otf connect webinar - connecting the 4-part math lesson to number sense and algebra

4-Part Math Lesson:Number Sense & Algebra

@MathletePearce

tapintoteenminds.com

@MathletePearcewww.tapintoteenminds.com

Last Time…


Two Groups of Students

Good at Math

Not Good at Math

Struggle withunfamiliarproblems



Good at Memorization

Not Good at Memorization


TEST QUESTION


TEST QUESTION


=EXAMPLE

TEST QUESTION


=HOMEWORK

TEST QUESTION


=TEXTBOOK


UNFAIR



Good atMath

NotGood at

Math






UNFAIR


New Knowledge


New Knowledge

Prior Knowledge


MATH

SILO1

SILO2

SILO3

SILO4


MATHSILO

1SILO

2SILO

3SILO

4


A VISION FOR MATHEMATICS

EDUCATION

VISION


Contextual

VISION


Visual and ConcreteContextual

VISION


Interconnected


VISION


Interconnected


CONFIDENCE


Interconnected


PERCEPTION


Interconnected


STUDENT SUCCESS

Connections

Minds On

Consolidate

Inquiry1.


2.

3. 4.

-Part Math Lesson4

Connections

Minds On

Consolidate

Inquiry

1.


2.

3.

4.

-Part Math Lesson4

Interconnected

Visual and Concrete

Contextual

VISION

Connections

Consolidate

Inquiry


2.

3.

4.

Interconnected


VISION

MINDS ON -Part Math Lesson4

Consolidate

Inquiry


2.

4.

Connect to New Learning Goal


VISION

MINDS ON

CONNECTIONS

-Part Math Lesson4



VISION

MINDS ON

INQUIRY

CONNECTIONS

-Part Math Lesson

Consolidate4.4

Prior Knowledge & Intuition




VISION

MINDS ON

CONNECTIONS

INQUIRYCONSOLIDATEPrior Knowledge

& Intuition


Apply New Skill Through Practice



MINDS ON

CONNECTIONS


& Intuition


4-PartLesson




MINDS ON

CONNECTIONS


& Intuition


4-PartLesson:Apply New Skill

Through Practice Number Sense & Algebra


Number Sense & Numeration



Grade 9 Academic



Grade 9 Applied


Algebra



MINDS ON

CONNECTIONS


& Intuition



4-PartLesson:

Number Sense & Algebra


“Chunk” Into Friendly Numbers

multipl

y

129 x3

3 3 3 2

3

3

10

9

12


Multiplication Chunking Model

multipl

y

3

3 3 3 2

3

3

10

9

9 (10 + 2)

10



multipl

y

3

2

3

3

9

9=9(10 + 2 )

(10)

10



multipl

y

3

2

3

3

9

9 (10 + 2 )9= (10) 9(2)+

10



multipl

y

3

2

3

3

9

9 (10 + 2 )9= (10) 9(2)+90=90

10



multipl

y

3

2

3

3

9

9 (10 + 2 )9= (10) 9(2)+90=90 18+18

10



multipl

y

3

2

3

3

9

9 (10 + 2 )9= (10) 9(2)+90=90 18+18

= 108108

10

3

multipl

y

510


1513 x15

13

13

multipl

y

510

13

15


510

(10 + 5)

1513 x

=

510

10

3

multipl

y

510

13

13


1513 x

=

( 10 + 5 )=

3

(10 + 3 )

( 10 + 5 )10

5

3

10

3

multipl

y

510

13

15

13


10 1513 x

=

( 10 + 5 )= (10 + 3 )

( 10 + 5 )10

5

3

10

3

multipl

y

510

13

15

13


10 1513 x

=

( 10 + 5 )=10

(10 + 3 )

( 10 + 5 )

= 100

100

3

10

10

3

multipl

y

510

13

13


5 1513 x

=

( 10 + 5 )=10

(10 + 3 )

( 10 + 5 )

= 100

100

10

3

10

3

multipl

y

510

13

13


5 1513 x

=

( 10 + 5 )=10

(10 + 3 )

( 10 + 5 )

= 100

100

+ 50

50

10

10

3

multipl

y

510

13


5 1513 x

=

( 10 + 5 )=

3

(10 + 3 )

