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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,

- 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?

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.

Charting Mathematical Connections

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

Making Sense of Addition and Subtraction of Integers: Listening to students…

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?

Listening to Students Reasoning…

- “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…

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.”

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?

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?

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.

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 11thACM meeting.

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?

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