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Did someone say rules? What Rules?. Academic Coaches – Math Meeting December 21, 2012 Beth Schefelker Bridget Schock Connie Laughlin Hank Kepner Kevin McLeod. Rational Numbers. At your table groups, C ome to consensus on a definition of rational numbers. - PowerPoint PPT PresentationTRANSCRIPT

Academic Coaches – Math MeetingDecember 21, 2012

Beth SchefelkerBridget SchockConnie LaughlinHank KepnerKevin McLeod

Did someone say rules?What Rules?

2

At your table groups, Come to consensus on a definition of

rational numbers.

Write a set of equivalent rational numbers.

Be prepared to share.

Rational Numbers

3

Learning Intentions and Success Criteria

• We 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.

4

• How does your textbook series introduce negative numbers?

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

Reflecting on Professional Practice

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Reflecting on the Two Problems Through the Lens

of MP2

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MP2. Reason abstractly and quantitatively

As 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.

7

Charting Mathematical Connections

Problem #1Elevation

Standards Connection6.NS.5 and 6

Problem #2Antifreeze

Standards Connection7.NS.1a and c

How did MP2 surface when working on the

Elevation and Antifreeze problems?

8

Construct a Number Line Representation

25 – 17

-10 – (-13)

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Making Sense of Addition and Subtraction of Integers:

Listening to students…

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Looking for Counterexamples

Decide 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?

11

1. “I 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 Reasoning…

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3. “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 ¾, minus a negative fraction, like – ½ , will always give you an answer that is more than one.”

Listening to Students Reasoning…

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Connections to Standards of Mathematical Practice

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MP2. Reason abstractly and quantitatively

Revisit 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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MP3 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?

16

Learning Intentions and Success Criteria

• We 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.

17

Apply: Professional Practice

• As 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.

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A Time to Reflect…

• How 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?