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South Carolina ETV
1101 George Rogers Boulevard
Columbia, SC 29201-4761
Phone: 803-737-3545

Famous Public Properties (Grades 6-8)

Master Teacher

LuAnn Shealy Graul

Time Allotment

1- 90 minute block

Overview

What are the basic algebraic properties? This lesson gives the students a chance to learn and practice the commutative properties of addition and multiplication, associative properties of addition and multiplication, and the distributive property of multiplication over addition. The lesson will use video clips from Power of Algebra and interactive websites. The lesson will also use the Algebra I, Part I App on the TI-83+SE or TI-84 graphing calculator.

Subject Matter

Mathematics

Learning Objectives

Students will be able to:

• identify and use the commutative properties of addition and multiplication, associative properties of addition and multiplication, and the distributive property of multiplication over addition.

South Carolina Standards

From the South Carolina Curriculum Standards available online at http://www.myscschools.com/offices/cso/

Grades 6–8

Number and Operations

STANDARD II. Understand meanings of operations and how they relate to one another.

EXPECTATION B. Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

6-1. Apply the commutative, associative, and distributive properties to simplify computations with whole numbers, fractions, and decimals.

7-1. Apply the associative, commutative, and distributive properties for operations on

integers, fractions, and decimals.

8-1. Apply the associative, commutative, and distributive properties to simplify expressions.

Media Components

Video

Power of Algebra: “ The Basic Properties” from http://www.streamlinesc.org. This is a video lesson that describes the Commutative Property of Addition and Multiplication, Associative Property of Addition and Multiplication, and the Distributive Property of Multiplication over Addition. The video also contains a real world application in the form of an interview with a structural engineer.

To access this video segment, log on to your account at the StreamlineSC Web page. In the search by keyword box, type Power of Algebra. Download the “The Basic Properties” video clips to your computer desktop and preview them. The segments combined run 15 minutes and 10 seconds.

(Note to Teacher: If you don’t have an account with StreamlineSC, check with your media specialist about signing up for your own account.)

Web Sites

Math Dork: http://www.mathdork.com This website contains 10 free lessons out of 24 lessons listed. Click on the Commutative Property to watch a 13 slide lesson and take a short quiz about the commutative property. The site requires Macromedia Flash Player 7.

AAA Math: http://www.aaamath.com/pro74b-propertiesmult.html and http://www.aaamath.com/B/pro74ax2.htm This website contains a lesson overview, an activity, and three games.

Quia Games: http://www.quia.com/rr/84369.html and http://www.quia.com/cm/58677.html This website contains games about the properties. The first website listed uses a “Who Wants to be a Millionaire?” format to ask questions about the properties and the real number system. The second website has a column match. One column consists of an expression and the second column lists the properties. The object is to match the expression that is an example of the property to the name of the property.

Equipment

• TI-84 or TI-83+SE graphing calculator with Algebra I Part I App loaded. App may be downloaded from www.education.ti.com.
• Computer—one per class
• Data projector—one per class
• TI-83+SE or TI-84 Graphing calculator—one per student

Materials

• Paper and pencil—one per student

Prep for Teachers

• Connect the computer to the data projector. Bookmark the websites listed above.

• Download or bookmark http://www.StreamlineSC.org for the Power of Algebra:The Basic Properties video.

• Make sure each of the graphing calculators has Algebra 1 Part 1 (ALG1PRT1) App loaded.

Introductory Activity

Step 1: CUE the Math Dork website (http://www.mathdork.com) to the commutative property lesson. Say, “You are going to watch a short slide show about the Commutative Property. You may want to take notes on the important concepts presented during the lesson.

Step 2: Click on the Commutative Property. Make sure the volume on the computer is up. Give a Focus for Media Interaction by asking, “On Slide 1, what is the big question the Commutative Property asks?”

Step 3: PLAY Slide 1. Ask for student responses for the big questions. (Correct answer—When you add/subtract/multiply/divide does order make a difference?)

Step 4: Provide a Focus for Media Interaction for slides 2-7: “Does order matter in addition?” Play Slides 2-7. Discuss the answer to the focus for media interaction. (Correct answer—No).

Step 5: Provide a Focus for Media Interaction for slides 8-9: “Does order matter in subtraction?” Play Slides 8-9. Discuss the answer to the focus for media interaction. (Correct answer—Yes).

