2015-16 Middle Years Collaborative Inquiry (MYCI) Project Session #3

SESSION#3
@MathletePearce www.tapintoteenminds.com @JustinLevack
2015-16

STUDENT SUCCESS
Superintendent Dan Fister
Lauren Segedin
SHSM
Jay Lynn
Student Success School
Support Initiative
Justin Levack
eLearning Contact / MYCI
Natalie Middleton-Bondy
Student Success Consultant
Angela Ciarlariello-Bondy
Re-engagement &
Alternative Education
Ed Kotevich
Ontario Youth
Apprenticeship Program
Kyle Pearce
Teacher / MYCI
Shelley Hudson
Information and
Innovation Services

oame2016.ca
LEAP INTO MATH
OAME 2016

kylep.ca/myci2
LEAP INTO MATH
OAME 2016
EXPRESSION OF INTEREST FORM:SOLD OUT!

QUESTIONS? INSIGHT?
#myci
TWEET YOUR QUESTION AND HASHTAG:
TWEET IT OUT!

QUESTIONS? INSIGHT?
#myci
TWEET YOUR QUESTION
AND HASHTAG:
TWEET IT OUT!
@gecdsbss
FOLLOW:

#MTBoS
The Best Teacher PD is
FREE on Twitter
Follow the Math
Twitter Blogosphere
@MathletePearcewww.tapintoteenminds.com

Purpose
Promoting cross-panel collaboration
Reduce gaps in student achievement
Building capacity in collaborative inquiry skills
Increase connections among middle years
educators

What is…
Collaborative Inquiry?
Relevant Reﬂective Reasoned
Collaborative Iterative
Adaptive
Reciprocal

What is…
Relevant
Reﬂective
Collaborative
Adaptive
Iterative
Reasoned

What is…
… 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

What is…
“There is no prescribed protocol,
nor is there a single path.”
Capacity Building Series, Collaborative Inquiry

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVE

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
MY
Conﬁdence and ability in
problem solving; retention
INQUIRY
QUESTION
What is the impact of introducing
topics with 3 act math tasks with an
inquiry approach on student
conﬁdence, understanding and
ability to solve problems in
mathematics?

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.

THEORY OF
ACTION
If I allow students to discover new
learning through contextual tasks, then
students will gain a deeper
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 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.

INQUIRY
QUESTION
THEORY OF
ACTION
PAIN POINT
INQUIRY
COLLABORATIVE

INQUIRY
QUESTION
THEORY OF
ACTION
PAIN POINT
INQUIRY
COLLABORATIVE
HURT

INQUIRY
QUESTION
THEORY OF
ACTION
PAIN POINT
INQUIRY
COLLABORATIVE
HURT ITCH

MATH
VISION
PAIN POINT
INQUIRY
COLLABORATIVE
HURT ITCH
THEORY OF
ACTION

MATH
VISION
ROADMAP
PAIN POINT
INQUIRY
COLLABORATIVE
HURT ITCH

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVEWhat is the most urgent student learning

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVE
What data sources do you have to support this?
What is the most urgent student learning

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVE
What data sources do you have to support this?
Is it related to content? Learning skill? Both?
What is the most urgent student learning

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVE
SHARING OUT WITH
DIFFERENT SCHOOLS

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVE
Uses neutral, exploratory language

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVE
Begins with “how” or “what”

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVE
Begins with “how” or “what”
Clearly speciﬁes the focus of your inquiry

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVE
What will you do and what are the expected
outcomes?

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVEServes as a storyline for your inquiry
outcomes?

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
INQUIRY
COLLABORATIVEServes as a storyline for your inquiry
Written as a series of “if… then…” statements
outcomes?