( 10 + 5 )

= 100

100

+ 50

50

10

1010

3

multipl

y

510

13


5 1513 x

=

( 10 + 5 )=

3

(10 + 3 )

( 10 + 5 )

= 100

100

+ 50

50

30+ 30

10

1010

3

multipl

y

510

13


5 1513 x

=

( 10 + 5 )=

3

(10 + 3 )

( 10 + 5 )

= 100

100

+ 50

50

30+ 30 + 15

15

10

3

multipl

y

510

13

15

13


510 1513 x

=

( 10 + 5 )=10

3

(10 + 3 )

( 10 + 5 )

= 100

100

+ 50

50

30+ 30 + 15

15= 195

195



MINDS ON

CONNECTIONS


& Intuition



4-PartLesson:

Number Sense & Algebra


Introducing Distribution With Unknowns

146( )( )


146( )( )mult

iply

146



146( )( )mult

iply

6

14



146( )( )10 + 4mult

iply

6

14


+x


16( )( )x 4mult

iply

64



multipl

y

6

14x 4

+x16( )( )x 44



6( )( )x + 4mult

iply

6

14x 4

6 x( )( )= 6 x( )( )=6

x



multipl

y

6

4

610=6x

1066x

14xx

6( )( )x + 4

6 x( )( )= 6 x( )( )=



4multipl

y

6 1066x

14xx

610=6x

6( )( )x + 4

6 x( )( )= 6 x( )( )=


6x

x


4multipl

y

6 1066x

x

=

6( )( )x + 4

6 x( )( )= 6 x( )( )=


6x

x


4multipl

y

6 1066x

x

=

6( )( )x + 4

6 x( )( )= 6 x( )( )= 6( )( )4+ 6( )( )4


6x

x


4multipl

y

6 1066x

x

=

6( )( )x + 4

6 x( )( )= 6 x( )( )= 6( )( )4+ 6( )( )464+24

6424


6x

x


4multipl

y

6 1066x

x

=

6( )( )x + 46 x( )( )= 6 x( )( )= 6( )( )4+ 6( )( )4

64+24

6424 =6( )( )14


60

10


4multipl

y

6 10660

=

6( )( )10 + 46 x( )( )= 6 10( )( )= 6( )( )4+ 6( )( )4

64+ 24

6424=

6( )( )14


60

10


4multipl

y

6 10660

=

6( )( )10 + 46 x( )( )= 6 10( )( )= 6( )( )4+ 6( )( )4

64+ 24

6424=

6( )( )14

84=

84


6xx


Digging Deeper

5( )( )+ 6multipl

y


The Distributive Property

multipl

y

6xx5( )( )+ 611111



multipl

y

6xx5( )( )+ 6x

11111



multipl

y

6xx5( )( )+ 61x 1 1 1 1 1

11111

5



multipl

y

6xx5( )( )+ 61x 1 1 1 1 1

11111

5( )( )



multipl

y

6xx

5( )( )+ 61x 1 1 1 1 1

11111

5( )( )= x5( )( )=



multipl

y

6xx

5( )( )+ 61x 1 1 1 1 1

11111

5( )( )=x5( )( )=

xxxxx



multipl

y

6xx

5( )( )+ 61x 1 1 1 1 1

11111

5( )( )=x5=

xxxxx

5( )( )6



multipl

y

6xx

5( )( )+ 61x 1 1 1 1 1

11111

5( )( )=x5=

xxxxx

5( )( )6+ 5( )( )6



multipl

y

6xx

5( )( )+ 61x 1 1 1 1 1

11111

5( )( )=x5=

xxxxx

5( )( )6+5( )( )6+ 30

1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 1



multipl

y

6xx

5( )( )+ 61x 1 1 1 1 1

11111

5( )( )=x5=

xxxxx

5( )( )6++ 30

1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 1


Extending to Solving Equations

multipl

y

6x

x

5( )( )+ 61x 1 1 1 1 1

11111

5( )( )=

x5=

xxxxx

5( )( )6+

+ 30

1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 1

= 85


multipl

y

6x

x

5( )( )+ 61x 1 1 1 1 1

11111

5( )( ) =

x5 =

xxxxx

5( )( )6+

+ 30

1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 1

= 85

85

85

Extending to Solving Equations


Digging Deeper

x + 59( )Find the missing “magic number”

