Math 7A: Monday, Sept. 12, 2011 Test Alert: Unit 1 Test on Friday! Test Alert: Unit 1 Test on...

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.

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.

Homework: – 1-1 Practice B w.s.– POW due Friday.

Warm UpEvaluate.

1. 21 2(3) 15

31

21

20.4

15.3

Course 3

5. 7(2.9) 5

4. 6(1.4) + 12

3. 2(9) + (3)

2. 4 + 3 9

Math 7: Monday, September 12

Test Alert: Unit 1 Test will be on Wednesday, September 21

Learn to evaluate algebraic 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.

Vocabularyvariablecoefficientalgebraic expressionconstantevaluatesubstitute

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

Course 3

1-1 Variables and Expressions

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.

Course 3

1-1 Variables and Expressions

An algebraic expression has one or more variables.

Evaluate each expression for the given value of the variable.

Additional Examples 1A: Evaluating Algebraic Expressions with One Variable

Substitute 12 for x.

Subtract.

x – 5 for x = 12

12 – 5

Course 3

1-1 Variables and Expressions

7

Course 3

1-1 Variables and Expressions

Order of Operations

PEMDAS: 1. Parentheses 2. Exponents3. Multiply and Divide from left to right.4. Add and Subtract from left to right.

Remember!

Evaluate each expression for the given value of the variable.

Additional Examples 1B: Evaluating Algebraic Expressions with One Variable

Course 3

1-1 Variables and Expressions

Substitute 4 for y.

Multiply.

2y + 1 for y = 4

2(4) + 1

8 + 1

Add.9

Evaluate the expression for the given values of the variable.

Additional Example 1C: Evaluating Algebraic Expressions with One Variable

6(n + 2) – 4 for n = 5, 6, 7

Course 3

1-1 Variables and Expressions

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

Evaluate each expression for the given value of the variable.

Check It Out: Examples 1

Substitute 3 for x.

Add.

A. x + 5 for x = 3

3 + 5

Course 3

1-1 Variables and Expressions

8

Substitute 11 for c.

Multiply.

B. 4c + 1 for c = 11

4(11) + 1

44 + 1

Add.45

Evaluate the expression for the given values of the variable.

Check It Out: Example 1

C. 5(n + 3) – 2 for n = 3, 4, 5

Course 3

1-1 Variables and Expressions

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

Evaluate each expression for the given values of the variables.

Additional Example 2: Evaluating Algebraic Expressions with Two Variables

Substitute 2 for x and 1 for y.

Multiply.

A. 4x + 3y for x = 2 and y = 1

4(2) + 3(1)

Course 3

1-1 Variables and Expressions

8 + 3

Substitute 3 for r and 5 for p.

Multiply.

B. 9r – 2p for r = 3 and p = 5

9(3) – 2(5)

27 – 10

Add.11

Subtract.17

Evaluate each expression for the given values of the variables.

Check It Out: Example 2

Substitute 3 for x and 4 for y.

Multiply.

A. 3x + 2y for x = 3 and y = 4

3(3) + 2(4)

Course 3

1-1 Variables and Expressions

9 + 8

Substitute 2 for q and 2 for r.

Multiply.

B. 8q – 3r for q = 2 and r = 2

8(2) – 3(2)

16 – 6

Add.17

Subtract.10

Use the expression 1.8c + 32 to convert the boiling point temperature from degrees Celsius to degrees Fahrenheit.

Additional Example 3A: Physical Science Application

Course 3

1-1 Variables and Expressions

Substitute 100 for c.

Multiply.

Boiling point of water at sea level: 100°C

1.8(100) + 32

180 + 32

1.8c + 32

Add.212

100°C = 212°F

Water boils at 212°F.

Additional Example 3B: Physical Science Application

Course 3

1-1 Variables and Expressions

Substitute 85 for c.

Multiply.

Boiling point of water at an altitude of 4400 t meters: 85°C

1.8(85) + 32

153 + 32

1.8c + 32

Add.185

85°C = 185°F

Water boils at 185°F at 4400 m.

Convert the temperature from degrees Celsius to degrees Fahrenheit.

Check It Out: Example 3A

Course 3

1-1 Variables and Expressions

Substitute 50 for c.

Multiply.

Europe’s highest recorded temperature (Seville, Spain): 50°C

1.8(50) + 32

90 + 32

1.8c + 32

Add.122

50°C = 122°F

The highest recorded temperature in Europe is 122°F.

Use the expression 1.8c + 32 to convert each boiling point temperature from degrees Celsius to degrees Fahrenheit.

Check It Out: Example 3B

Course 3

1-1 Variables and Expressions

Substitute 10 for c.

Multiply.

10°C

1.8(10) + 32

18 + 32

1.8c + 32

Add.50

10°C = 50°F

Lesson QuizEvaluate 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

4. 1.6x – 2.9y for x = 19, y = 6

5. If n is the amount of money in a savings account, then the expression n + 0.03n 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

$515Course 3

1-1 Variables and Expressions

Course 3

1-1 Variables and Expressions

Assignment: •P. 8 (11-47 odd)•1-1 Practice A w.s.