemplars

72

Mathematics Sample Item – Grade 3a scaffolded item

73

Mathematics Items

• Assess students’ conceptual and computational understanding

• Tasks require students to– Apply the mathematics they know to real world problems– Express mathematical reasoning by showing their work or

explaining their answer

74

Where do you Find the Items?

75

rt1234567890

student

Georgia Department of Education Assessment and Accountability

Melissa FincherAssociate SuperintendentAssessment and [email protected]

Dr. Melodee Davis Director Assessment Research and [email protected]

Robert Anthony Assessment SpecialistFormative Item BankRace to the [email protected]

Jan ReyesAssessment SpecialistInterim Benchmark AssessmentsRace to the [email protected]

Dr. Dawn SouterProject ManagerRace to the [email protected]






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 - 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

https://www.georgiastandards.org/Common-Core/Pages/Math.aspx

http://secc.sedl.org/common_core_videos/

http://www.illustrativemathematics.org/

http://www.ccsstoolbox.com/

http://www.azed.gov/standards-practices/mathematics-standards/

http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRelationID=1704

http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRelationID=1704

http://www.corestandards.org/

http://commoncoretools.me/

http://serpmedia.org/daro-talks/index.html

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/

http://www.insidemathematics.org/

http://www.learner.org/index.html

http://www.edutopia.org/

http://www.teachingchannel.org/

http://www.map.mathshell.org.uk/materials/index.php

http://www.ccsstoolbox.org/

http://www.parcconline.org/parcc-states

http://blog.mrmeyer.com/

http://mrpiccmath.weebly.com/3-acts.html

http://blog.recursiveprocess.com/tag/wcydwt/

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



Resources• Dan Meyer’s Three-Act Math Tasks

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



As you start your day tomorrow…

…the standards are not units of instruction; you don’t always “teach a standard” in one chunk, whatever the order…The standards describe achievements we want students to have. As my colleague Jason Zimba likes

to say, you don’t teach standards, you teach mathematics.

Bill McCallum – lead writer of the CCSM

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)

[email protected]

James PrattProgram Specialist (6-12)

[email protected]

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


https://www.georgiastandards.org/Common-Core/Pages/Math.aspx



CCGPS Mathematics Unit-by-Unit Grade Level Webinar 8 th Grade Unit 3: Geometric Applications of...

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