Where We’ve Been……. Properties, Part I…….. If I say “order,” you say……… If I say...
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Where We’ve Been……. Properties, Part I…….. If I say “order,” you say……… If I say “grouping,” you say……… If I say “identity,” you say……… If I keep saying “properties,” you are probably thinking ……. commutative associative Value stays the same
Where We’ve Been……. Properties, Part I…….. If I say “order,” you say……… If I say “grouping,” you say……… If I say “identity,” you say……… If I
Where Weve Been. Properties, Part I.. If I say order, you say
If I say grouping, you say If I say identity, you say If I keep
saying properties, you are probably thinking . commutative
associative Value stays the same
Slide 3
Where We Are Going. Today, we are going to investigate one of
the most important properties you will use this year and in future
classes. Distributive Property Algebra Just listen. Associative
PropertiesCommutative Properties Identity Properties Order of
Operations Translating Expressions
Slide 4
The Distributive Property 2.4 p. 40 The Big Dog of Properties
!!!
Slide 5
Naming What You Know Once again, you already use this property.
Lets say you bought 23 CDs for $6.00 each. $6 each Is there a way
you could mentally rearrange these values to find your total
without a pencil and paper? Notes.
Slide 6
Many of you would mentally multiply the $6 by 20, multiply the
$6 by 3, and add the products. 6(20 + 3) $6 each Lets try this
mentally. 6(20) 120 + 6(3) 18 = 138 If you have ever tried this
mental math, you have used the distributive property!!
Slide 7
What Is Our Objective? Use the distributive property to rewrite
and simplify multiplication problems What property will we use?
What will we do with this property? Distributive Property We will
simplify multiplication problems with this property! Notes.
Slide 8
To Your Notes Vocabulary: This is given in your notes The
Distributive Property states that multiplying a sum (or difference)
by a number gives the same result as multiplying each number in the
sum (or difference) by the number and adding (or subtracting) the
products. Now lets use real words to understand the official
definition. Just listen.
Slide 9
What does this mean? Lets take a basic multiplication problem:
6 x 23 We will rewrite 23 as an addition problem. 6 x (20 + 3) Now
we will multiply the 6 by EACH of the values that add up to 23. 6 x
20 + 6 x 3 120 + 18 138
Slide 10
What it looks like. Algebraically, the distributive property is
defined with variables. a(b + c) = a(b) + a(c) or a(b - c) = a(b)
a(c) Think about our CD example. In expanded form, how would we
write 23? 20 + 3 Now, lets use our price of 6 6(20 + 3) = 6(20) +
6(3) = 120 + 18 = 138 Notes.
Slide 11
Guided Practice: 5 x 27 Lets take the larger factor and write
it in expanded form. 5 (20 + 7) Remember, no sign means to
multiply! Lets distribute the 5. It is the factor used on both the
20 and the 7. (5 x 20)+(5 x 7) = (100) + (35) = 135
Slide 12
4 x 28 Take the larger factor and write it in expanded form. 4
(20 + 8) Lets distribute the 4. It is the value used on both the 20
and the 8. (4 x 20)+(4 x 8) = (80) + (32) =112 7 x 108 =7 (100 + 8
) (7 x 100) + (7 x 8) =700 + 56 = 756
Slide 13
What Is Our Objective? Use the distributive property to rewrite
and simplify multiplication problems What property will we use?
What will we do with this property? Distributive Property We will
simplify multiplication problems with this property!
Slide 14
Small Group Work With your partners, use the pattern we started
in your notes to simplify these examples using the distributive
property. First rewrite the problem, breaking up the larger value.
Next, show how the single multiplier is distributed to both parts
of the expanded number. WE ARE ONLY BREAKING UP THE LARGER VALUE
AND DISTRIBUTING THE SINGLE-MULTIPLIER! After completing the first
four problems, move on to the next three. Try to find a value
(evaluate) the expression after you rewrite it! I will check as you
work to make sure you are progressing accurately. You will have
about 10 minutes.
Application FoodCost Organic Chili$6.00 Chicken Tacos$4.00
Fruit Salad$5.00 Organic Salad$5.00 Veggie Plate$6.00 Big Group
Menu Discuss with your group.. The 6 th graders ordered from the
Big Group Menu. They ordered 22 organic chilis and 8 veggie plates.
Create a problem using the distributive property to represent this
situation.
Slide 18
Take a moment to reread your definition of the distributive
property. Did we leave something out?????? We rewrote all problems
as addition. Lets look at two problems and change them to
subtraction.
Slide 19
Our first problem in the Guided Practice was 5 x 27 Could we
use a subtraction problem to create a value of 27???? 30 3 = 27 5 x
27 = 5 ( )30 - 3 5(30)- 5(3) 150 - 15 = 135
Slide 20
Could we use a subtraction problem to create a value of
8(78)???? 80 2 = 78 8 x 78 = 8 ( )80 - 2 8(80)- 8(2) 640 - 16 =
624
Slide 21
Think Critically Look at the expressions represented by the
properties we have studied.. 14x 3 = 3 x 14 14 + 4 = 3 + 14 (4 x 5)
x 12 = 4 x (5 x 12) (4 + 5) + 12 = 4 + (5 + 12) 12 X 6 = (6 x 10) +
(6 x 2) What is the one distinct difference that separates the
distributive property from the commutative and associative
properties?
Slide 22
Lets Summarize What was the goal of our lesson? Have we
accomplished our lessons objective?
Slide 23
Distributive Property Extension You can apply the Distributive
Property to unknown values (models). = 1 = x You are looking at a
model that represents 2x + 5 that is written three times. Instead
of writing 2x + 5 + 2x + 5 + 2x + 5, we could write 3(2x + 5) We
have to use the distributive property to pull the values out of the
parentheses 3(2x) + 3(5) We use the associative property to
multiply 3(2)x = 6x and we multiply 3(5). 6x + 15 represents our
simplified value. We can do no more.
Slide 24
( + ) 3 2x 5 6x + 15 Use your imagination! What just happened
here? (3 2x) + ( 3 5 ) = 6x + 15
Slide 25
Slide 26
What is our common factor? Which number is used twice in
multiplication? What do we have left?
Slide 27
You can apply the Distributive Property to unknown values
(models). = 1 = x What expression represents this model? We have 3x
+ 7 that is written two times. 2(3x + 7) = 2(3)x 6x + 2(7) +
14
Slide 28
Lets add one more value to this process..
Slide 29
What have we done? We have used the distributive property to
solve multiplication problems. We have written problems with
variables using the distributive property.