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#3459. Mathematical Properties

, level: all
Posted Thu Apr 28 19:16:21 PDT 2005 by Gessica Childress (glchildress@rmwc.edu).
Randolph-Macon Woman's College, Lynchburg, Virginia
Activity Time: 30 Minutes

Subject: Mathematical Properties

SOL 7.3 -- TSW identify and apply the following properties of operations with real numbers: a.) commutative and associative properties of addition; b.) the distributive property; c.) the additive and multiplicative inverse property; d.) the additive and multiplicative inverse properties; and e.) the multiplicative property of zero.

Rationale: The properties exhibited on SOL 7.3 help students to understand the mathematical relationships involving real numbers.


Day 1

Objective: TSW use problem solving, mathematical communication, mathematical reasoning, connections, and representation to: a.) Identify the real number equation that represents the associative and commutative properties with real numbers, when given several real number equations; b.) test the validity of the associative and commutative properties by using examples with real numbers; and c.) identify the property of operations with real numbers that is illustrated by a real number equation.

Materials:
1. Cards labeled: walker, car rider, bus rider (one set per student)
2. Sentence strips
3. Transparencies
4. Overhead
5. Overhead and transparencies can be replaced with chalkboard
6. Students' journals

Technology: Overhead projector

Procedure:
1. When the students come in there will be 3 cards on each desk.
2. Each card will have one word written on it: walker, car rider, or bus rider.
3. Once the students have all been seated, ask them to hold up which card tells how they got to school this morning.
4. Ask the students to hold up a card saying how they will be going home this afternoon.
5. Brainstorm with the students through class discussion to come up with words that would describe traveling to and from school.
6. Introduce and establish the term commute.
7. Relate the term commute to commutative.
8. Have the students read an introduction to the properties. ("Properties of Real Numbers" Beginning Algebra, p. 39. Readability: 7th Grade)
9. Place a transparency on the overhead with 2 groups of 2 problems written down.
10. Ask the students if they see any numbers that are commuting.
11. Have a class discussion regarding the commuting of numbers and establish the commutative property.
12. Reinforce that the numbers can be put in different orders, but that the equations are still equal.
13. Write the commutative property and at least two examples on a sentence strip and display in the front of the classroom.
14. Next we will discuss the associative property.
15. Ask students what they think of when they think of the word associate.
16. As the students brainstorm with you, write their responses on the board.
17. Place the second transparency on the overhead and discuss how the numbers are "associating."
18. Display a second sentence strip beneath the first one with "Associative Property" and two examples written.
19. Discuss with the class some of the similarities and differences of the two properties.
20. Once both properties have been established give the students approximately 3 minutes, to come up with three examples of each property in their notebooks.
21. Call on a few students to share their examples.
22. This opportunity will be taken to find the source of any confusion and further explain.
Closure: Select students to define associative property and commutative and give examples. Then allow the students 3 minutes to do a Quick Write in their journals - What did they learn? What do they feel they understand well? What do they still not understand? What did they like about today's lesson? What did they dislike about today's lesson?

Assessment:
Informal: Assigned 6 problems involving both properties. Each student will work independently. When they have finished they will work with the person sitting next to them comparing answers and working out any questions they have together. I will go around the room helping with any additional questions. I will collect each students work to make sure they all have a sufficient understanding of the material.