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1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

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Page 1: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

1

Breakout 3Patterning and Algebra

Responding to Student

Mathematical Thinking

Page 2: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Partners Around the Clock

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No time to talkNor share a thoughtJust write your namesTo play this game

Page 3: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Partners Around the Clock

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New friend’s name and your name

New friend’s name on your clock AND your name on her clock

You need the names of 4 different people on your clock

You need the names of 4 different people on your clock

You need the names of 4 different people on your clock

Page 4: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Session Goals• understand the difference

between additive thinking and multiplicative thinking

• use a Frayer model to define multiplicative thinking

• examine student work and match it to the stages of multiplicative thinking chart

• write descriptive feedback on the content

• discuss the processes and how they engage students in mathematical thinking

• become familiar with the DI process cards and re-write prompts appropriate for students in K-4

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Page 5: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Read with your Elbow Partner

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Page 6: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

A Frayer Model

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concept /

word

Definition Characteristics

Non-ExamplesExamples

Page 7: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

A Frayer Model

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Fraction

Any part of a whole, a set, or a measure.

• has two numbers written one over another

• top number numerator tells how many parts are being considered

• bottom number denominator tells how many parts in the whole

45366.5

- 12

3 4

17 3

Page 8: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

A Frayer Model

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Have a date with your 6:00 partner!

Page 9: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

The Right Number of Elephants

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Jeff Sheppard and Felicia Bond

Sharm counted 10 trunks. How many legs would there be on the elephants belonging to those 10 trunks?

Page 10: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Examining Student Work

• Sit at a table with another pair of 12:00 partners so there are 4 of you

• Peruse the samples of student work• Pick 1 sample that the 4 of you want to

talk about

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Find your 12:00 partner!

Page 11: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Stages in Development of Multiplicative Thinking

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Page 12: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Responding (in the moment) to Mathematical Content• Consider the stages of development of

multiplicative thinking• Identify (as a table of 4) where your

work sample “fits” the continuum• For your 1 student sample write

descriptive feedback on a BLUE post-it note focusing on the content of the mathematical thinking you are seeing

• Post your descriptive feedback on the wall on the sample of student work

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Page 13: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Before Break

• Please clean up your table space.• Leave any student samples not used, in

the middle of the table.

• During break – please wander through the Descriptive Feedback Gallery and be ready to comment on what you read…

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Page 14: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

BREAK

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And Gallery Walk

Page 15: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

When you return from break

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Sit down with your 3:00 partner…

Page 16: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Descriptive Feedback… over time

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Communicating Connecting

Problem solvingReflecting

Reasoning and proving

Selecting tools and strategies

Representing

Page 17: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

DI process cards

• The set has one card to describe each process• Read the sample questions and sample

prompts for REPRESENTING• Pick another few processes and read these

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Page 18: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

The Right Number of Elephants

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Jeff Sheppard and Felicia Bond

Sharm counted 10 trunks. How many legs would there be on the elephants belonging to those 10 trunks?

Page 19: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Writing Descriptive Feedback

• Use YELLOW post-it notes to write descriptive feedback to the student about the process of representing and ???

• Post your notes on the posted student sample.

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Page 20: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

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Find your 9

:00 partner!

DI cards and Tongue depressors

Page 21: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

DI process cards

• Turn and talk at your table about how effective the prompts and questions would they be with your students?

• Pick another few processes and read these• Re-write prompts appropriate for K-4• Sticks are for yourself.

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Page 22: 1 Breakout 3 Patterning and Algebra Responding to Student Mathematical Thinking

Journal

• Write descriptive feedback about what you learned today.

• Be sure to comment on content and process.

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