1. Math 7A: Monday, Sept. 12, 2011 Test Alert: Unit 1 Test on Friday!
Homework:
Holt “Ready to Go On?” p. 90
POW due Friday.
Warm-up: “The Error Detective”
Work with a partner to try to determine what errors each person made.
Both people need to write down the answers.

2. Math 7A Agenda
Essential Question: What models for positive and negative numbers would help in showing the relationships in a problem situation?
GPS: M7N1. Students will understand the meaning of positive and negative rational numbers and use them in computation.
“Sums & Products” puzzle lesson.

3. Math 7: Monday, September 12
Homework:
1-1 Practice B w.s.
POW due Friday.
Warm Up
Evaluate.
1. 21  2(3)
Test Alert: Unit 1 Test will be on Wednesday, September 21 15
 9 31
3. 2(9) + (3) 21
4. 6(1.4) + 12
20.4
5. 7(2.9)  5
15.3
Course 3

4. Variables and Expressions
Course 3
1-1
Variables and Expressions
Essential Question: What properties and conventions do I need to understand in order to simplify and evaluate algebraic expressions?
GPS: M7A1.b: Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate.
Learn to evaluate algebraic expressions.

5. Variables and Expressions
Course 3
1-1
Variables and Expressions
Vocabulary
variable
coefficient
algebraic expression
constant
evaluate
substitute

6. Variables and Expressions
Course 3
1-1
Variables and Expressions
A variable is a letter that represents a value that can change or vary.
The coefficient is the number multiplied by the variable.
Coefficient
Variable

7. Variables and Expressions
Course 3
1-1
Variables and Expressions
An algebraic expression has one or more variables.
In the algebraic expression x + 6, 6 is a constant because it does not change.
To evaluate an algebraic expression, substitute a given number for the variable, and find the value of the resulting numerical expression.

8. Variables and Expressions
Course 3
1-1
Variables and Expressions
Additional Examples 1A: Evaluating Algebraic Expressions with One Variable
Evaluate each expression for the given value of the variable.
x – 5 for x = 12
12 – 5
Substitute 12 for x. 7
Subtract.

9. Variables and Expressions
Course 3
1-1
Variables and Expressions
Order of Operations
PEMDAS:
1. Parentheses
2. Exponents
3. Multiply and Divide from left to right.
4. Add and Subtract from left to right.
Remember!

10. Variables and Expressions
Course 3
1-1
Variables and Expressions
Additional Examples 1B: Evaluating Algebraic Expressions with One Variable
Evaluate each expression for the given value of the variable.
2y + 1 for y = 4
2(4) + 1
Substitute 4 for y.
8 + 1
Multiply. 9
Add.

11. Variables and Expressions
Course 3
1-1
Variables and Expressions
Additional Example 1C: Evaluating Algebraic Expressions with One Variable
Evaluate the expression for the given values of the variable.
6(n + 2) – 4 for n = 5, 6, 7 5 6 7
n Substitute Parentheses Multiply Subtract
6(5 + 2) – 4
6(7) – 4
42 – 4 38
6(6 + 2) – 4
6(8) – 4
48 – 4 44
6(7 + 2) – 4
6(9) – 4
54 – 4 50

12. Variables and Expressions
Course 3
1-1
Variables and Expressions
Check It Out: Examples 1
Evaluate each expression for the given value of the variable.
A. x + 5 for x = 3
3 + 5
Substitute 3 for x. 8
Add.
B. 4c + 1 for c = 11
4(11) + 1
Substitute 11 for c.
44 + 1
Multiply. 45
Add.

13. Variables and Expressions
Course 3
1-1
Variables and Expressions
Check It Out: Example 1
Evaluate the expression for the given values of the variable.
C. 5(n + 3) – 2 for n = 3, 4, 5 3 4 5
n Substitute Parentheses Multiply Subtract
5(3 + 3) – 2
5(6) – 2
30 – 2 28
5(4 + 3) – 2
5(7) – 2
35 – 2 33
5(5 + 3) – 2
5(8) – 2
40 – 2 38

14. Variables and Expressions
Course 3
1-1
Variables and Expressions
Additional Example 2: Evaluating Algebraic Expressions with Two Variables
Evaluate each expression for the given values of the variables.
A. 4x + 3y for x = 2 and y = 1
4(2) + 3(1)
Substitute 2 for x and 1 for y.
8 + 3
Multiply. 11
Add.
B. 9r – 2p for r = 3 and p = 5
9(3) – 2(5)
Substitute 3 for r and 5 for p.
27 – 10
Multiply. 17
Subtract.

15. Variables and Expressions
Course 3
1-1
Variables and Expressions
Check It Out: Example 2
Evaluate each expression for the given values of the variables.
A. 3x + 2y for x = 3 and y = 4
3(3) + 2(4)
Substitute 3 for x and 4 for y.
9 + 8
Multiply. 17
Add.
B. 8q – 3r for q = 2 and r = 2
8(2) – 3(2)
Substitute 2 for q and 2 for r.
16 – 6
Multiply. 10
Subtract.

16. Variables and Expressions
Course 3
1-1
Variables and Expressions
Additional Example 3A: Physical Science Application
Use the expression 1.8c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit.
Boiling point of water at sea level: 100°C
1.8c + 32
1.8(100) + 32
Substitute 100 for c.
Multiply.
212
Add.
100°C = 212°F
Water boils at 212°F.

17. Variables and Expressions
Course 3
1-1
Variables and Expressions
Additional Example 3B: Physical Science Application
Boiling point of water at an altitude of t meters: 85°C
1.8c + 32
1.8(85) + 32
Substitute 85 for c.
Multiply.
185
Add.
85°C = 185°F
Water boils at 185°F at 4400 m.

18. Variables and Expressions
Course 3
1-1
Variables and Expressions
Check It Out: Example 3A
Convert the temperature from degrees Celsius to degrees Fahrenheit.
Europe’s highest recorded temperature (Seville, Spain): 50°C
1.8c + 32
1.8(50) + 32
Substitute 50 for c.
Multiply.
122
Add.
50°C = 122°F
The highest recorded temperature in Europe is 122°F.

19. Variables and Expressions
Course 3
1-1
Variables and Expressions
Check It Out: Example 3B
Use the expression 1.8c + 32 to convert each boiling point temperature from degrees Celsius to degrees Fahrenheit.
10°C
1.8c + 32
1.8(10) + 32
Substitute 10 for c.
Multiply. 50
Add.
10°C = 50°F

20. Variables and Expressions
Course 3
1-1
Variables and Expressions
Lesson Quiz
Evaluate each expression for the given values of the variables.
1. 6x + 9 for x = 3
2. x + 14 for x = 8
3. 4x + 3y for x = 2, y = 3
x – 2.9y for x = 19, y = 6
5. If n is the amount of money in a savings account, then the expression n n can be used to find the amount in the account after it has earned interest for one year. Find the total in the account after one year if $500 is the initial amount. 27 22 17 13
$515

21. Variables and Expressions
Course 3
1-1
Variables and Expressions
Assignment:
P. 8 (11-47 odd)
1-1 Practice A w.s.