Did someone say rules? What Rules?

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

5

Reflecting on the Two Problems Through the Lens

of MP2

6

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)

9

Making Sense of Addition and Subtraction of Integers:

Listening to students…

10

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…

12

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…

13

Connections to Standards of Mathematical Practice

14

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?

15

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.

18

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?