Students As Creators - Not Curators - Of Math | ECOO BIT14 Conference Slide Deck

Students As Creators
- Not Curators -
Of Math
Kyle Pearce
tapintoteenminds.com/bit14
kyle.pearce@outlook.com
www.tapintoteenminds.com
@MathletePearce

ABOUT ME
Windsor, ON
Math Teacher / Math Coach
Apple Distinguished
Educator
Apple Authorized Trainer
Google Certified Teacher
www.tapintoteenminds.com @MathletePearce

WHERE

Student Learning Need
Inability to demonstrate understanding of
algebra through multiple representations.

Theory of Action

Theory of Action
Contextual Problems

Theory of Action
Contextual Problems
Promote Creation of Concrete
Representations Through Discovery

Theory of Action
Contextual Problems
Promote Creation of Concrete
Representations Through Discovery
Understanding of Algebraic Representations

4 3
-Part Math Lesson

1.
4 -Part Math Lesson
Minds On

4 -Part Math Lesson
1. Minds On 2.
Inquiry

4 -Part Math Lesson
Minds On
1. Inquiry
2.
3. Connections

4 -Part Math Lesson
1. Minds On
Inquiry
Connections
Consolidate
2.
3. 4.

Workflow

Workflow
GoodNotes 4

Previous Day

Previous Day
Mr. Pearce stacks reams of paper with a
thickness of 4.95 cm vertically against a
wall. If the height of the room is 273
cm, how many reams of paper would he
need to reach the ceiling?

Previous Day
need to reach the ceiling?
FUN, RIGHT?

Previous Day
How many packs of paper would
need it take to reach to reach the the ceiling?
ceiling?

Previous Day
4.95 cm
How many packs of paper would
it take to reach the ceiling?
273 cm

Previous Day
How many packs of paper would it
take to reach the ceiling?
273 cm
4.95 cm

Previous Day
How many packs of
paper will it take to reach
a height of 273 cm?
273 cm
4.95 cm
= 55.15

of 273 cm? packs of paper
How many will it take to reach a
height

How many packs of paper will it take
to reach a height of 273 cm?
packs of paper height
Independent Dependent

0 0

0 0
1 4.95

0 0
1 4.95
2 9.9

0 0
1 4.95
2 9.9
… …

height : packs of paper

height 4.95 cm
packs of paper

How many
packs of paper will it take
4h.e9i5g hctm
1 pack
packs of paper
273 cm

4.95 cm
1 pack
= 273 cm
How many?
x

4.95 cm
1 pack
= 273 cm
How xmany?

4.95 cm
1 pack
x ?
= 273 cm
How xmany?

4.95 cm
1 pack
x 55.15
= 273 cm
How xmany?

4.95 cm
1 pack
x 55.15
= 273 cm
How xmany?
x ?

4.95 cm
1 pack
x 55.15
= 273 cm
How xmany?
x 55.15

4.95 cm
1 pack
x 55.15
= 273 cm
Ho5w5 m.1a5ny?
x 55.15
packs

1. Minds On

1. Minds On
How many ‘thick’ packs of paper
would it take to reach the ceiling?

1. Minds On
6 cm
How many ‘thick’ packs of paper
would it take to reach the ceiling?

1. Minds On
6 cm How many ‘thick’ packs of
paper would it take to reach
the ceiling?

4 -Part Math Lesson
1. Minds On 2. Inquiry
3. Connections 4. Consolidate

2. Inquiry

2. Inquiry
How tall is the table?

3. Connections

3. Connections
How tall is the table?
130.75 cm

How tall is the table? 130.75 cm

5
packs
How tall is the table? 130.75
cm

5
packs
How tall is the table? 130.75
cm
5

5
packs
5 130.75

5
packs
5 130.75 ) x y (

5
packs
( 5 130.75 ) x y
Slope

4. Consolidate

The Next Day…

The Next Day…
How tall is
this table?