= 99



MINDS ON

CONNECTIONS


& Intuition



Area, Perimeter, & Volume

23x3x 2


2nd Degree Polynomials

2x( )( )+multipl

y


multipl

y

23x3x 22x( )( )+x

x

x x x 1 1

x

x

x x x


multipl

y

23x3x 22x( )( )+x

x

x x x 1 1

x

x

x x x

2x( )( )


multipl

y

23x3x

22x( )( )+x

x

x x x 1 1

x

x

x x x

)2x( )( )=


multipl

y

23x3x 22x( )( )+x

x

x x x 1 1

x2x

x

x

x x

x2 x2

x2 x2 x2

3x2x( )( )= 6x23x2x( )( )=

6x


multipl

y

23x3x 22x( )( )+x

x

x x x 1 1

x

x

x x

x x

x x x=

3x2x( )( )=

2x( )( )+

6x


multipl

y

23x3x2

2x( )( )+x

x

x x x 1 1

x

x

x x

x x

x x x=

3x2x( )( )= 2x( )( )++x

xx

x

xx

6x


multipl

y

23x3x2

2x( )( )+x

x

x x x 1 1

x

x

x x

x x

x x x=

3x2x( )( )= 2x( )( )++x

xx

x

xx

22x( )( )+ 4x

4x6x2


multipl

y

23x3x2

2x( )( )+x

x

x x x 1 1

x2

x

x x

x2 x2

x2 x2 x2

=3x2x( )( )= 2x( )( )+

x

xx

x

xx

+6x2 4x

3x3x


4x( )( )

2nd Degree Equations

Find the missing “magic number”

=300



MINDS ON

CONNECTIONS


& Intuition




8x


7x( )( )

2nd Degree Equations

Find the missing “magic number”

=2,744



MINDS ON

CONNECTIONS


& Intuition




Task



I’ve got a yard…So…


… and I needI’ve got a yard…

… and I need


What do we What is the … and I need


a fence.


What do we


PERIMETER


What is the perimeter…


2 ft



2 ft 2 ft




n+

24n

+2

4

nn1212



n+

24n

+2

4

nn1212

n+

24n

+2

4

nn1212


P = l+ l +w+ w

n+

24n

+2

4

nn1212

n+

24n

+2

4

nn1212


P = ll +w+ w2

n+

24n

+2

4

nn1212

n+

24n

+2

4

nn1212


P = ll + ww2

n+

24n

+2

4

nn1212

n+

24n

+2

4

nn1212

2


P = ll + ww2

n+

24n

+2

4

nn1212

n+

24n

+2

4

nn1212

2( )

[email protected]

P = + ww2

n+

24n

+2

4

n

n12

12

n+

24n

+2

4

n

n

12

122( )

[email protected]

P = + ww2

n+

24

n+24n

n12

12

n+

24

n+24

n

n

12

122( )

[email protected]

P = +2

n+

24

n

n12

12

n+

24

n12

( )n+24


n+

24

n12

n+

24

n12

LIKE TERMS

llP = +2 n12( )n+24


n+

24

n12

n+

24

n12

LIKE TERMS

llP = +2 n12( )n+2416


n+

24

n12

n+

24

n12

llP = +2 n12( )n+2416ll +n12( )n+2416


n+

24

n12

n+

24

n12

llP = +2 n12( )n+2416ll +n12( )n+2416 ( )n+216+


n+

24

n12

n+

24

n12

llP = +2 n12( )n+2416ll +n12( )n+24162


n+

24

n12

n+

24

n12

llP = +2 n12( )n + 2416ll +n12 ()n + 2416 2


n+

24

n12

n+

24

n12

llP = +2 n12 )n + 2416ll +n12 (n + 2416 232


n+

24

n12

n+

24

n12

llP = +2 n12n + 2416ll +n12n + 2416 232 4


I also need…

fertilizer.


I also need…

What do we


fertilizer.