INQUIRY
QUESTION
THEORY OF
ACTION
STUDENT
LEARNING NEED
MONITORING
Pre- & Post-Assessment

VALUE
TIME
LEARNING
EARNING
versus
Exploring the similarities
between maximizing
return in the stock market
and the classroom

LEARNING
2. Understanding
1. Invest With Intention
Avoid Wide-Diversification
Maximize Reward,
Minimize Risk
The formula is knowing
there is no formula
3. Formula
EARNING

2. Understanding
1. Teach With Intention
Strategies With a Purpose
Maximize Reward,
Minimize Risk
there is no formula
3. Formula
2. Understanding
1. Invest With Intention
Avoid Wide-Diversification
Maximize Reward,
Minimize Risk
there is no formula
3. Formula
LEARNINGEARNING

kylep.ca/gecdsbvision
Math Vision

Math Vision

CONCEPTUAL
UNDERSTANDING
PROCEDURAL FLUENCY
STRATEGIC COMPETENCE
ADAPTIVE REASONING
PRODUCTIVE DISPOSITION
kylep.ca/gecdsbvision
Math Vision

PROCEDURAL FLUENCY
ADAPTIVE REASONING
Math Vision
CONCEPTUAL
UNDERSTANDING

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

Math Vision
PROCEDURAL FLUENCY
ADAPTIVE REASONING
CONCEPTUAL
UNDERSTANDING

PROCEDURAL FLUENCY
ADAPTIVE REASONING
CONCEPTUAL
UNDERSTANDING
The Four Stages of Learning

The Four Stages
of
Learning

The Four Stages
of
Mastery

The Four Stages of Mastery
COMPETENCE
CONSCIOUSNESS

Learning journey
begins at the origin
COMPETENCE
CONSCIOUSNESS

Learning journey
(0, 0)
COMPETENCE
CONSCIOUSNESS

Learning journey
(0, 0)
Competence
COMPETENCE
CONSCIOUSNESS

Learning journey
(0, 0)
Competence Consciousness
COMPETENCE
CONSCIOUSNESS

Learning journey
(0, 0)
Competence
COMPETENCE
CONSCIOUSNESS
Consciousness
Unconsciously
Incompetent

COMPETENCE
CONSCIOUSNESS
“I don’t know what
I don’t know.”
Unconsciously
Incompetent

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

COMPETENCE
CONSCIOUSNESS
don’t know.”
Unconsciously
Incompetent
1

COMPETENCE
CONSCIOUSNESS
don’t know.”
Unconsciously
Incompetent
1
Student Might Be Thinking:
“I’ll count the candies.”

COMPETENCE
CONSCIOUSNESS
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

COMPETENCE
CONSCIOUSNESS
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.”

COMPETENCE
CONSCIOUSNESS
1

COMPETENCE
CONSCIOUSNESS
1
2

COMPETENCE
CONSCIOUSNESS
1
2 Consciously
Incompetent

COMPETENCE
CONSCIOUSNESS
1
2 Consciously
Incompetent
“I know what I
don’t know.”

COMPETENCE
CONSCIOUSNESS
1
2 Consciously
Incompetent
“I know what I
don’t know.”
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21

COMPETENCE
CONSCIOUSNESS
1
2 Consciously
Incompetent
“I know what I
don’t know.”

COMPETENCE
CONSCIOUSNESS
1
2 Consciously
Incompetent
“I know what I
don’t know.”
“I know I’m supposed to multiply, but I’m not sure how.”

COMPETENCE
CONSCIOUSNESS
1
2 Consciously
Incompetent
“I know what I
don’t know.”
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21

COMPETENCE
CONSCIOUSNESS
1
2 3

COMPETENCE
CONSCIOUSNESS
1
2 3 Consciously
Competent

COMPETENCE
CONSCIOUSNESS
1
2 3 Consciously
Competent
“I grow and I know; it
starts to show.”

COMPETENCE
CONSCIOUSNESS
1
2 3
Consciously
Competent
“I grow and I know;
it starts to show.”
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21

COMPETENCE
CONSCIOUSNESS
1
2 3
Consciously
Competent
“I see 7 groups of 3 candies.”

COMPETENCE
CONSCIOUSNESS
1
2 3
Consciously
Competent
“I added 3 candies, 7 times. There are 21 total candies.”
3 6 9 12 15 18 21

COMPETENCE
CONSCIOUSNESS
1
2 3
Consciously
Competent
7
14
21

COMPETENCE
CONSCIOUSNESS
1
2 3
4

COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously
Competent

COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously
Competent
“I simply go because
of what I know.”

COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously
Competent
of what I know.”
7
14
21

“There are 3 groups of 7 candies.”
“There are 21 candies because 7 times 3 is 21.
COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously
Competent
of what I know.”
7
3

Four Stages
of
Mastery
COMPETENCE
CONSCIOUSNESS
2 3
41

Four Stages
of
Mastery
COMPETENCE
CONSCIOUSNESS
2 3
41
Unconsciously
Incompetent

Four Stages
of
Mastery
COMPETENCE
CONSCIOUSNESS
2 3
4
Consciously
Incompetent
1
Unconsciously
Incompetent

Four Stages
of
Mastery
COMPETENCE
CONSCIOUSNESS
2 3
4
Consciously
Competent
Consciously
Incompetent
1
Unconsciously
Incompetent

Four Stages
of
Mastery
COMPETENCE
CONSCIOUSNESS
2 3
4
Consciously
Competent
Consciously
Incompetent
1
Unconsciously
Incompetent
Unconsciously
Competent

Consciously Incompetent
The Four Stages
of
Mastery
COMPETENCE
CONSCIOUSNESS
1
2 3
4
Unconsciously Competent
Consciously Competent
Unconsciously Incompetent1
2
3
4

Guess How Many Of Each Colour There Are

Group your cubes by colour

Fairly share a minimum of one cube of each
colour with as many friends as possible.

16 red and 12 green
1 Friend

8 red and 6 green
8 red and 6 green
Two Friends

4 red and 3 green
4 red and 3 green
4 red and 3 green
4 red and 3 green
Four
Friends

Group your candies by colour

3 Friends Get 7 Red and 6 Blue

3 Friends Get 7 Red and 6 Blue
YOUR TURN!

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?

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?

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.

Paul's Quilt
Unknown Connections

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

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

Shared by Michael Fenton
CHECK THIS OUT

Stage 1

Stage 2

Stage 3
?

Stage 3

Stage 4
?

Stage 4

Stage 1 Stage 2
Stage 3 Stage 4

Stage 1 Stage 2
Stage 3 Stage 4
Initial Value:
Rate of Change:
Equation:

Stage 1 Stage 2
Stage 3 Stage 4
Initial Value:
Rate of Change:
Equation:
2

Stage 1 Stage 2
Stage 3 Stage 4
Initial Value:
Rate of Change:
Equation:
2
3

Stage 1 Stage 2
Stage 3 Stage 4
Initial Value:
Rate of Change:
Equation:
2
3
y = 2 + 3x

1
4

1
4 +
2
4

1
4 +
2
4
+

1
4 +
2
4
=
=
+

1
4 +
2
4
=
=
3
+

1
4 +
2
4
=
=
3
4
+

2
3

2
3 +
2
3

2
3 +
2
3
+

2
3 +
2
3
+ =
=

2
3 +
2
3
+ =
4
=

2
3 +
2
3
+ =
4
3=

2
3 +
2
3
+ =
4
3=
=
=

2
3 +
2
3
+ =
4
3=
=
= 1

2
3 +
2
3
+ =
4
3=
=
= 1
1
3

2
3 +
3
4
+ =
=
?
?
?

4
6 +
3
4
+ =
=
?
?
?

4
6 +
6
8
+ =
=
?
?
?

6
9 +
6
8
+ =
=
?
?
?

6
9 +
9
12
+ =
=
?
?
?

8
12 +
9
12
+ =
=
?
?
?

8
12 +
9
12
+ =
=
?
12

8
12 +
9
12 = 12
+ =
17

8
12 +
9
12 = 12
+ =
17
= 1
5
12

QUESTION
Make the smallest difference by ﬁlling in the boxes
below using the whole numbers 1 through 9, no more
than one time each.
-
Shared by openmiddle.com

What is happening?
=?
4
4
or 1
1
4

What is happening?
=
4
4
or 1
1
4 x 4

WHAT IF…
…we multiplied the following by 3?
x 3 = ?

