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