2 ft 2 ft

What do we


2 ft 2 ft

AREA


2 ft 2 ft

What is the area


2 ft 2 ft

n2

n

n


2 ft 2 ft

n2

n

n n2

n


2 ft 2 ft

n2

n

n n2

n

n2 n2 n2 n2 n2 n2

n2 n2 n2 n2 n2 n2 n2 n2

n2 n2 n2 n2 n2 n2 n2 n2

n2 n2 n2 n2 n2 n2 n2 n2

n2 n2 n2 n2

n2 n2 n2 n2

n2 n2 n2 n2

n2 n2 n2 n2

n n n n n n n n n n

n

n

n


2 ft 2 ft

n2

n

n n2

n

n2 n2 n2 n2 n2 n2

n2 n2 n2 n2 n2 n2 n2 n2

n2 n2 n2 n2 n2 n2 n2 n2

n2 n2 n2 n2 n2 n2 n2 n2

n2 n2 n2 n2

n2 n2 n2 n2

n2 n2 n2 n2

n2 n2 n2 n2

n n n n n n n n n n

n

n

n

2n 2n 2n 2n 2n 2n 2n 2n 2n 2n 2n 2n


n+

24n

+2

4 n+

24 n

+2

4

nn1212

nn1212


n+

24n

+2

4

nn1212

n+

24n

+2

4

nn1212A = lw


n+

24n

+2

4

n

n

12

12

n+

24n

+2

4

nn1212A = l w( )

n+24n12 n+ 24( )( )@MathletePearcewww.tapintoteenminds.com

n+

24

n+24

n

n

12

12

n+

24

n+ 24nn1212

A = l w( )( )


n+

24

n+24

n

n

12

12

n+

24

n+ 24nn1212

A = ( )( )n+24n12 n+ 24( )( )


n+

24

n+24

n

n

12

12

n+

24

n+ 24nn1212

A = w( )( )n12 n+ 24( )( )


n+

24

n+24

n

n

12

12

n+

24

n+ 24nn1212

A = w( )( ) n12 n+ 2 4( )( )= n12 n4( )( )


n+

24

n+24

n

n

12

12

n+

24

n+ 24nn1212

A = w( )( ) n12 n+ 2 4( )( )=

n12 n4( )( )


n+

24

n+24

n

n

12

12

n+

24

n+ 24nn1212

A = w( )( ) n12 n+ 2 4( )( )=

n12 n4( )( )

n+24n12 n+ 24 w( )( )+ 2


n+

24

n+24

n

n

12

12

n+

24

n+24nn1212

A = w( )( ) n12 n+ 4( )( )=

n12 n4( )( )

n+4 n12+w ( )( )+ 2n12( )( )2


n+

24

n+24

n

n

12

12

n+

24

n+24nn1212

A = w( )( ) n12 n+ 4( )( )=

n12 n4( )( )

n+4 n12+w ( )( )+ 2

n12( )( )2

+


n+

24

n+24

n

n

12

12

n+

24

n+24nn1212

A = w( )( ) n12 n+ 4( )( )=

n12 n4( )( )

n+4 +w+

n12( )( )2

n12( )( )2+


n+

24

n+24

n

n

12

12

n+

24

n+24nn1212

A = w( )( ) n12 n+ 4=

n12 n4

n+4 +w+

n12( )( )2

n12( )( )2+

48

48


n+

24

n+24

n

n

12

12

n+

24

n+24nn1212

A = w( )( ) n12n+ 4=

n12 n4

n+4 +w+

n12( )( )2

n12( )( )2+

48

48

n2

n2


n+

24

n+24

n

n

12

12

n+

24

n+24nn1212

A = w( )( ) n12n+ 4=

n12 n4

n+4 +w+

n122

n122+

48

48

n2

n2

24

24


If…


fencing has a cost of


fencing has a cost of$24.50 per foot…


and


fertilizer


fertilizerhas a cost of


… and covers 1800 feet-squared


$24.50 per foot…

How … and covers 1800 feet-squared


$24.50 per foot…

covers 1800 feet-squared

How

5.25 feet

Your Turn…


Your Turn…


Think of an example involving number sense and algebra that

you could introduce using context and visuals.

Share…


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otf connect webinar - connecting the 4-part math lesson to number sense and algebra

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