Real Numbers and Their Properties

Real Numbers and Their Properties School Counselor: Andrea Rasmussen and Math department chair Date: July 30, 2014 Activity: Real Numbers and their Properties Notes Grade(s): Rising 9th grade students attending Champe Camp ASCA Student Standards: A:A1 Improve Academic Self-concept A:A1.1, A:A1.2, A:A1.3, A:A1.4, A:A1.5 A:A2 Acquire Skills for Improving Learning A:A2.2, A:A2.3, A:A3 Achieve School Success A:A3.2, A:A3.5 A:B1 Improve Learning A:B1.1, A:B1.2, A:B1.3, A:B1.4, A:B1.5, A:B1.7 C:C1 Acquire Knowledge to Achieve Career Goals C:C1.1, C:C1.2, C:C1.3 PS:A2 Acquire Interpersonal Skills PS:A2.6, PS:A2.7 Learning Objective(s): 1. Students familiarize themselves with math terminology and then able to apply terms to specific problems/equations. 2. Students will be able to identify skills and habits that lead to successful high school preparedness, specifically in math. 3. Students recognize how effort and practice positively influence learning and performance. Materials: - handout - pencils - promethean pen and remote - computer Procedure: All students receive a two-page handout that covers math concepts and vocabulary. Initially, students work individually and later in small groups then with the whole class to cement answers and learn material. Students are then given a handout and instruction on how to use a “foldable” for studying. Varied instruction is given that mimics high school math instruction and proves mastery of material. Plan for Evaluation: Process Data: 38 students from the Class of 2018 participated in Champe Camp and subsequent small group lessons throughout the first semester. Perception Data: Students will complete a post-evaluation at the end of the first semester. Outcome Data: 34 of 38 students passed their state math Standard of Learning (SOL) exam at the end of freshman year (twelve of which passed at the Advanced level) and 4 students did not pass. Of those 4 students who did not pass, three scored high enough to qualify for an expedited retake and passed on their second attempt.

Follow Up: Moving forward, students will be equipped with the math skills, study skills, and familiarity with teaching approaches in order to be successful in a high school level math course. These students should also be better prepared to pass their year-end math SOL.

Real Numbers and Their Properties Notes What is a real number?

Properties of Real Numbers: If a = b, then b = a

a+0=a 0+a=a

If a = b, then

a 0=0

If a = b, and b = c, then a = c

If a = b, then a + c = b + c

a(b + c) = a b + a c

a=a

a+b=b+a

a + (−a) = 0

(a + b) + c = a + (b + c)

(a b)c = a (b c)

a 1=a

If a = b, then

1 a=a

, where c ≠ 0

If a = b, then a − c = b − c

Real Numbers and Their Properties Practice Name the property shown by each statement using the word bank provided: Word Bank: Reflexive + Inverse

Commutative

Distributive

x Identity

Associative

x Inverse

+ Identity

Transitive

Symmetric

Property of Zero

1. 4 + (9 + 6) = (4 + 9) + 6

2. (7 • 3) • 5 = 7 • (3 • 5)

3. (3 + y ) + 0 = 3 + y

4. x •1 = x

5. (2 + x) • 0 = 0

6. If a = b, then b = a

7. 14 xy = 14 yx

8. x + 12 = 12 + x

9. 2( x + 3) = 2 x + 6

10. 0 = −14 + 14

11.

1 •3 =1 3

12. (2 • 5) • 1 = 2 • 5

13. 5 = 5

14. 7 + −7 = 0

15. 4 x + 8 = 2(2 x + 4)

16. If x + 3 = 5 and 5 = x – 7, then x + 3 = x -7 Fill in the blanks: 17. What is the special number that indicates the additive identity?

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18. What is the special number that indicates the multiplicative identity?

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19. When using the multiplicative inverse, we multiply by the

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20. When using the additive inverse, we add the

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