students as creators - not curators - of math | ecoo bit14 conference slide deck

Students As Creators - Not Curators - Of Math

[email protected]

@MathletePearce

www.tapintoteenminds.com

Kyle Pearce

tapintoteenminds.com/bit14

http://www.tapintoteenminds.com/myci

http://tapintoteenminds.com/ettipad

ABOUT MEWindsor, ONMath Teacher / Math CoachApple Distinguished EducatorApple Authorized TrainerGoogle Certified Teacher

@MathletePearcewww.tapintoteenminds.com

WHERE


Student Learning Need


Inability to demonstrate understanding of algebra through multiple representations.

Theory of Action

Understanding of Algebraic Representations


Theory of Action


Contextual Problems

Theory of Action


Theory of Action

Contextual Problems

Promote Creation of Concrete Representations Through Discovery


Contextual Problems

Theory of Action



4 -Part Math Lesson


3

Inquiry

Consolidation

Inquiry 1.


Minds On

Consolidation

-Part Math Lesson4

Minds On Inquiry1.


2.

Consolidation

-Part Math Lesson4

Minds On

Consolidate

Inquiry1.


2.

3. Connections

-Part Math Lesson4

Connections

Minds On

Consolidate

Inquiry1.


2.

3. 4.

-Part Math Lesson4

Workflow


Workflow


GoodNotes 4

Connections

Minds On

Consolidate

Inquiry1.


2.

3. 4.

-Part Math Lesson4

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








Previous Day


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


-Part Math Lesson


4. Consolidate3. Connections

2. Inquiry

Previous Day

273

cm

4.95

cm


-Part Math LessonHow many packs of paper would it

take to reach the ceiling?


2. Inquiry

Previous Day

273 cm

4.95 cm


-Part Math LessonHow many packs of paper would it

take to reach the ceiling?


2. Inquiry

Previous Day

273 cm

4.95 cm= 55.15

How many packs of paper will it take to reach

a height of 273 cm?



-Part Math Lesson

How many packs of paper will it take to reach a

height of 273 cm? 4. Consolidate3. Connections

2. Inquirypacks of paper

height


-Part Math LessonHow many packs of paper will it take

to reach a height of 273 cm?


2. Inquirypacks of paper height

Independent Dependent







0 0







0 01 4.95







0 01 4.952 9.9







0 01 4.952 9.9… …





2. Inquiry

packs of paperheight :





2. Inquiry

packs of paper

height

4.95

cm





2. Inquiry

packs of paper

height4.95 cm

1 pack

273

cm

How many





2. Inquiry4.95 cm

1 pack= 273 cm

How many?x


-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?


2. Inquiry4.95 cm

1 pack= 273 cm

How many?x

x ?




2. Inquiry4.95 cm

1 pack= 273 cm

How many?x

x 55.15




2. Inquiry4.95 cm

1 pack= 273 cm

How many?x

x 55.15

x ?




2. Inquiry4.95 cm

1 pack= 273 cm

How many?x

x 55.15

x 55.15




2. Inquiry4.95 cm

1 pack= 273 cm

How many?55.15

x 55.15

x 55.15packs

Consolidate


-Part Math Lesson

1. Minds On

1. Minds On

Consolidate


-Part Math Lesson

Consolidate


-Part Math Lesson

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

1. Minds On

Consolidate


-Part Math Lesson


1. Minds On6

cm


-Part Math Lesson

How many ‘thick’ packs of paper would it take to reach

the ceiling?

1. Minds On6

cm


2. Inquiry


2. Inquiry1. Minds On


-Part Math Lesson4


2. Inquiry


-Part Math Lesson

4. Consolidate

2. Inquiry


-Part Math Lesson

How tall is the table?

4. Consolidate

Minds On


-Part Math LessonHow tall is the table?

2. Inquiry

Minds On

Inquiry2. -Part Math Lesson




-Part Math Lesson4

Minds On


-Part Math Lesson

3. Connections

Minds On


-Part Math LessonHow tall is the table?

