CCGPS Mathematics Unit-by-Unit Grade Level Webinar Third Grade Unit 4: Operations and Algebraic Thinking: Patterns in Addition and Multiplication October.

CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Third GradeUnit 4: Operations and Algebraic Thinking:

Patterns in Addition and MultiplicationOctober 9, 2012

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CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Third Grade Unit 4: Operations and Algebraic Thinking:

Patterns in Addition and MultiplicationOctober 9, 2012

Turtle Toms– [email protected] Mathematics Specialist

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

copyright infringement.

Welcome!

GPS

http://ccgpsmathematicsK-5.wikispaces.comTurtle Gunn Toms– [email protected]

Elementary Mathematics Specialist

Wiki Questions

Wiki QuestionsWhy are you doing a Unit 4 webinar now? We aren’t evendone with unit 1.

Wiki QuestionsWhy aren’t there answer keys? Has anyone at the state-level “dugin” and worked through the tasks as you are asking Georgiaeducators to do? Are these tasks vertically and horizontallyaligned?

Wiki QuestionsWhat about homework and other resources? Where and what are

teachers suppose to pull for those? Are the tasks supposed to go home? How are parents supposed to help their children without books or other resources?

• How are you letting districts know about changes in units?

Unit 1, Page 75, Part II“Watch How Numbers Grow”

If you are given a ten dollar bill on day one, and get 2 ten dollar bills on day 2, and 3 ten dollar bills on day 3, and this pattern continues, how much will you receive on day 9? On what day would you have collected a total of $1000 byadding together the money collected each day?

Wiki Questions• Do teachers have to complete all of the tasks? • What about grades?

Wiki Questions• What about students who are not progressing as they

should using only the tasks?• What about students with disabilities?

Need more?

VandeWalle- ACTIVITIES AT A GLANCE

Wiki QuestionsWhat does mathematize mean? Do you understand what it is like to be in a classroom?

So, there are the answers.

We can’t change how people think by telling them what we think and we can’t change how people

teach by telling them how to teach. They have to experience good teaching – first as a learner, then

as a teacher.-a really smart person

No support? On your own?

How can we get support?

Collaboratively solve tasks and discuss.

Plan for the math by doing the mathLearn alongside your learners

http://resources.curriculum.org/secretariat/coplanning/approach.shtml

How can we get support?

Inquire at a local college or university. Mathematicians are inexpensive! Some are free…

Does your district have a 10-15% ELL population?

http://www.coe.uga.edu/clase/instructional-conversation/

Make time this year for the wiki and the webinars.

If the square is one square unit, what is the area of any of these shapes?

Activate your Brain

Mathematical CommunicationThe development of students’ mathematical communication shifts in precision and sophistication throughout the primary, junior and intermediate grades, yet the underlying characteristics remain applicable across all grades.

CBS Mathematics

Mathematical CommunicationMathematical communication is an essential process for learning mathematics because through communication, students reflect upon, clarify and expand their ideas and understanding of mathematical relationships and mathematical arguments.

Ontario Ministry of Education

Mathematical Communication•Developing effective mathematical communication•Categories of mathematical communication•Organizing students to think, talk, and write•Updating the three-part problem-solving lesson

Gallery WalkMath CongressBansho (Board Writing)

Mathematical Communication“Because mathematics is so often conveyed in symbols, oral and written, communication about mathematical ideas is not always recognized as an important part of mathematics education. Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so.”

Cobb, Wood, & Yackel

Mathematical Communication“The role of the teacher during whole-class discussion is to develop and to build on the personal and collective sense-making of students rather than to simply sanction particular approaches as being correct or demonstrate procedures for solving predictable tasks.”

Stein, Engle, Smith, & Hughes

Mathematical CommunicationWhen teacher talk dominates whole-class discussion, students tend to rely on teachers tobe the expert, rather than learning that they can work out their own solutions and learn from other students.

CBS Mathematics

If the square is one square unit, what is the area of any of these shapes?

