Transcript Distributive Property PPx

21st Century Lessons
Distributive Property
Primary Lesson Designers:
Kristie Conners
Sean Moran
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This project is funded by the
American Federation of Teachers.
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21st Century Lessons – Teacher Preparation
Please do the following as you prepare to deliver this lesson:
•
Spend AT LEAST 30 minutes studying the
Lesson Overview, Teacher Notes on each
slide, and accompanying worksheets.
•
Set up your projector and test this PowerPoint file to make
sure all animations, media, etc. work properly.
•
Feel free to customize this file to match the language and
routines in your classroom.
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Lesson Overview (1 of 4)
Lesson Objective
.
Lesson Description
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Students will be able to apply the distributive property to write
equivalent expressions.
Students will be able explain how to use the distributive property
verbally and in writing.
This lesson is the second lesson for the standard 6.EE.3. The
Distributive Property is a crucial concept in mathematics. The warm
up in the lesson is a multiplication problem where the Distributive
Property was used. This will trigger students to start to think about
multiplication this way to prep them for the Distributive Property.
The Launch uses a basketball court to introduce finding the area,
which can be solved using two methods, one being the Distributive
Property. Students then continue in their groups using divided
rectangles to find their areas. Again, students will be asked to use
both methods to later connect them as being equivalent; one method
being the Distributive Property. The Summary part of the lesson is
where students will be given the definition and explanation of the
Distributive Property. Students are asked to finish the activity with
challenging problems. The lesson finishes with an Exit Slip that
contains three terms inside the parentheses. This was designed to
push students to think about the process of the Distributive Property.
Lesson Overview (2 of 4)
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Lesson Vocabulary
Distributive Property: an mathematical property which helps to
multiply a single term and two or more terms inside
parenthesis.
Expression: numbers and symbols grouped together that show
the value of something.
Commutative Property: changing the order of numbers does
not change the sum or product.
Materials
Copies of the class work assignment, Exit Slip, and homework.
Common Core
State Standard
6.EE.3 Apply the properties of operations to generate
equivalent expressions. For example, apply the distributive
property to the expression 3 (2 + x) to produce the equivalent
expression 6 + 3x; apply the distributive property to the
expression 24x + 18y to produce the equivalent expression
6(4x + 3y); apply properties of operations to y + y + y to produce
the equivalent expression 3y.
Lesson Overview (3 of 4)
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Scaffolding
This lesson is designed around using area models as supposed to an
algebraic way to show Distributive Property. Therefore, this lesson
tailors to ELL students and students with learning disabilities providing
visuals throughout the lesson to access this relatively abstract
algebraic concept.
Enrichment
In the Activity portion of this lesson, there is an opportunity provided
for students who seem to have grasped the Distributive Property
relatively quickly. These questions challenge students a bit more by
writing equivalent expressions using Distributive Property.
Online Resources for
Absent Students
Tutorial:
http://learnzillion.com/lessons/372-apply-the-distributive-propertyusing-area-models
http://flash.learning.com/ahamath-demo/The-Distributive-PropertyLesson/SCORMDriver/indexAPI.html
http://coolmath.com/prealgebra/06-properties/05-propertiesdistributive-01.htm
Practice:
http://www.ixl.com/math/grade-6/distributive-property
Lesson Overview (4 of 4)
Before and After
Expressions and Equations is a crucial topic for students to become
successful in a future Algebra course. This content standard concepts and
processes are a critical part in students’ career in mathematics. Thus far in
this unit, students have been exposed to writing, reading and evaluating
numerical and algebraic expressions. The lessons for this standard continue
working on those topics, but taking their understanding of expressions to
the next level. The first lesson for this standard deals with the properties of
mathematics, where this lesson strictly focuses on the Distributive Property.
It is advised that both lessons be used consecutively. With a strong
background of the properties and the Distributive Property, students will be
successful in continuing their wok in this standard; where students are
expected to prove equivalent expressions and then solve equations.
Topic Background The link below is a quick reference to the properties in mathematics. This
link is a also a helpful resource for students.
http://mathforum.org/dr.math/faq/faq.property.glossary.html
The link below is an article, “I See It: The Power of Visualization”. This
supports the basic idea behind the lesson of using the idea of visuals as
means to the lesson.
http://www.mathrecap.com/category/conferences/nctm/page/3/
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Warm Up
Objective: Students will be able to apply the distributive property to
write equivalent expressions.
Language Objective: Students will be able explain how to use the
distributive property verbally and in writing.
Ronisha and Kalyn are arguing whether the answer
to 8(27) can be found by doing the following work.
8 20  160
8 7  56
216
Do you think this is correct? Explain.
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
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Agenda
Agenda:
Objective: Students will be able to apply the distributive property to
write equivalent expressions.
Language Objective: Students will be able explain how to use the
distributive property verbally and in writing.
1) Warm Up
Individual
4 minutes
2) Launch
13 minutes
3) Explore
High School Vs. College B-ballWhole Class, Pairs
Splitting Athletic Fields- Groups
4) Summary
The Distributive Property- Whole Class
10 minutes
5) Explore
Splitting Athletic Fields– Groups
12 minutes
6) Assessment Exit Slip- Individual
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17 minutes
4 minutes
Launch- High School Vs. College B-ball
A standard size high school basketball court is 84ft
long and 50ft wide in the shape of a rectangle.
84 ft
50 ft
To find the area of the court you can
use the formula of A=l  w
A = 84 ft  50ft
2
ft
A = 4200
Agenda
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Launch- High School Vs. College B-ball
Did you know that a college basketball court is
usually 10ft longer than a high school basketball
court?
84 ft
10 ft
50 ft
College
Basketball Court
Can you think of a method to find the
area of the college basketball court?
Agenda
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Launch- High School Vs. College B-ball
84 ft
10 ft
50 ft
Why parenthesis?
Method 1
50(84+10)
84+10
94  50
2
ft
A = 4700
Can you think of a
method to find the area
of the college basketball
court?
Method 2
84  50 + 10  50
4200 + 500
2
ft
A = 4700
What can we say about these two expressions?

