welcome to: a “hands-on” approach to the distributive property presenter: dave chamberlain math...

Welcome to:A “Hands-On” Approach to the Distributive Property

Presenter:Dave Chamberlain

Math Curriculum Specialist, Capistrano USDPast President, Orange County Math Council

Creator, TEAM UP! For Common Core Learning

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 x^2 + 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.


Content standards which include the word “distributive”:3.OA.5 3.MD.7c

Grade 4 Critical Area 1 - They apply their understanding of models for multiplication (equal-sized groups, arrays, area models),place value, and properties of operations, in particular the

distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of

multi-digit whole numbers. 6.NS.4 6.EE.3

7.NS.2.a8.NS.7b

N-CN-2 N-VM-9

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

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

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”?


(10 - 1)


(10 - 1) x


(10 - 1) x (10 - 2) =


(10 - 1) x (10 - 2) = 100


(10 - 1) x (10 - 2) = 100 - 20


(10 - 1) x (10 - 2) = 100 - 20 - 10


(10 - 1) x (10 - 2) = 100 - 20 - 10 + 2 =


(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


semi-interesting


semi-interestinguseless


semi-interestinguselessand/or



soooo NOT “Hands-On”…



soooo NOT “Hands-On”…...I’m looking through my program

now for another session.

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 is11 x 13?

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?

Dave, that’s kind of…

Dave, that’s kind of…genius


semi-genius


semi-geniusstill useless



and/or



and/ora cool bar trick, but how would this

help a kid in, oh I don’t know, an Algebra 1 class?

Well, does…(x + 4)(x + 3)

pique your interest?


pique your interest?

I thought so…


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 + 4

2

Now let’s FACTOR…x + 6x + 9

2

Now let’s FACTOR…x - 6x + 9

2

Now let’s FACTOR…x - 2x - 8

2

Now let’s FACTOR…x + x + x + 1

23

Dave, the session has been…

Dave, the session has been…life-changing


worth the 60 minutes ofmy life I’ll never get back


bearable…I’m still here!



bearable…I’m still here!and/or



bearable…I’m still here!and/or

OK, OK…I’m going to update my Facebook page when I get home!


welcome to: a “hands-on” approach to the distributive property presenter: dave chamberlain math...

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