ccgps mathematics unit-by-unit grade level webinar third grade unit 4: operations and algebraic...
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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?
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.
Join the listserve! [email protected]
Follow on Twitter!Follow @GaDOEMath
Follow @turtletoms (yep, I’m tweeting math resources in a very informal manner)