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![Page 1: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/1.jpg)
Principal's Workshop: How Does the Common Core Change
What We Look For in the Math Classroom?
Panama City, FloridaJanuary 22 & 23, 2013
Presenter: Elaine Watson, Ed.D.
![Page 2: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/2.jpg)
Hunt Institute Video: The Importance of Mathematical Practice
http://vimeo.com/album/1702025/video/29568008
![Page 3: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/3.jpg)
1. Make Sense of Problems and Persevere in Solving
“It’s not that I’m so smart, it’s just that I stay with problems longer.”
Albert Einstein
![Page 4: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/4.jpg)
1. Make Sense of Problems and Persevere in Solving
5th Grade Perseverance
![Page 5: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/5.jpg)
1. Make Sense of Problems and Persevere in Solving
Mathematically proficient students:
• Explain to self the meaning of a problem and look for entry points to a solution
• Analyze givens, constraints, relationships and goals• Make conjectures about the form and meaning of
the solution
![Page 6: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/6.jpg)
1. Make Sense of Problems and Persevere in Solving
Mathematically proficient students:
• Plan a solution pathway rather than simply jump into a solution attempt
• Consider analogous problems• Try special cases and simpler forms of original
problem
![Page 7: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/7.jpg)
1. Make Sense of Problems and Persevere in Solving
Mathematically proficient students:
• Monitor and evaluate their progress and change course if necessary…
• “Does this approach make sense?”
![Page 8: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/8.jpg)
1. Make Sense of Problems and Persevere in Solving
Mathematically proficient students:
Persevere in Solving by:
• Transforming algebraic expressions
• Changing the viewing window on a graphing calculator
• Moving between the multiple representations of:
Equations, verbal descriptions, tables, graphs, diagrams
![Page 9: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/9.jpg)
1. Make Sense of Problems and Persevere in Solving
Mathematically proficient students:
• Check their answers• “Does this answer make sense?”
• Does it include correct labels?• Are the magnitudes of the numbers in the solution in the
general ballpark to make sense in the real world?
![Page 10: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/10.jpg)
1. Make Sense of Problems and Persevere in Solving
Mathematically proficient students:
• Check their answers• Verify solution using a different method• Compare approach with others:
• How does their approach compare with mine?• Similarities• Differences
![Page 11: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/11.jpg)
2. Reason Abstractly and QuantitativelyMathematically proficient students:• Make sense of quantities and their relationships in a problem situation• Bring two complementary abilities to bear on problems involving quantitative
relationships: The ability to… decontextualize
to abstract a given situation, represent it symbolically, manipulate the symbols as if they have a life of their own
contextualizeto pause as needed during the symbolic manipulation in order to look
back at the referent values in the problem
![Page 12: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/12.jpg)
2. Reason Abstractly and QuantitativelyMathematically proficient students:
Reason Quantitatively, which entails habits of:• Creating a coherent representation of the problem at hand
considering the units involved• Attending to the meaning of quantities, not just how to
compute them• Knowing and flexibly using different properties of operations
and objects
![Page 13: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/13.jpg)
Watch the video and note where you see evidence of Middle School Classifying Equations1. Make Sense of Problems and Persevere in Solving2. Reason Abstractly and Quantitatively
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3.Construct viable arguments and critique the reasoning of others
Mathematically proficient students:
Understand and use… stated assumptions, definitions, and previously established results…
when constructing arguments
![Page 15: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/15.jpg)
3.Construct viable arguments and critique the reasoning of others
• In order for students to be practicing this standard, they need to be talking to each other, so teachers need to plan lessons that include a lot of large group and small group discussions.
• A classroom culture must be cultivated in which it is as safe to disagree as it is to agree.
![Page 16: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/16.jpg)
3.Construct viable arguments and critique the reasoning of others
• Here are some sentence structures from the first video:• I agree that ______________ because __________• I disagree because __________________________• How can we be sure?• What do you think?• Are you convinced?• Do we all agree?
![Page 17: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/17.jpg)
3.Construct viable arguments and critique the reasoning of others
What SMPs do you observe the students practicing?
Here's the Problem from the video:Write several different types of equations for 2.4.
Draw some different types of pictures to represent 2.4.
Is 2.4 the same thing as the quotient 2 remainder 4?
Why or why not?http://youtu.be/EA3YkawKEWc
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4. Model with Mathematics
Modeling is both a K - 12 Practice Standard
and a 9 – 12 Content Standard.
![Page 19: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/19.jpg)
4. Model with MathematicsMathematically proficient students:
Use powerful tools for modeling:Diagrams or graphs
SpreadsheetsAlgebraic Equations
![Page 20: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/20.jpg)
4. Model with MathematicsMathematically proficient students:
Models we devise depend upon a number of factors:• How precise do we need to be?• What aspects do we most need to undertand,
control, or optimize?• What resources of time and tools do we have?
