CSD Foundations in CCSS Part 2 The Standards of Math Practice 8 Standards of Math Practice.
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Transcript of CSD Foundations in CCSS Part 2 The Standards of Math Practice 8 Standards of Math Practice.
CSD Foundations in CCSS Part 2The Standards of Math Practice
8 Standards of Math Practice
Standards for Mathematical Practice
Reasoning and
Explaining
Modelingand
Using Tools
Seeing Structureand
Generalizing
Get into 8 groups
• Each group take one or two of the standards of math practice at each of the tables.– After reading the description of the standard, jot down an
example of this practice being demonstrated at your grade level—
– What would the teacher be doing?– What would the students be doing?– label the grade levels.– Visit each others standards and examples– Yes, and…if you have something that comes to mind– circulate
P. 2 of the SMP handout
• Look at the grid on p. 2• Discuss how this might be used at your school
Make sense of problems and persevere in solving them. Explain the meaning of the problem to themselves Look for entry points Analyze givens, constraints, relationships, goals Make conjectures about the solution Plan a solution pathway Consider analogous problems Try special cases and similar forms Monitor and evaluate progress, and change course if necessary Check their answer to problems using a different method Continually ask themselves “Does this make sense?”
#1: Mathematically Proficient Students …
Gather Information
Make a plan
Anticipate possible solutions
Continuously evaluate progress
Check results
Question sense of solutions
Go to livebinders , the math tasks tab
• Go to tab for Math Tasks• Go to the sub-tab for Dan Meyer
– #45 Pyramid of Pennies
Attend to precision.
#6: Mathematically Proficient Students …
• communicate precisely to others; use clear definitions• state the meaning of the symbols they use• specify units of measurement• label the axes to clarify correspondence with problem• calculate accurately and efficiently• Express answers with an appropriate degree of precision
Comic: http://forums.xkcd.com/viewtopic.php?f=7&t=66819
P. 5 of SMP handout
• Look-fors for students and teachers• Discuss the look-fors we found on our charts
-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.
Reason abstractly and quantitatively.
#2: Mathematically Proficient Students …
DecontextualizeRepresent as symbols, abstract the situation
ContextualizePause as needed to refer back to situation
x x x x
P
5
½ Mathematical Problem
Go to Livebinders
• Go to tab for Math Tasks• Go to the sub-tab for Illustrative Math Project
– Search for an example that would be quantitative and abstract
– Grade 3, fractions 3 and 3a
Construct viable arguments and critique the reasoning of others.
#3: Mathematically Proficient Students …
Use assumptions, definitions, and previous results
Make a conjecture
Build a logical progression of statements to explore the conjecture
Analyze situations by breaking them into cases
Recognize and use counter examples
Whitesides, E. (2011). The CCSS Mathematical Practices. Presentation at the CCSSO Mathematics SCASS meeting, November 2011).
Justify conclusionsRespond to arguments
Communicate conclusionsDistinguish
correct logic
Explain flaws
Ask clarifying
questions
Go to Livebinders
• Go to tab for Math Tasks• Go to the sub-tab for K-8 tasks • Go to “by math strand”• Number sense and operations
– Class Line Up– Puzzled by Time
Discovery Education
• Go to Discovery Education –it is under
Model with mathematics.
#4: Mathematically Proficient Students …
Problems in everyday life…
Mathematically proficient students• make assumptions and approximations to simplify a situation, realizing these may need revision later
• interpret mathematical results in the context of the situation and reflect on whether they make sense
…reasoned using mathematical methods
-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.
Go to Livebinders
• Go to tab for Math Tasks• Go to the sub-tab for 6-12 estimates &
Number Sense– Estimation 180
Use appropriate tools strategically.
#5: Mathematically Proficient Students …
Proficient students• are sufficiently familiar with
appropriate tools to decide when each tool is helpful, knowing both the benefit and limitations
• detect possible errors• identify relevant external
mathematical resources, and use them to pose or solve problems
p. 10 SMP handout
• Answer the questions :• How will you ensure these things are
happening in your classroom?
-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.
Look for and make use of structure.
#7: Mathematically Proficient Students …
• look closely to discern a pattern or structure• step back for an overview and shift perspective• see complicated things as single objects, or as
composed of several objects
Go to Livebinders
• Go to tab for Math Tasks• Go to the sub-tab for visual patterns
Look for and express regularity in repeated reasoning.
#8: Mathematically Proficient Students …
• notice if calculations are repeated and look both for general methods and for shortcuts
• maintain oversight of the process while attending to the details, as they work to solve a problem
• continually evaluate the reasonableness of their intermediate results
-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.
GMP Flipbooks
http://www.livebinders.com/play/play?id=187117
Go to the Content Unpacked taGo to the KA K-8 FlipbooksGr 4
Handout
• P. 2—fill out Practice 8 row• P. 5 Look-Fors• P. 6-12 good questions to ponder• P. 13 sample lesson plan tool• P. 15 High Level Instructional Practices
P. 13-14 SMP handout
• Lesson planning template for the SMPs
Mathematical Practices Postershttp://elemmath.jordandistrict.org/mathematical-practices-by-standard/
Henry Ford once observed:
“If I had asked people what they wanted, they would have said a faster horse.”
If we cannot truly measure something, it might just be the most important thing.
We laminate our lives to reuse next year.
Video –Expanded Learning
EVALUATION FORM