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Academic Coaches Math MeetingDecember 21, 2012

Beth SchefelkerBridget SchockConnie LaughlinHank KepnerKevin McLeod

Did someone say rules?What Rules?

1At your table groups, Come to consensus on a definition of rational numbers.

Write a set of equivalent rational numbers.

Be prepared to share.

2Rational Numbers

.3, .33, .333, .33333.2Learning Intentions and Success CriteriaWe are learning to apply and extend the operations of addition and subtraction to negative numbers.

We will be successful when we can use reasoning to articulate how negative numbers behave when we use the properties of addition and subtraction.33How does your textbook series introduce negative numbers?

How does your textbook promote sense making of the operations involving negative numbers?

4Reflecting on Professional Practice

Turn and talkShare4Reflecting on the Two Problems Through the Lens of MP2

5Distribute the posters from December 75MP2. Reason abstractly and quantitativelyAs you read Math Practice Standard 2 (p.6 CCSSM):Underline key phrases that identify student expectations.

How did MP2 surface when working on the Elevation and Antifreeze problems?Use a different colored marker to add ideas of MP2 to the standards box of your chart for each problem.

620 minutes including debrief of completed charts with problem and CCSSMPopcorn strategy - Debrief the key phrases as a whole group

Tables post their final charts and facilitates pull out common connections to summarize6Charting Mathematical ConnectionsProblem #1Elevation

Standards Connection6.NS.5 and 6Problem #2Antifreeze

Standards Connection7.NS.1a and c7How did MP2 surface when working on the Elevation and Antifreeze problems?7Construct a Number Line Representation25 17

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Looking for the difference between two numbers8Making Sense of Addition and Subtraction of Integers: Listening to students

9The rules that students follow. If we have them follow these rules, are we giving them the best experience if we follow these rules.9Looking for CounterexamplesDecide if each statement will always be true.If the statement is not always true, show an example for which it is false ( a counterexample).

If it is always true, present an argument to convince others that no counterexamples can exist.Record your thinking for each card on a separate white board.Have you included a number line representation?

10Cards and 4 white boards at each tables (and markers)3 minutes for each question 12 minutes total Groups work on all 4 to come up with a counter exampleFacilitators pick the example for each one to share (only 2 minutes sharing per question) use document camera to show counterexampleTotal of 20 minutes for entire activity10I tried four different problems in which I added a negative number and a positive number, and each time, the answer was negative. So a positive plus a negative is always a negative.

2. I noticed that a negative number minus a positive number will always be negative because the subtraction makes the answer even more negative.Listening to Students Reasoning11113. I think a negative number minus another negative number will be negative because with all those minus signs it must get really negative.

4. A positive fraction, like , minus a negative fraction, like , will always give you an answer that is more than one.

Listening to Students Reasoning12Connections to Standards of Mathematical Practice

135 minutesTurn and talk and surface a few connections13MP2. Reason abstractly and quantitativelyRevisit Math Practice Standard 2 (p.6 CCSSM):How is the last sentence of this standard (Quantitative reasoning.) reflected in the counterexample task?

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1415MP3 Construct viable arguments and critique the reasoning of others.As you read Math Practice Standard 3 (p.6 CCSSM):Underline key phrases that identify student expectations. How did MP3 surface when working on the counterexample task?

Learning Intentions and Success CriteriaWe are learning to apply and extend the operations of addition and subtraction to negative numbers.

We will be successful when we can use reasoning to articulate how negative numbers behave when we use the properties of addition and subtraction.1616Apply: Professional PracticeAs you work in classrooms, record examples of rules you hear students /teachers using that could lead to misconceptions when they are operating with numbers.

Bring two examples with you to the January 11th ACM meeting.

17Could the professional practice be to study their curriculum materials to see how deep understanding of addition and subtraction of integers (or rational numbers) is promoted?17A Time to ReflectHow did the counterexample task deepen your understanding of operations with negative numbers?How did the counterexample task deepen your understanding of Standards for Mathematical Practice?

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