Activate your Brain

If the square is one square unit, what is the area of any of these shapes? •Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so.•The role of the teacher during whole-class discussion is to develop and the build on the personal and collective sense-making of students.•…learning that they can work out their own solutions and learn from other students.

Activate your Brain

What’s the big idea?•Deepen understanding relationship between area model, addition, and multiplication.•Deepen understanding of commutative property•Develop an understanding of area and area model.•Develop an understanding of factors and dimensions of rectangle.• Standards for Mathematical Practice.

oImitative

Bad Math?

oPassive/receptive

Bad Math?

oMinimal student explanations, comparisons

Bad Math?

Passive Active

Transmission Challenging

Research - Communication•The value of student interaction•Challenges the teachers face in engaging students•The teacher’s role•Five strategies for encouraging high-quality student interaction

1. The use of rich math tasks2. Justification of solutions3. Students questioning one

another4. Use of wait time5. Use of guidelines for Math Talk

Mathematical Communication•Tips on Getting Started

1. Organizing the classroom learning environment

2. Preparing yourself mathematically

3. Coordinating student discussion and analysis of solutions

Recipe for Success

How do students learn math?

• Misconceptions• Understandings

Pre-Assessment

• Misconceptions• Understandings

Pre-Assessment

Hmmm..All three are

communication

Worthwhile Taskhttps://www.teachingchannel.org/videos/counting-collections-lesson?resume=0

Worthwhile TaskTeacher sets up the task…how? Supports include…what ?Suggestion included….what?Student ideas emerge, take form, and are shared….how? Conjectures are made and explored, and evolve into

strategies…how? Strategies become retrievable practices…how? The plenary discussion at the end helps to cement these

ideas….how and why?

How are Number Talks Useful?

From Math Solutions

Want more? http://www.insidemathematics.org/index.php/number-talks

Number Talk• Who does the math thinking during the number talk?• What specific mathematics do the students demonstrate they understand?• What does the teacher do to support the student discourse?• What recording techniques might the teacher employ that supported learning in the class?

Assessment?

Assessment?

http://www.parcconline.org/samples/mathematics/grade-3-mathematics

Assessment?

http://www.parcconline.org/samples/mathematics/grade-3-mathematics

This is how students learn mathematics.This is also how teachers learn mathematics.

How do teachers change practice?

Progressions

http://ime.math.arizona.edu/progressions/

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.

Resources• Books

Van De Walle and Lovin, Teaching Student-Centered Mathematics, K-3 and 3-5

Parrish, Number TalksFosnot and Dolk, Young Mathematicians at WorkShumway, Number Sense RoutinesWedekind, Math Exchanges

Resources Common Core Resources

SEDL videos -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/Inside Mathematics- http://www.insidemathematics.org/ 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://serpmedia.org/daro-talks/index.html

Resources• Professional Learning Resources

Inside Mathematics- http://www.insidemathematics.org/ Edutopia – http://www.edutopia.org Teaching Channel - http://www.teachingchannel.orgAnnenberg Learner - http://www.learner.org/

• Assessment Resources PAARC- http://www.ccsstoolbox.org/ MARS - http://www.nottingham.ac.uk/~ttzedweb/MARS/ MAP - http://www.map.mathshell.org.uk/materials/index.php PARCC - http://www.parcconline.org/parcc-states

A little something extra:• Instead of 30 minutes of television tonight, watch this:http://www.ted.com/talks/lang/en/stuart_brown_says_play_is_more_than_fun_it_s_vital.htmlThird Grade resources: http://www.livebinders.com/play/play/187117

Shaky foundations…

“ It ain’t what people don’t know that hurts them. It’s what they do know that ain’t so.”

Will Rogers

Thank You!Please visit http://ccgpsmathematicsK-5.wikispaces.com/ to provide us with

your feedback!

Turtle Gunn TomsProgram Specialist (K-5)[email protected]

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

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Follow @turtletoms (yep, I’m tweeting math resources in a very informal manner)