1. Connections among Representatives

2. Horses and Birds Horses and Birds
Marie’s family went to Kentucky for their vacation. While in Kentucky, Marie noticed there were many horse farms. To occupy her time while the family was touring the countryside one day, Marie kept a total of the number of legs on the horses and birds in each pasture. At the end of the day, Marie asked her sister Michelle how many horses and how many birds had Marie counted if she counted a total of 284 legs. Michelle was able to quickly calculate the number of horses and the number of birds. Marie asked Michelle how she was able to do this so quickly. Michelle simply stated, “I used patterns and math.” Develop a strategy to determine the number of horses and birds if Marie counted a total of 284 legs.

3. Horses and Birds Each horse has ________ legs
Each bird has ________ legs
h number of legs for horses
b number of legs for birds
What equation can we use to represent the number of legs for more than one horse or bird
H * 4 = B*2=
If we count 54 legs total our equation should be?
4h + 2b = 54 legs

4. Notes
Variable:
a symbol, usually a letter that represents one or more numbers. Any letter may be used as a variable
Mathematical expression:
consists of numbers, variables, and operations
To evaluate a mathematical expression, substitute the given numeric value in for the variable and perform the given operation.

5. Examples The sum of a number and 10 The difference of a number and 21
The quotient of 48 and a number
48/n
The product of 6 and a number 6n
One forth of a number
1/4n

6. Evaluating
Evaluate the variable expression
3x - 5y, if x = 7 and y = 4.
Substitute 7 for x and 4 for y. Put substituted values in parentheses. 3(7) – 5(4)
• Simplify the resulting expression using order of operations.
3(7) – 5(4)
21 – 5(4)
21 – 20
= 1

7. Evaluate the each expression below if
a = 6.2 and b = (− 9).
a. 8a
8(6.2)
= 49.6
b. ab
(6.2) (− 9)
= (−55.8)
c. b(a – 3)
(−9)(6.2 – 3)
= (−28.8)
d. 6b2
6(−9)2
6(81)
= 486

8. Example 1
An electrician charges $45 per hour, plus $50 for the service call. Let x represent the number of hours worked.
Equation
45x + 50

9. Example 2
The number of freshmen is ¼ of the number of total students. Let x represent the number of freshmen and n is the total number of students.
Equation
n * ¼ = x
¼ is also equal to 0.25

10. Example 3
The number of hours, x, worked at $15 an hour is the total pay, y.
Equation
y = 15x

11. Your work! 1. 7(8 + 4) = 2. 6(x – 7) = 3. 3(4x – 5) = 4. 12(4y + 12) =
(8 + 4) =
(x – 7) =
(4x – 5) =
(4y + 12) =
/5(x – 35) =

12. Distributive Property: distributing something as you separate or break it into parts. The distributive property makes numbers easier to work with, you are distributing.
1. 4(y + 9) =
2. 3(x + 4) =
3. 2(x + 3) =
4. 4(y + 12) =
5. 4(n + 5) =
6. 2(2n – 6) =
7. 4(x + 14) =
8. 12(x + 4) =
9. 5(x + 3) =
10. 3(y + 13) =

13. Word Problems 11. The students in Mrs. Lane's class are building
balloon-powered cars for a Mathematics
project. Each student needs a balloon that
costs $0.05, a package of wheels for $1.00,
and a car frame kit for $1.50. Which equation
can be used to find y, the amount in dollars,
spent by all of Mrs. Lane's students, as related
to x, the number of students in Mrs. Lane's
class?
A. y = ($ $ $1.50)
B. y = $2.55x
C. y = $ x
D. y = $3.00x

14. Word Problems
12. Which expression is equivalent to the sum of 3 times a number and 6?
A 3x + 6
B 3(x + 6)
C x(3+6)
D 3 + 6x

15. Word Problem
13. Which of the following represents the algebraic expression 6 less than a number n?
A 6 ÷ n
B 6 – n
C n – 6
D n + 6