3. Connections13

0.7

5 cm

Minds On


-Part Math LessonHow tall is the table?13

0.7

5 cm

packs of paper heightIndependent Dependent

Minds On



0.7

5 cm


5packs13

0.7

55

Minds On



0.7

5 cm


5packs

5

130

.75

Minds On



0.7

5 cm


5packs

130.755

Minds On



0.7

5 cm


5packs

130.755 )x y(

Minds On



0.7

5 cm


5packs

130.755( )x ySlope

3. Connections





-Part Math Lesson4

4. Consolidate


2. Inquiry




-Part Math Lesson4

GoodNotes 4


The Next Day…

GoodNotes 4


The Next Day…

GoodNotes 4

How tall is this table?


The Next Day…

GoodNotes 4


142

.75

cm


The Next Day…

GoodNotes 4


142

.75

cm

100

.75

cm


The Next Day…

GoodNotes 4


142

.75

cm

100

.75

cm

6 c

m

142

.75

cm

100

.75

cm

Equations Given 2 Points

Volume of a Sphere


Volume of a Sphere


4 r3πr3π33

=V

Volume of a Sphere


4 r3πr3π33

=V

or4 r3πr3π

33=V

Discovering the Formula for Volume of a Sphere

@MathletePearce tapintoteenminds.com


Recall Volume of a Cylinder

r2π



r2π

V = Area of Base



r2π

V = πr2



r2π

V = x Heightπr2



r2π

hV = πr2 h



r2π

hV = πr2h

3


r2π

hV = πr2h

3

Recall Volume of a


r2π

hV = πr2h

3

Recall Volume of a Cone


r2π



r2π


+


r2π


+ =


r2π

h


+ =


r2π


+ =h


r2π


+ = h


r2π


+ =


r2π


+ =r


r2π


+ = r


r2ππr2h

3


+ =


r2ππr2h

3


+ =πr2h

3+


r2ππr2h

3


+ =πr2h

3+ = Volume of

a Sphere


r2ππr2h

3


+ = hr

πr2h3

+ = Volume ofa Sphere

r


r2ππr2h

3

+ = hr

πr2h3


r

r

r


r2ππr h

3

+ =πr h

3+ = Volume of

a Sphere

r

r

r

rh

r

r

r

r


r2ππr h

3

+ =πr h

3+ = Volume of

a Sphere

r

r

r

rh

r r r r( )+ ( )+


r2ππr

3

+ =πr

3+ = Volume of

a Sphere

r

r

r

rh

r r r r( )+ ( )+


r2ππr

3

+ =πr

3+ = Volume of

a Sphere

r

r

r

rh

rr rr( )+ ( )+


r2ππr

3

+ =πr

3+ = Volume of

a Sphere

r

r

r

rh

( )2r ( )2rr r

rπrπ


r2ππr3

+ =πr3


r

r

r

rh

2 2r r

rπrπ


r2π3

+ =

3+ = Volume of

a Sphere

r

r

r

rh

2 2r r

r3πr3π


r2π3

+ =

3+ = Volume of

a Sphere

r

r

r

rh

2 2

r3πr3π


r2π3

+ =

3+ = Volume of

a Sphere

r

r

r

rh

2 2( )

r3πr3π


r2π3

+ =

3+ = Volume of

a Sphere

r

r

r

rh

22( )

4 r3πr3π


r2π3

+ =

3= Volume of

a Sphere

r

r

r

rh

( )

4 r3πr3π


r2π3

+ =

3= Volume of

a Sphere

r

r

r

rh

4 r3πr3π


r2π33=V

Volume ofa Sphere

4 r3πr3π


r2π33=V or 4 r3πr3π

33

Volume ofa Sphere

=V


Contextual Problems

Theory of Action



or…


Assist Students In Creating Their OWN Math Understanding,



or…



Force Student Curation and Consumption of OUR Math Understanding

or…

Resources & FeedbackPlease complete the survey

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Reach Out!

[email protected]

www.tapintoteenminds.com

Kyle Pearce

@MathletePearce


http://www.tapintoteenminds.com

http://www.tapintoteenminds.com/myci

http://tapintoteenminds.com/bit14

students as creators - not curators - of math | ecoo bit14 conference slide deck

Education

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multiple representations

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understanding of algebra