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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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

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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.

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