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# Did someone say rules? What Rules? - PowerPoint PPT Presentation

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.

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### Did someone say rules?What Rules?

December 21, 2012

Beth Schefelker

Bridget Schock

Connie Laughlin

Hank Kepner

Kevin McLeod

• Come to consensus on a definition of rational numbers.

• Write a set of equivalent rational numbers.

• Be prepared to share.

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.

Reflecting on Professional Practice

• How does your textbook series introduce negative numbers?

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

Reflecting on the Two Problems Through the Lens of MP2

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.

• How did MP2 surface when working on the Elevation and Antifreeze problems?

25 – 17

-10 – (-13)

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?

• “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.”

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.”

Connections to Standards of Mathematical Practice

Revisit Math Practice Standard 2 (p.6 CCSSM):

• How is the last sentence of this standard (Quantitative reasoning….) reflected in the counterexample task?

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 others.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.

Apply: Professional Practice others.

• 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 11thACM meeting.

A Time to Reflect… others.

• 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?