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21 st Century Lessons. Distributive Property. Primary Lesson Designers: Kristie Conners Sean Moran. This project is funded by the American Federation of Teachers. 21 st Century Lessons – Teacher Preparation. Please do the following as you prepare to deliver this lesson:. - PowerPoint PPT Presentation
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21st Century Lessons
Distributive Property
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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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*1st Time Users of 21st Century Lesson:Click HERE for a detailed description of our project.
21st Century Lessons – Teacher Preparation
• 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.
Please do the following as you prepare to deliver this lesson:
• Feel free to customize this file to match the language and routines in your classroom.
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Lesson Objective 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.
Lesson Description 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 (1 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 (2 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-property-using-area-modelshttp://flash.learning.com/ahamath-demo/The-Distributive-Property-Lesson/SCORMDriver/indexAPI.htmlhttp://coolmath.com/prealgebra/06-properties/05-properties-distributive-01.htmPractice:http://www.ixl.com/math/grade-6/distributive-property
Lesson Overview (3 of 4)
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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.htmlThe 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/
Warm UpObjective: Students will be able to apply the distributive property to write equivalent expressions.
Agenda8
Ricardo and Keyla are arguing whether the answer to can be found by doing the following work.
Do you think this is correct? Explain.
8(27)
820
87
160
216
Yes, this method can be used because 27 is still being multiplied by 8. 27 is just split into 20 and 7 first before it is multiplied by 8.
Language Objective: Students will be able explain how to use the distributive property verbally and in writing.
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Agenda:
1) Warm Up
2) Launch
3) Explore 4) Summary
5) Explore
6) Assessment
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Objective: Students will be able to apply the distributive property to write equivalent expressions.
Individual
High School Vs. College B-ball- Whole Class, Pairs
Splitting Athletic Fields– Groups
Exit Slip- Individual
Splitting Athletic Fields- Groups
The Distributive Property- Whole Class
Language Objective: Students will be able explain how to use the distributive property verbally and in writing.
4 minutes
13 minutes
17 minutes
10 minutes
4 minutes
12 minutes
Launch- High School Vs. College B-ball
Agenda10
84 ft
50 ftTo find the area of the court you can use the formula of A=l w
A standard size high school basketball court is 84ft long and 50ft wide in the shape of a rectangle.
A = 84 ft 50ftA = 4200
ft 2
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Agenda
Can you think of a method to find the area of the college basketball court?
Did you know that a college basketball court is usually 10ft longer than a high school basketball court? 84 ft
50 ft
10 ft
College Basketball Court
Launch- High School Vs. College B-ball
1212
Agenda
Can you think of a method to find the area of the college basketball court?
84 ft
50 ft
10 ft
84+1094 50
A = 4700
ft 2 4200
A = 4700
ft 2 500+
+50(84+10)
What can we say about these two expressions?
Why parenthesis?
Launch- High School Vs. College B-ball
84 50 10 50
Method 1 Method 2
Explore- Splitting Athletic Fields
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Agenda
50 yds
120 yds
50 yds
80 yds 40 yds
Allison 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
120 yds
30 yds
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Agenda
50 yds120 yds
20 yds
120 yds30 yds
1. Find the area of this field near Allison’s house.
2. This field is divided into two parts.
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?
22400yds 23600yds+ 26000yds
26000yds
Explore- Splitting Athletic Fields
20 120=2400
30 120=3600
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Agenda
b. Write one numerical expression that will calculate the area based on the work you did in part a.
c. Find a different way to calculate the area of the entire field and write it as one numerical expression.
20 yds
120 yds
30 yds
20120 30120
120(20 30)
Explore- Splitting Athletic Fields
20 120=2400
30 120=3600
20 120
30 120
20 yds
120 yds30 yds+
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Agenda
3. The field is divided into two parts.
40 yds80 yds
50 ydsa. Write 2 different numerical expressions that will calculate the area of the entire field.
4. The field below is split into two parts but are missing the dimensions. 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(80 40)
5080504050
100 20
501005020
Explore- Splitting Athletic Fields
Summary- The Distributive Property
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Agenda
20 yds
120 yds
30 yds50 yds
80 yds 40 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
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Agenda
50
80 40
50805040
The Distributive Property
50
80 40
50
120+
50(80 40)50
80 40
50
80 40
50
Summary- The Distributive Property
50 yds
80 yds 40 yds
6000 400020006000
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Agenda
The Distributive Property
2(35)
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The Distributive Property is a property in mathematics which helps to multiply a single term and two or more terms inside parenthesis.
Lets use the distributive property to write an equal expression.
252
3 5+2
Check it out!
8(3 x)
83
8x
a(3 5) aa 53
Examples
Summary- The Distributive Property
Formal definition
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Agenda
8x
5
x2
3
x 4
a. Write two different expressions to represent the area of each rectangle below.
5. An algebraic expression to represent the area of the rectangle below is .
8x 8x
x(52)
5x 2x
3(x 4)
3x 34
x5 x2
Explore- Splitting Athletic Fields
3x 12
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Agenda
6. Use the distributive property to re-write each expression. You may want to draw a rectangle to represent the area.
Explore- Splitting Athletic Fields
a) 10( a + 7) = ___________
c) x( 3 + 10)= ___________
b) 7(x + 3)=________________
d) a(10 + 9)= _______________
e) -2(x + 10)=_______ f) 3x(x + 10)= ______________
10a107
7x 73
x3 x10
a10 a9
3xx 3x101022 x
Assessment- Exit Slip
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Agenda
Who correctly used the distributive property to write an equivalent expression? Provide evidence to support your answer.
7(4 10 y)
74 710 y
7(4 10 y)
74 710 7y
Riley
Michael
Michael did because he correctly distributed the 7 to all terms inside the parenthesis.
The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons. These lessons are intended to:
• Support an increase in student achievement; • Engage teachers and students; • Align to the National Common Core Standards and the Massachusetts curriculum
frameworks;• Embed best teaching practices, such as differentiated instruction; • Incorporate high-quality multi-media and design (e.g., PowerPoint); • Be delivered by exemplary teachers for videotaping to be used for professional
development and other teacher training activities; • Be available, along with videos and supporting materials, to teachers free of charge via the
Internet. • Serve as the basis of high-quality, teacher-led professional development, including mentoring
between experienced and novice teachers.
21st Century LessonsThe goal…
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Directors:Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues CommitteeTed Chambers - Co-director of 21st Century LessonsTracy Young - Staffing Director of 21st Century LessonsLeslie Ryan Miller - Director of the Boston Public Schools Office of
Teacher Development and AdvancementEmily Berman- Curriculum Director (Social Studies) of 21st Century LessonsCarla Zils – Curriculum Director (Math) of 21st Century LessonsBrian Connor – Technology Coordinator
21st Century LessonsThe people…
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