![Page 21: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/21.jpg)
4. Model with MathematicsMathematically proficient students:
Models we devise are also constrained by:• Limitations of our mathematical, statistical, and
technical skills• Limitations of our ability to recognize significant
variables and relationships among them
![Page 22: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/22.jpg)
Modeling Cycle
The word “modeling” in this context is used as a verb that describes the process of transforming a real situation into an abstract mathematical model.
![Page 23: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/23.jpg)
Modeling Cycle
Problem Formulate
Compute Interpret
Validate Report
![Page 24: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/24.jpg)
Modeling Cycle
Problem• Identify variables in the situation
• Select those that represent essential features
![Page 25: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/25.jpg)
Modeling Cycle
FormulateSelect or create a geometrical, tabular, algebraic, or
statistical representation that describes the relationships between the variables
![Page 26: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/26.jpg)
Modeling Cycle
ComputeAnalyze and perform operations on these relationships to
draw conclusions
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Modeling Cycle
InterpretInterpret the result of the mathematics in terms of the
original situation
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Modeling Cycle
ValidateValidate the conclusions by comparing them with the
situation…
![Page 29: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/29.jpg)
Modeling Cycle
Validate
Re - Formulate
Report on conclusions and
reasoning behind them
![Page 30: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/30.jpg)
Modeling Cycle
Problem Formulate
Compute Interpret
Validate Report
![Page 31: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/31.jpg)
6. Attend to precisionMathematically proficient students:
Try to communicate precisely to others:• Use clear definitions• State the meaning of symbols they use• Use the equal sign consistently and appropriately• Specify units of measure• Label axes
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6. Attend to precisionMathematically proficient students:
Try to communicate precisely to others• Calculate accurately and efficiently• Express numerical answers with a degree of
precision appropriate for the problem context• Give carefully formulated explanations to each other• Can examine claims and make explicit use of
definitions
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6. Attend to precision
Students Practicing and Discussing Precision
![Page 34: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/34.jpg)
Use the Standards for Mathematical Practice Lesson Alignment Template.
What SMPs do you see?
http://ummedia04.rs.itd.umich.edu/~dams/umgeneral/seannumbers-ofala-xy_subtitled_59110_QuickTimeLarge.mov
![Page 35: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/35.jpg)
7. Look for and make use of structureMathematically proficient students:
• Look closely to discern a pattern or structureIn x2 + 9x + 14, can see the 14 as 2 x 7 and the 9 as 2 + 7
• Can see complicated algebraic expressions as being composed of several objects:
5 – 3 (x – y)2 is seen as 5 minus a positive number times a square, so its value can’t be more than 5 for any real numbers x and y
![Page 36: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/36.jpg)
8. Look for and express regularity in repeated reasoning.
Mathematically proficient students:
• Notice if calculations are repeated• Look for both general methods and for shortcuts• Maintain oversight of the process while attending to
the details.
![Page 37: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/37.jpg)
What Practice Standards do you see?
Sean: Is 6 Even and Odd?
![Page 38: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/38.jpg)
Do All 8 Practice Standards Need to be Used in Every Lesson?
There are some rich problems that elicit all 8 of the Practice Standards. However, these types of problems can’t be done on a daily basis. Instructional time still needs to be balanced between building the students’ technical skills and
No…but the teacher should plan so that over the span of a few days, the students are given learning opportunities to of the practicing standards
![Page 39: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/39.jpg)
A Balanced Approach math facts how to approach
and a novel situation procedures mathematically
![Page 40: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/40.jpg)
Math Facts and Procedures
Memorizing Math Facts and Naked Number Exercises are Important!Practice Standards that apply:#2 Reason Quantitatively#6 Attend to Precision#7 Look for and Use Structure#8 Use Repeated Reasoning
![Page 41: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/41.jpg)
Does Every Worthwhile Problem Have to Model a Real World Situation?
![Page 42: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/42.jpg)
![Page 43: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/43.jpg)
What SMPs Do You Observe Maya Practicing? What errors do you
notice? What would you do to have Maya notice the errors?
Maya Representing 52
![Page 44: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/44.jpg)
Let’s Practice Some ModelingStudents can: • start with a model and interpret what it means in
real world terms OR• start with a real world problem and create a
mathematical model in order to solve it.
![Page 45: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/45.jpg)
Possible or Not?
Here is an example of a task where students look at mathematical models (graphs of functions) and determine whether they make sense in a real world situation.
![Page 46: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/46.jpg)
Possible or Not?
