P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Making Algebraic ConnectionsMath Science Partnership Grant

Funded bythe United States Department of Education

through the Kentucky Department of Education

P-12 Mathematics and Science Outreach

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Making Algebraic Connections

September 28, 2010Mt. Sterling, KY

University of KentuckyPartnership Institute for Math & Science Education Reform

Kentucky Department of Education

Welcome!Help yourself to some

refreshments

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

What’s going on here?1. Write down a three digit number in which no digits are

repeated 2. Reverse the digits of your number and subtract the

smaller number from the larger number3. Reverse this new number and add it to the difference

obtained in #2.4. Compare your answer with other people at your table.

What do you notice?5. Try this with a different three digit number6. What is happening? Why is it happening?

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Meeting Norms

5

oPlease Put Your Cell Phone on Vibrate…

oUse The Rule of Two Feet…

oSide-bar talkingPlease limit talking with other participants unless group work is under way.oParticipate ActivelyRespect and solicit opinions

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

September AgendaSeptember 28, 2010

• Opening Activity• Kentucky Core Academic Standards

– Reflections on Processes, Proficiencies, and Practices

– Mathematical Practices Carousel– Mathematical Practices and Planning for

Classroom Lessons• Words to Symbols: Different Perspectives

– Context– Models– Estimation and Invented Strategies– Practice

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

September Agenda

• Breakouts:–TI-73 and SmartView–Make and Take

• Reflections• Sounding Boards

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Flashback: NCTM Processes

Problem Solving Reasoning & proofCommunicationConnectionsRepresentation

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Flashback: ProficienciesC.U.P.F.A.R.S.C.P.D.

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Flashback: Proficiencies

C.U.P.F.A.R.S.C.P.D.

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Flashback: Proficiencies

C.U.P.F.A.R.S.C.P.D.

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

-launched by Council of Chief State School Officers (CCSSO) and the National Governors Association Center for Best Practices (NGA Center).

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Standards for Mathematical Practice

The standards for mathematical Practice are important “processes and proficiencies” and describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. See page 6.They are based on ideas important to mathematics education from –the NCTM process standards of: problem solving, reasoning and proof, communication, representation, andconnections.

the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding, (comprehension of mathematical concepts, operations and relations),

procedural fluency, and (skill in carrying out procedures flexibly, accurately, efficiently and appropriately),

productive disposition. (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Standards for Mathematical Practice - pgs 6-8.

#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.

Posted on the overview page for every grade level!

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

How are the lists of mathematical

practices and the the core standards related

to one other?

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Mathematical Practice

During this activity you will work in 2 groups.

Home Group – A group of 8 people. Each person has a different mathematical practice. (color coded)

Expert Group – A group of 6 or 7 people. Everyone has the same mathematical practice.

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Mathematical Practices

Individually, in your home group:• Read the front and back pages of the

mathematical practice.• On the recording sheet, answer the

question in the first column, “What is it?”

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Mathematical Practice

• Move to your expert group when signaled.• As a group, agree on the ‘Key Ideas’

(Column 2) about the practice that you will share with your home group.

• List essential vocabulary, give specific examples, write a summary in your own words, and/or illustrate the practice with a graph, icon, or drawing that describes it.

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Mathematical Practices

• In your expert group• What does the mathematical practice

‘Look /Sound Like’? (Column 3)• Connect ideas to last month’s “Crossing

the River” problem

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Everyone Needs a Break

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

• Mathematical Practices in Lessons

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

-launched by Council of Chief State School Officers (CCSSO) and the National Governors Association Center for Best Practices (NGA Center).

Connections???

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Reflecting on the Mathematical Practices

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Words to Symbols

I’m Thinking of a Number

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Words to Symbols:Four Different Perspectives

• Context • Models • Estimation and Invented Strategies • Practice

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Breakouts

TI-73 and SmartViewor

Make and Take

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Reflection Time

What did we do?

What did we learn?

P-12 Mathematics and Science Outreach MAC ’10-’11PIMSER

Wrap Up• Reflections

• Sounding Boards

• Return name tags to the meeting box