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Agenda
Explore- Splitting Athletic Fields
Ambria lives in a neighborhood with three rectangular fields
that all have the same area. The fields are split into different
sections for different sports.
20 yds
50 yds
30 yds
120 yds
120 yds
50 yds
80 yds
40 yds
Agenda
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Explore- Splitting Athletic Fields
1. Find the area of this field near Ambria’s house.
50 yds
120 yds
600yds
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2. This field is divided into two parts.
20 yds
30 yds
120 
yds
a. Find the area of each part and record your steps as you go.
Prove the area is the same as in the first field?
20  120=240
240yds + 360yds 2 600yds 2
2
30  120=360
Agenda
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Explore- Splitting Athletic Fields
20 yds
20  120
20  120=240
30 yds
30  120
120 yds
30  120=360
b. Write one numerical expression that will calculate the
area based on the work you did in part a.
20 120  30 120
c. Find a different way to calculate the area of the entire field
and write it as one numerical expression.
120(20  30)

20 yds
+
30 yds
120 yds
Agenda
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Explore- Splitting Athletic Fields
3. The field is divided into two parts.
50 yds
80 yds 40 yds
a. Write 2 different numerical
expressions that will calculate
the area of the entire field.
50(80  40)
50 80  50 40
4. The field below is split into two parts but are missing the dimensions.
50
______
100 20
_________

______
a. Fill in the missing dimensions of
the rectangular field whose area can
be calculated using the expression.
50(100  20)
b. Write a different numerical expression to calculate the area of the field.
50 100  50 20
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Agenda
Summary- The Distributive Property
20 yds
50 yds
30 yds
80 yds
40 yds
120 yds
Let’s look at the two equivalent ways of finding the area and
connect it to an important property in math.
The Distributive Property
Agenda
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Summary- The Distributive Property
The Distributive Property
50 yds
80 yds 40 yds
50 (80  40)  50 80  50 40

50
80 120+ 40
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 
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50
80
40
Agenda
Summary- The Distributive Property
The Distributive Property
The Distributive Property is a property in mathematics which
helps to multiply a single term and two or more terms inside
parenthesis.
Check it out!
Lets use the distributive property to write an equal expression.
2(3  5) 
2 3  2 5
2
3 + 5
Examples
8(3 x)  8 3  8 x
a(3  5)  a 3  a 5
 
Formal
definition
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Agenda
Explore- Splitting Athletic Fields
5. An algebraic expression to represent the area of
the rectangle below is 8 x  8x .
8
x
a. Write two
 different expressions to represent the area
of each rectangle below.
5
2
3
x
x(5  2)
x 5  x 2
5x  2x
x
4
3(x  4)
3x  3 4
3x 12
Agenda
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Explore- Splitting Athletic Fields
6. Use the distributive property to re-write each expression.
You may want to draw a rectangle to represent the area.
a) 10( a + 7) = 10
___________
a 10 7 b) 7(x + 3)=________________
7 x  7 3
c) x( 3 + 10)= ___________
x 3  x 10 d) a(10 + 9)= _______________
a 10  a 9




e) -2(x + 10)=_______
 2  x  2 10 f)
3x(x + 10)= 3x
______________
x  3x 10

Agenda
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Assessment- Exit Slip
Who correctly used the distributive property to
write an equivalent expression?
Provide evidence to support your answer.
Riley
7(4 10  y)  7 4  7 10  y
Michael
7(4 10  y)  7 4  7 10  7y
Michael
 did because he correctly distributed
the 7 to all terms inside the parenthesis.
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Agenda
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