2015-16 Middle Years Collaborative Inquiry (MYCI) Project Session #3 Slide Deck for the Greater Essex County District School Board (GECDSB). Presented on Friday May 13th, 2016.
6. QUESTIONS? INSIGHT?
#myci
TWEET YOUR QUESTION
AND HASHTAG:
TWEET IT OUT!
@MathletePearce www.tapintoteenminds.com @JustinLevack
@gecdsbss
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7. #MTBoS
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8. Purpose
Promoting cross-panel collaboration
Reduce gaps in student achievement
Building capacity in collaborative inquiry skills
Increase connections among middle years
educators
@MathletePearce www.tapintoteenminds.com @JustinLevack
11. What is…
Collaborative Inquiry?
@MathletePearce www.tapintoteenminds.com @JustinLevack
… an iterative process in which teachers
collaborate to develop reasonable inquiry
questions by implementing research-based
strategies and reflecting on how they impact
relevant student learning needs in the classroom.Relevant
Reflective
Collaborative
Adaptive
Iterative
Reasoned
12. What is…
Collaborative Inquiry?
@MathletePearce www.tapintoteenminds.com @JustinLevack
“There is no prescribed protocol,
nor is there a single path.”
Capacity Building Series, Collaborative Inquiry
26. @MathletePearcewww.tapintoteenminds.com
THEORY OF
ACTION
If I allow students to discover new
learning through contextual tasks, then
students will gain a deeper
understanding of the learning goal.
If I wait to introduce algorithms and
procedures until students have solved a
problem through inquiry, then student
confidence and procedural fluency will
increase.
27. @MathletePearcewww.tapintoteenminds.com
understanding of the learning goal.
If I wait to introduce algorithms and
procedures until students have solved a
problem through inquiry, then student
confidence and procedural fluency will
increase.
If curriculum is organized using a
spiralled approach, then student
understanding and ability to solve
problems will increase.
47. @MathletePearce www.tapintoteenminds.com @JustinLevack
2. Understanding
1. Teach With Intention
Strategies With a Purpose
Maximize Reward,
Minimize Risk
The formula is knowing
there is no formula
3. Formula
2. Understanding
1. Invest With Intention
Avoid Wide-Diversification
Maximize Reward,
Minimize Risk
The formula is knowing
there is no formula
3. Formula
LEARNINGEARNING
53. @MathletePearce www.tapintoteenminds.com @JustinLevack
PRODUCTIVE
DISPOSITION
Ability to formulate, represent & solve
mathematical problems using an effective strategy
STRATEGIC
COMPETENCE
PROCEDURAL
FLUENCY
Understanding and using a variety of
mathematical procedures
ADAPTIVE REASONING
Capacity for logical thought, reflection,
explanation, and justification
Inclination to see mathematics as
useful and valuable.
Ability to understand mathematical concepts,
operations, and relationships
CONCEPTUAL
UNDERSTANDING
67. @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.”
68. @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
69. @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.”
74. @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’ll count the candies.”
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.”
76. @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.”
77. @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.”
82. @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:
“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.”
83. @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.”
84. @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
85. @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
90. @MathletePearcewww.tapintoteenminds.com
The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously
Competent
“I simply go because
of what I know.”
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
91. @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
127. @MathletePearcewww.tapintoteenminds.com
Sample Extension Questions
If there are 25 red and 30 blue candies,
how many of each colour could you fairly
share to as many friends as possible?
If there are 36 green and 18 blue candies, what is
the ratio of green to blue candies in lowest terms?
128. @MathletePearcewww.tapintoteenminds.com
Kyle's Candy
Kyle is preparing candy bags for the upcoming
MYCI Participants. James from Kingsville Public
requests that for every 7 candies his team
receives, 3 are blue and 4 are red.
If the Kingsville candy bag has a total of 140
candies, how many of each colour are there?
129. Paul's Quilt
EQAO Winter Assessment Grade 9 Applied 2005-2006, Question 2b [Adapted]
Paul’s grandmother asks him to cut red and
white pieces. Every 5 pieces in the quilt
consist of 2 red pieces and 3 white pieces.
If the quilt has a total of 60 pieces, how many pieces are there
of each colour? Show your work.
Paul’s grandmother is sewing a quilt for him.
A quilt consists of pieces of fabric of
different shapes sewn together.
@MathletePearcewww.tapintoteenminds.com
130. Paul's Quilt
EQAO Winter Assessment Grade 9 Applied 2005-2006, Question 2b [Adapted]
@MathletePearcewww.tapintoteenminds.com
Paul’s grandmother asks him to cut red and
white pieces. Every 5 pieces in the quilt
consist of 2 red pieces and 3 white pieces.
If the quilt has a total of 60 pieces, how many pieces are there
of each colour? Show your work.
Paul’s grandmother is sewing a quilt for him.
A quilt consists of pieces of fabric of
different shapes sewn together.
138. 0
“When there are 0
red pieces, there
are 0 white.”
Initial Value
is 0
3 White
2 Red
32 “We need 3 white
pieces per 2 red
pieces”
W = Initial
Value +
Rate of
Change r
139. 0
“When there are 0
red pieces, there
are 0 white.”
Initial Value
is 0
3 White
2 Red
32 “We need 3 white
pieces per 2 red
pieces”
W = Initial
Value +
Rate of
Change r
W = + r0 3
2