The Next Day…
How tall is
this table?
142.75 cm

The Next Day…
How tall is
this table?
142.75 cm
100.75 cm

The Next Day…
How tall is
this table?
142.75 cm
100.75 cm
6 cm

142.75 cm
100.75 cm
Equations Given 2 Points

Volume of a Sphere

Volume of a Sphere
4 ππr3
3
V =

Volume of a Sphere
4 ππr3
3
V =
or
4 r3 πr3 π3
3
V =

Discovering the Formula for
Volume of a Sphere
@MathletePearce tapintoteenminds.com

Recall Volume of a Cylinder

V = Area of Base

r2 π
V = πr2

r2 π
V = πr2 x Height

r2 π
V = πr2 h

3
r2 π
V = πr2h h

r2 π
Recall Volume of a
h V = πr2h
3

Recall Volume of a Cone
r2 π
h V = πr2h
3

+

+ =

h
+ =

h + =

+ h =

+ = h

+ =
r

+ = r

πr2h
3
+ =

πr2h
3
+ =
πr2h
3
+

πr2h
3
+ =
πr2h
3
+ = Volume of
a Sphere

r
πr2h
3
+ = h
r
πr2h
3
+ = Volume of
a Sphere

πr2h
3
+ = rh
πr2h
3
r
+ = Volume of
a Sphere

πr2h
3
+ = h
r
r
πr2h
3
+ = Volume of
a Sphere

πr2h
3
+ = h
πr2h
3
r
r
+ = Volume of
a Sphere

r
r
πr2h
3
r
+ = h
r
πr2h
3
+ = Volume of
a Sphere

r
r
πr h
3
r
+ =
r
πr h
3
h
+ = Volume of
a Sphere

r
r
(r+r) (r+r)
πr h
3
r
+ =
r
πr h
h
+ = Volume of
3
a Sphere

πr
r
r
(r+r) (r+r)
3
r
+ =
r
πr
h
+ = Volume of
3
a Sphere

πr
r
r
( +r ) ( +r )
3
r
+ =
r
πr
h
+ = Volume of
3
a Sphere

πr
r
r
( 2r ) ( 2r )
3
r
+ =
r
πr
h
+ = Volume of
3
a Sphere

r
+ =
r
r
r
2 r 2 r
πr
πr
3
h
+ = Volume of
3
a Sphere

r
+ =
r
r
r
2 r 2 r
πr πr
3
h
+ = Volume of
3
a Sphere

r
+ =
r
r
r
2 2
πr3 πr3
3
h
+ = Volume of
3
a Sphere

r
+ =
r
h
2 2
+ = Volume of
r
r
πr3 πr3
3
3
a Sphere

r
+ =
r
h
( 2 2)
+ = Volume of
ππr3
r
r
3
3
a Sphere

r
+ =
r
ππr3
( 2 2)
3 +
3
h
= Volume of
a Sphere
r
r

r
+ =
r
ππr3
( 2 )
3 +
3
h
= Volume of
a Sphere
r
r

r
+ =
r
( )
4 ππr3
3
h
= Volume of
a Sphere
r
r

r
+ =
r
4 ππr3
3
h
= Volume of
a Sphere
r
r

Volume of
a Sphere
4 ππr3
3
V =

Volume of
a Sphere
V = 4 ππr3
or V =
4 3
π3
πr3 r3 3

Assist Students In Creating
Their OWN Math Understanding,

Assist Students In Creating
Their OWN Math Understanding,
or…

Assist Students In Creating Their OWN
Math Understanding,
or…
Force Student Curation and Consumption
of OUR Math Understanding

Resources & Feedback
Please complete the survey
to help me improve
Your feedback is appreciated!

Reach Out!
Kyle Pearce
kyle.pearce@outlook.com
www.tapintoteenminds.com
@MathletePearce

Students As Creators - Not Curators - Of Math | ECOO BIT14 Conference Slide Deck

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Students As Creators - Not Curators - Of Math | ECOO BIT14 Conference Slide Deck