welcome to: a “hands-on” approach to the distributive property (session 538) presenter: dave...
DESCRIPTION
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 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 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.TRANSCRIPT
Welcome to:A “Hands-On” Approach to the Distributive Property
(Session 538)
Presenter: Dave [email protected]
Math Curriculum Specialist, Capistrano USDPresident, Orange County Math Council
When/How is theDistributive Property Important?
When/How is theDistributive 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?
14x 13
What is 14 x 13?
14x 13
What is 14 x 13?
14x 13
2
What is 14 x 13?
14x 13
2
1
What is 14 x 13?
14x 13
2
1
4
What is 14 x 13?
14x 13
2
1
40
What is 14 x 13?
14x 13
2
1
4x
What is 14 x 13?
14x 13
2
1
40
What is 14 x 13?
14x 13
2
1
404
What is 14 x 13?
14x 13
2
1
4041
What is 14 x 13?
14x 13
2
1
4041+
What is 14 x 13?
14x 13
2
1
4041+
What is 14 x 13?
14x 13
2
1
40412
+
What is 14 x 13?
14x 13
2
1
404128
+
What is 14 x 13?
14x 13
2
1
4041281
+
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 youmay 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-interestinguseless
Dave, that’s kind of…brilliant
semi-interestinguselessand/or
Dave, that’s kind of…brilliant
semi-interestinguselessand/or
soooo NOT “Hands-On”…
Dave, that’s kind of…brilliant
semi-interestinguselessand/or
soooo NOT “Hands-On”…...I’m rating this session a “0”!
Wait! Let’s go back to14 x 13…
Wait! Let’s go back to14 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 is15 x 14?
What is16 x 15?
What is19 x 19?
What is21 x 21?
What is99 x 98?
What is21 x 12?
What is31 x 22?
What is101 x 11?
At this point youmay 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-geniusstill useless
Dave, that’s kind of…genius
semi-geniusstill useless
and/or
Dave, that’s kind of…genius
semi-geniusstill useless
and/orirrelevant…I teach Algebra…
Dave, that’s kind of…genius
semi-geniusstill useless
and/orirrelevant…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…x + 5x + 42
Now let’s FACTOR…x + 6x + 92
Now let’s FACTOR…x - 6x + 92
Now let’s FACTOR…x - 2x - 82
Now let’s FACTOR…x + x + x + 123
At this point youmay 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 ofmy life I’ll never get back
Dave, the session has been…life-changing
bearable…I’m still here!
worth the 90 minutes ofmy life I’ll never get back
Dave, the session has been…life-changing
bearable…I’m still here!and/or
worth the 90 minutes ofmy life I’ll never get back
Dave, the session has been…life-changing
bearable…I’m still here!and/or
OK, OK…
worth the 90 minutes ofmy life I’ll never get back
Dave, the session has been…life-changing
bearable…I’m still here!and/or
OK, OK…I’m rating this session a “333”!
worth the 90 minutes ofmy life I’ll never get back