Step 6: Provide a Focus for Media Interaction for slides 10-11: “Does order matter in multiplication?” Play Slides 10-11. Discuss the answer to the focus for media interaction. (Correct answer—No).

Step 7: Provide a Focus for Media Interaction for slides 12-13: “Does order matter in division?” Play Slides 12-13. Discuss the answer to the focus for media interaction (Correct answer—Yes).

Step 8: Say “This website demonstrates one of the most important properties of algebra—the Commutative Property. During class today, we are going to examine other important properties of algebra. Let’s keep a running list of properties, an example, and what makes the property important so we have a reference sheet.

Ask “What property have we already discussed today?” Have students respond. Copy the responses in a table with the headings of Property, Example, and Why. (Possible responses: First entry should be the Commutative Property of Addition. Example: .75 + .5 = .5 + .75. Why: This property is important since it shows that order does not matter in addition. Next, we should include the Commutative Property of Multiplication. Example: -3 *5 = 5 * -3. Why: This property is important since it shows that order does not matter in multiplication.)

Learning Activities

Step 1: Say “Next, we are going to look at a video clip that discusses another property.” Cue The Power of Algebra—The Basic Properties to the point where Dave (the guy in the gray shirt and pants) says “They say two is company and three’s a crowd because…” This scene occurs immediately after the interview with the structural engineer. The scene begins with a single Dave who then is doubled and finally a third appears while he is talking. Provide a

Focus for Media Interaction by asking “How many numbers can you work with in algebra? What property is being demonstrated?” (Answers: Two and Associative Property of Addition and Multiplication) PLAY the video. STOP the video when Dave says “You can’t do your subtractions and divisions in any order or you’ll be in a mess.” Say “Let’s continue filling in our table. What are the next two properties we’ve seen?” (Associative Property of Addition and Associative Property of Multiplication) Give an example of each. ((1+2)+3=1+(2+3) and (3*4)*5=3*(4*5)) Why are these important? (Associative Property of Addition allows you to regroup addition. Associative Property of Multiplication allows you to regroup multiplication.)

Step 2: Restart the video when Dave says “Well, I’ve commuted to work and associated with my fellow workers, now…” This scene occurs just after the previous stop. Provide a Focus for Media Interaction by asking, “What two operations are discussed? What is the name of the property discussed?” (Answers: Multiplication and addition and Distributive Property of Multiplication over Addition). PLAY the video. STOP the video when Dave says “Once you know the basic properties of the number systems—the commutative, associative, and distributive property, you can rearrange algebraic equations to make them easier to solve.” Say “Let’s finish our table. What property have we just examined?” (Distributive Property of Multiplication over Addition) “What is an example?” (4*(5+6) = 4*5+4*6) “Why is this property important?” (This property allows us to by-pass order of operation rules involving solving inside the parentheses first.)

Culminating Activity

Step 1: Give each student a TI-83+SE or TI-84 with the Algebra I Part I App loaded. Direct the student to the App by pressing the APPS key and scrolling down to ALGIPRTI. Press ENTER. Press ENTER again. Click on Number Sense. Scroll down to Real Numbers. Press ENTER. Scroll down to Activities. Press ENTER. Press the right arrow key once. Press the down arrow key once. Select “What is My Property?” Press ENTER. Use the up and down arrows to select answer choices and press ENTER when the property is correct.

Step 2: Option: Go to http://www.aaamath.com/B/pro74ax2.htm . Click on the Play tab. The games may be played as a whole class or by dividing the class into teams and rotating turns. Also check out http://www.aaamath.com/pro74b-propertiesmult.html . Again, click on the Play tab. Once again, the games may be played as a whole class or by dividing the class into teams and rotating turns.

Step 3: Option: Go to http://www.quia.com/cm/58677.html . Play column match with the properties. Also check out http://www.quia.com/rr/84369.html . Rags to Riches involves more than just properties questions, but most middle school math students should be able to answer the questions.

Cross-Curricular Extensions

Language Arts: Compare the basic properties to basic rules in grammar.

Language Arts: Create a booklet featuring the basic algebraic properties.

Community Connections

• View “People and Numbers” from Power of Algebra--The Basic Properties. This brief video segment shows an interview with a structural engineer and how he uses algebra in his job.