![Page 47: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/47.jpg)
Questions:
Mr. Hedman is going to show you several graphs. For each graph, please answer the following:
A. Is this graph possible or not possible?
B. If it is impossible, is there a way to modify it to make it possible?
C. All graphs can tell a story, create a story for each graph.
![Page 48: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/48.jpg)
One
A. Possible or not?
B. How would you modify it?
C. Create a story.
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Two
A. Possible or not?
B. How would you modify it?
C. Create a story.
![Page 50: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/50.jpg)
Three
A. Possible or not?
B. How would you modify it?
C. Create a story.
![Page 51: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/51.jpg)
Four
A. Possible or not?
B. How would you modify it?
C. Create a story.
![Page 52: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/52.jpg)
Five
A. Possible or not?
B. How would you modify it?
C. Create a story.
![Page 53: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/53.jpg)
Six
A. Possible or not?
B. How would you modify it?
C. Create a story.
![Page 54: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/54.jpg)
Seven
A. Possible or not?
B. How would you modify it?
C. Create a story.
![Page 55: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/55.jpg)
Eight
A. Possible or not?
B. How would you modify it?
C. Create a story.
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Nine
A. Possible or not?
B. How would you modify it?
C. Create a story.
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Ten
A. Possible or not?
B. How would you modify it?
C. Create a story.
![Page 58: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/58.jpg)
All 10 Graphs
What do all of the possible graphs have in common?
![Page 59: Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649cb85503460f9497ecf3/html5/thumbnails/59.jpg)
And now...
For some brief notes on functions!!!!
Lesson borrowed and modified from Shodor.Musical Notes borrowed from Abstract Art Pictures Collection.
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Pyramid of Pennies
Here is an example of a task where students look at a real world problem, create a question, and create a mathematical model that will solve the problem.
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Dan Meyer’s 3-Act Process
Act IShow an image or short video of a real world situation in which a question can be generated that can be solved by creating a mathematical model.
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Pyramid of Pennies 3-Act
http://mrmeyer.com/threeacts/pyramidofpennies/
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Dan Meyer’s 3-Act Process
Act I (continued)1. How many pennies are there?
2. Guess as close as you can. 3. Give an answer you know is too high.4. Give an answer you know is too low.
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Dan Meyer’s 3-Act Process
Act 2Students determine the information
they need to solve the problem.The teacher gives only the information
students ask for.
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Dan Meyer’s 3-Act Process
What information do you need to solve this problem?
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Dan Meyer’s 3-Act Process
Act 2 continuedStudents collaborate with each other to create a mathematical model and solve
the problem. Students may need find text or online
resources such as formulas.
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Dan Meyer’s 3-Act Process
Go to it!
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Dan Meyer’s 3-Act Process
Act 3
The answer is revealed.
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Standards for Mathematical PracticeDescribe ways in which
student practitioners of the discipline of mathematics
increasingly ought to engage with the subject matter
as they grow in mathematical maturity
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Standards for Mathematical PracticeProvide a balanced combination of
Procedure and UnderstandingThey shift the focus to ensure
mathematical understanding over
computation skills
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Standards for Mathematical PracticeStudents will be able to:1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.
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Think back to the Pyramid of Pennies. At what point during the problem did you do the following?1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.
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See Inside Mathematics Videos for good examples of the Practice Standards in
action.
http://www.insidemathematics.org/index.php/mathematical-practice-
standards
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Resources for Rich Mathematical Taskshttp://illustrativemathematics.org/
The “Go-To” site for looking at the Content Standards and finding rich tasks, called “Illustrations” that can be used to
build student understanding of a particular Content Standard.
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Resources for Rich Mathematical Taskshttp://insidemathematics.org/index.php/home
is a website with a plethora of resources to help teachers transition to teaching in a way that reflects the Standards
for Mathematical Practice.It’s worth taking the 6:19 minutes to watch the
Video Overview of the Video Tours to familiarize yourself to all of the resources. There are more video tours that can be
accessed by clicking on a link below the overview video.
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Resources for Rich Mathematical Taskshttp://map.mathshell.org/materials/stds.php
There are several names that are associated with the website: MARS, MAPS, The Shell Center…however the tasks
are usually referred to as The MARS Tasks. The link above will show tasks aligned with the Practice Standards
They have been developed through a partnership with UC Berkeley and the University of Nottingham
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Resources for Rich Mathematical Taskshttp://commoncoretools.me/author/wgmccallum/
Tools for the Common Core is the website of Bill McCallum, one of the three principle writers of the CCSSM.
Highlights of this site are the links (under Tools) to the Illustrative Mathematics Project, the Progressions Documents, and the Clickable Map of the CCSSM.
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Resources for Rich Mathematical TasksMy blog WatsonMath has a lot of resources listed in the
right hand columnThis powerpoint (with the links removed, but the URLs for the links included) can be accessed on watsonmath.com