Transcript 2014 CMC-South Presentation - Chamberlain, Dave

Welcome to:
A “Hands-On” Approach to
the Distributive Property
(Session 538)
Presenter: Dave Chamberlain
[email protected]
Math Curriculum Specialist, Capistrano USD
President, Orange County Math Council
When/How is the
Distributive Property Important?
When/How is the
Distributive Property Important?
Math Practice Standard 7 Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or
structure. Young students, for example, might notice that three and
seven more is the same amount as seven and three more, or they may
sort a collection of shapes according to how many sides the shapes have.
Later, students will see 7 x 8 equals the well-remembered 7 x 5 + 7 x 3, in
preparation for learning about the distributive property. In the
expression x2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9
as 2 + 7. They recognize the significance of an existing line in a geometric
figure and can use the strategy of drawing an auxiliary line for solving
problems. They also can step back for an overview and shift perspective.
They can see complicated things, such as some algebraic expressions, as
single objects or as being composed of several objects. For example, they
can see 5 – 3(x – y)2 as 5 minus a positive number times a square and
use that to realize that its value cannot be more than 5 for any real
numbers x and y.
What is 14 x 13?
What is 14 x 13?
Convince me…
Write down as many
different ways to prove that
14 x 13 = 182
What is 14 x 13?
What was the most efficient
method?
What was the least efficient
method?
What is 14 x 13?
How is the
“standard algorithm”
taught?
What is 14 x 13?
What is 14 x 13?
14
What is 14 x 13?
14
x 13
What is 14 x 13?
14
x 13
What is 14 x 13?
14
x 13
2
What is 14 x 13?
1
14
x 13
2
What is 14 x 13?
1
14
x 13
42
What is 14 x 13?
1
14
x 13
42
0
What is 14 x 13?
1
14
x 13
42
x
What is 14 x 13?
1
14
x 13
42
0
What is 14 x 13?
1
14
x 13
42
40
What is 14 x 13?
1
14
x 13
42
1 40
What is 14 x 13?
1
14
x 13
42
+ 1 40
What is 14 x 13?
1
14
x 13
42
+ 1 40
What is 14 x 13?
1
14
x 13
42
+ 1 40
2
What is 14 x 13?
1
14
x 13
42
+ 1 40
82
What is 14 x 13?
1
14
x 13
42
+ 1 40
1 82
What is 14 x 13?
What are the advantages of
teaching the “standard algorithm”?
What are the disadvantages of
teaching the “standard algorithm”?
What is 14 x 13?
Let’s look at the
“partial products”
method…
What is 14 x 13?
(10 + 4)
What is 14 x 13?
(10 + 4) x
What is 14 x 13?
(10 + 4) x (10 + 3) =
What is 14 x 13?
(10 + 4) x (10 + 3) =
100
What is 14 x 13?
(10 + 4) x (10 + 3) =
100 + 30
What is 14 x 13?
(10 + 4) x (10 + 3) =
100 + 30 + 40
What is 14 x 13?
(10 + 4) x (10 + 3) =
100 + 30 + 40 + 12 =
What is 14 x 13?
(10 + 4) x (10 + 3) =
100 + 30 + 40 + 12 =
182
What is 14 x 13?
What are the advantages of teaching
the “partial products” method?
What are the disadvantages of teaching
the “partial products” method?
What is 9 x 8…
…using “partial products”?
What is 9 x 8…
…using “partial products”?
(10 - 1)
What is 9 x 8…
…using “partial products”?
(10 - 1) x
What is 9 x 8…
…using “partial products”?
(10 - 1) x (10 - 2) =
What is 9 x 8…
…using “partial products”?
(10 - 1) x (10 - 2) =
100
What is 9 x 8…
…using “partial products”?
(10 - 1) x (10 - 2) =
100 - 20
What is 9 x 8…
…using “partial products”?
(10 - 1) x (10 - 2) =
100 - 20 - 10
What is 9 x 8…
…using “partial products”?
(10 - 1) x (10 - 2) =
100 - 20 - 10 + 2 =
What is 9 x 8…
…using “partial products”?
(10 - 1) x (10 - 2) =
100 - 20 - 10 + 2 =
72
At this point you
may be thinking…
Dave, that’s kind of…
Dave, that’s kind of…
brilliant
Dave, that’s kind of…
brilliant
semi-interesting
Dave, that’s kind of…
brilliant
semi-interesting
useless
Dave, that’s kind of…
brilliant
semi-interesting
useless
and/or
Dave, that’s kind of…
brilliant
semi-interesting
useless
and/or
soooo NOT “Hands-On”…
Dave, that’s kind of…
brilliant
semi-interesting
useless
and/or
soooo NOT “Hands-On”…
...I’m rating this session a “0”!
Wait! Let’s go back to
14 x 13…
Wait! Let’s go back to
14 x 13…
For now, let’s make each of
your wrists worth 10 and
your fingers worth 1 each...
Too bad that this “hand
multiplication” trick only
works for 14 x 13.
Too bad that this “hand
multiplication” trick only
works for 14 x 13.
Just kidding!
What is
15 x 14?
What is
16 x 15?
What is
19 x 19?
What is
21 x 21?
What is
99 x 98?
What is
21 x 12?
What is
31 x 22?
What is
101 x 11?
At this point you
may be thinking…
Dave, that’s kind of…
Dave, that’s kind of…
genius
Dave, that’s kind of…
genius
semi-genius
Dave, that’s kind of…
genius
semi-genius
still useless
Dave, that’s kind of…
genius
semi-genius
still useless
and/or
Dave, that’s kind of…
genius
semi-genius
still useless
and/or
irrelevant…I teach Algebra…
Dave, that’s kind of…
genius
semi-genius
still useless
and/or
irrelevant…I teach Algebra…
...I’m rating this session a “0”!
Wait! Does…
(x + 4)(x + 3)
pique your interest?
Wait! Does…
(x + 4)(x + 3)
pique your interest?
I thought so…
Wait! Does…
(x + 4)(x + 3)
pique your interest?
This time, let’s make each
of your wrists worth x and
your fingers worth 1 each...
What is
(x + 5)(x + 2)?
What is
(x + 3)(x - 2)?
What is
(x - 4)(x - 4)?
What is
(x + 5)(x - 5)?
Now let’s FACTOR…
Now let’s FACTOR…
2
x + 5x + 4
Now let’s FACTOR…
2
x + 6x + 9
Now let’s FACTOR…
2
x - 6x + 9
Now let’s FACTOR…
2
x - 2x - 8
Now let’s FACTOR…
2
3
x +x +x+1
At this point you
may be thinking…
Dave, the session has been…
Dave, the session has been…
life-changing
Dave, the session has been…
life-changing
worth the 90 minutes of
my life I’ll never get back
Dave, the session has been…
life-changing
worth the 90 minutes of
my life I’ll never get back
bearable…I’m still here!
Dave, the session has been…
life-changing
worth the 90 minutes of
my life I’ll never get back
bearable…I’m still here!
and/or
Dave, the session has been…
life-changing
worth the 90 minutes of
my life I’ll never get back
bearable…I’m still here!
and/or
OK, OK…
Dave, the session has been…
life-changing
worth the 90 minutes of
my life I’ll never get back
bearable…I’m still here!
and/or
OK, OK…
I’m rating this session a “333”!