Slide deck from the Ontario Teachers Federation (OTF) Connect Session - Working With Two Variable Relationships held on Thursday April 21st, 2016.

1. Working With Two
Variable Relationships
tapintoteenminds.com/OTF
Ontario Teachers’ Federation
CONNECT

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BUZZWORDS

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ENGAGEMENT
“There are several types/categories of engagement – academic,
cognitive, intellectual, institutional, emotional, behavioral,
social, psychological, to name a few.”
Parsons, J., & Taylor, L. (2011). Student Engagement: What do we know
and what should we do? University Partners (pp 3). University of Alberta.

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ENGAGED YET?

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MATH
PROBLEMS

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MATH
PROBLEMS

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4. Homework
3. Examples
2. Definitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class

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The Four Stages
of
Learning

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The Four Stages
of
Mastery

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The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS

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The Four Stages of Mastery
Learning journey
begins at the origin
(0, 0)
COMPETENCE
CONSCIOUSNESS

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The Four Stages of Mastery
Learning journey
begins at the origin
(0, 0)
Competence
COMPETENCE
CONSCIOUSNESS
Consciousness
Unconsciously
Incompetent

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The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
“I don’t know what
I don’t know.”
Unconsciously
Incompetent

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Count how many candies there are.
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
“I don’t know what I
don’t know.”
Unconsciously
Incompetent
1

16. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
“I don’t know what I
don’t know.”
Unconsciously
Incompetent
1
Count how many candies there are.
Student Might Be Thinking:
“I’ll count the candies.”

17. @MathletePearcewww.tapintoteenminds.com
Count how many candies there are.
Student Might Be Thinking:
“I’ll count the candies.”
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
“I don’t know what I
don’t know.”
Unconsciously
Incompetent
1
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
Answer & Justification:
“I counted each candy and there are 21 total.”

18. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 Consciously
Incompetent
“I know what I
don’t know.”

19. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 Consciously
Incompetent
“I know what I
don’t know.”
Count how many candies there are.
Student Might Be Thinking:
“I know I’m supposed to multiply, but I’m not sure how.”

20. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 Consciously
Incompetent
“I know what I
don’t know.”
Count how many candies there are.
Student Might Be Thinking:
“I know I’m supposed to multiply, but I’m not sure how.”
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
Answer & Justification:
“I counted each candy and there are 21 total.”

21. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3 Consciously
Competent
“I grow and I know; it
starts to show.”

22. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3
Consciously
Competent
“I grow and I know;
it starts to show.”
Count how many candies there are.
Student Might Be Thinking:
Answer & Justification:
“I see 7 groups of 3 candies.”

23. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3
Consciously
Competent
“I grow and I know;
it starts to show.”
Count how many candies there are.
Student Might Be Thinking:
Answer & Justification:
“I see 7 groups of 3 candies.”
“I added 3 candies, 7 times. There are 21 total candies.”
3 6 9 12 15 18 21

24. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3
Consciously
Competent
“I grow and I know;
it starts to show.”
Count how many candies there are.
Student Might Be Thinking:
Answer & Justification:
“I see 3 groups of 7 candies.”
“I added 7 candies, 3 times. There are 21 total candies.”
7
14
21

25. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously
Competent
“I simply go because
of what I know.”

26. @MathletePearcewww.tapintoteenminds.com
Count how many candies there are.
Student Might Be Thinking:
“There are 3 groups of 7 candies.”
Answer & Justification:
“There are 21 candies because 7 times 3 is 21.
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously
Competent
“I simply go because
of what I know.”
7
3

27. @MathletePearcewww.tapintoteenminds.com
Four Stages
of
Mastery
COMPETENCE
CONSCIOUSNESS
2 3
4
Consciously
Competent
Consciously
Incompetent
1
Unconsciously
Incompetent
Unconsciously
Competent

28. @MathletePearcewww.tapintoteenminds.com
Consciously Incompetent
The Four Stages
of
Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously Competent
Consciously Competent
Unconsciously Incompetent1
2
3
4

29. Interconnected
Visual and Concrete
Contextual
VISION
@MathletePearcewww.tapintoteenminds.com

30. Interconnected
VISION
@MathletePearcewww.tapintoteenminds.com
Visual and Concrete
Contextual
TASKS

31. Visual and Concrete
Contextual
TASKS
VISION
@MathletePearcewww.tapintoteenminds.com
INQUIRY
Construct Conceptual
Understanding
Interconnected

32. Connect to Prior
Knowledge
Visual and Concrete
Contextual
TASKS
CONNECTIONS
VISION
@MathletePearcewww.tapintoteenminds.com
INQUIRY
Construct Conceptual
Understanding

33. Visual and Concrete
Contextual
TASKS
CONSOLIDATE
VISION
@MathletePearcewww.tapintoteenminds.com
INQUIRY
Move Towards
Procedural Fluency
Connect to Prior
Knowledge
CONNECTIONS
Construct Conceptual
Understanding

34. 3 Act Math Tasks
iTunes U
kylep.ca/curiousmath1p
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35. 3 Act Math Tasks
tapintoteenminds.com/3act-math
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On The Web

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playkh.complaykh.comGo to:

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wiz623

38. @MathletePearcewww.tapintoteenminds.com
Tap
wiz623

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Tap
wiz623

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Tap
wiz623

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Tap, then wait.
wiz623

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Tap
wiz623

43. “Walk Out”
tapintoteenminds.com/3act-math/walk-out/
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wiz623

45. “Candle's Burning”
tapintoteenminds.com/3act-math/candles-burning/
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46. “Candle's Burning”
tapintoteenminds.com/3act-math/candles-burning/
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47. “Draining the Pool”
tapintoteenminds.com/draining-the-pool/
@MathletePearcewww.tapintoteenminds.com

48. “Draining the Pool”
tapintoteenminds.com/draining-the-pool/
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49. “Draining the Pool”
tapintoteenminds.com/draining-the-pool/
@MathletePearcewww.tapintoteenminds.com

50. “Draining the Pool”
tapintoteenminds.com/draining-the-pool/
@MathletePearcewww.tapintoteenminds.com

51. @MathletePearcewww.tapintoteenminds.com
Consciously Incompetent
The Four Stages
of
Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously Competent
Consciously Competent
Unconsciously Incompetent1
2
3
4

52. Visual and Concrete
Contextual
TASKS
CONSOLIDATE
VISION
@MathletePearcewww.tapintoteenminds.com
INQUIRY
Move Towards
Procedural Fluency
Connect to Prior
Knowledge
CONNECTIONS
Construct Conceptual
Understanding

53. Working With Two
Variable Relationships
tapintoteenminds.com/OTF
Ontario Teachers’ Federation
CONNECT