WHAT IF…
…we multiplied the following by 3?
x 3 = ?
1
2

x 3 = ?1
2
1
2
1
2
1
2 = ?
+ + 2
1 1 1

1
2
1
2
1
2
x 3 = ?1
2
1
2
1
2
1
2 =+ + 2
1113

1
2
1
2
1
2
x 3 = ?1
2
1
2
1
2
1
2 =+ + 2
11131
2

1
2
1
2
1
2
x 3 = ?1
2
1
2
1
2
1
2
=+ + 2
1113
+ =11 1
2

1
2
1
2
1
2
x 3 = ?1
2
1
2
1
2
1
2
=+ + 2
1113
+ =1 1 1
2

Evaluate the following:
=
x 5
3
4
3
4
3
4
3
4
3
4
3
4

=
x 5
3
4
15
4
or 3
3
4

1
2 x
1
2
x =
=
?
?
?

1
2 x
1
2
x
= ?

1
2 x
1
2 =
1
4
x

2
3 x
3
4 = ?
x

2
3 x
3
4
x
= ?

2
3 x
3
4 =
6
12
x

=
6
12
?
?

=
6
12
1
2

3
5 x
2
7
x
= ?

3
5 x
2
7
x
=
6
35

=
6
35
?
?

6
35

Shared by David Wees
GET READY
TO HAVE A
LOOK

Shared by David Wees
THINK OF A
SHORTCUT TO
COUNT HOW MANY
WHITE SQUARES
THERE ARE

?
What is happening?
=
3 Kit Kat Bars
1
2
1
2
1
2
1
2
1
2
1
2

?
What is happening?
=
3 Kit Kat Bars
1
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1

?
What is happening?
=
3 Kit Kat Bars
1
2
1
2
1
2
1
2
1
2
1
2
1111116 halves

÷
What is happening?
=
3 Kit Kat Bars
1
2
1
2
1
2
1
2
1
2
1
2
1111116 halves
1
2

=
÷ 3
4

=
÷ 3
4
3
4
3
4
3
4
3
4

=
÷ 3
4
3
4
3
4
3
4
3
4
4 Total

2
÷3
1
3

2
÷3
1
3 = 2
= 2

2
÷3
1
3 = 2
= 2
Two thirds can be split up
into two groups of one third
groups

3
4

3
÷4
2
4

1.5
3
÷4
2
4 =
= 1.5

1.5
3
÷4
2
4 =
= 1.5 = 3
2
=
3
2

1.5
3
÷4
2
4 =
= 1.5 = 3
2
=
3
2
= 1
2
1
=
1
21

1.5
3
÷4
2
4 =
= 1.5 = 3
2
=
3
2
= 1
2
1
=
1
21
Three quarters can be divided into one
and a half groups of two quarters.

4
5

4
5
3
5÷

4
5
3
5÷
= 4
3
4
3=

4
5
3
5÷
= 4
3
4
3=
= 1
3
1
=
1
31

4
5
3
5÷
= 4
3
4
3=
= 1
3
1
=
1
31
Four fifths can be divided into one and a
third groups of three fifths.

2
33

2
3
1
3÷3 1

= 11
4
2
3
1
3÷3 1
11
4=

= 11
4
= 3
4
2
2
3
1
3÷3 1
11
4= =
3
42

= 11
4
= 3
4
2
2
3
1
3÷3 1
11
4= =
3
42
Three and two-thirds can be divided by one and
one-third into two and three-quarter groups.

1
2
2
3÷4 1

1
2
2
3÷4 1
1 1 1 1
1
2

1
2
2
3÷4 1
1
2
3

1
2
2
3÷4 1
1 Whole = 2 Candies
1 Whole = 3 Candies

1
2
2
3÷4 1
1 Whole = 4 Candies
1 Whole = 3 Candies

1
2
2
3÷4 1
1 Whole = 6 Candies
1 Whole = 3 Candies

1
2
2
3÷4 1
1 Whole = 6 Candies
1 Whole = 6 Candies

1
2
2
3÷4 1
= 27
10
27
10=

1
2
2
3÷4 1
= 27
10
27
10=
= 7
10
2
=
7
102

khmath.comGo to:
HOMEWORK & GAMESHOW

3 Act Math Tasks
iTunes U
kylep.ca/curiousmath1p

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SESSION#2
2015-16
kylep.ca/myciexit3

2015-16 Middle Years Collaborative Inquiry (MYCI) Project Session #3

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