1. 2-2 Variables and Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 2-2 Variables and Expressions Warm Up Simplify. 1. 4 + 7  3  1 2. 87  15  5 3. 6(9 + 2) + 7 4. 35  7  5 24 84 73 25

3. 2-2 Variables and Expressions Problem of the Day How can the digits 1 through 5 be arranged in the boxes to make the greatest product?  4 3 1 5 2

4. 2-2 Variables and Expressions MA.6.A.3.1 Write and evaluate mathematical expressions…given situations. Sunshine State Standards

5. 2-2 Variables and Expressions Vocabulary variable constant algebraic expression evaluate

6. 2-2 Variables and Expressions A variable is a letter or symbol that represents a quantity that can change. A constant is a quantity that does not change.

7. 2-2 Variables and Expressions An algebraic expression contains one or more variables and may contain operation symbols. So p  7 is an algebraic expression. Algebraic Expressions NOT Algebraic Expressions 150 + y85 ÷ 5 35  w + z 10 + 3  5 To evaluate an algebraic expression, substitute a number for the variable and then find the value by simplifying.

8. 2-2 Variables and Expressions Evaluate the expression to find the missing values in the table. Additional Example 1A: Evaluating Algebraic Expressions Substitute for y in 5  y. y 5  y 16 27 35 80 y = 16; 5  16 = 80 135 175 27135 35175 y = 27; 5  = y = 35; 5  = The missing values are 135 and 175.

9. 2-2 Variables and Expressions Evaluate the expression to find the missing values in the table. Additional Example 1B: Evaluating Algebraic Expressions z z  5 + 4 20 45 60 8 z = 20; 20  5 + 4 = 8 z = 45; __  5 + 4 = __ z = 60; __  5 + 4 = __ 13 16 45 13 60 16 The missing values are 13 and 16. Substitute for z in z  5 + 4.

10. 2-2 Variables and Expressions Check It Out: Example 1A Evaluate each expression to find the missing values in the table. t 8t 10 20 30 80 160 240

11. 2-2 Variables and Expressions Evaluate each expression to find the missing values in the table. Check It Out: Example 1B m 5 2 - 2  m 4 7 10 17 11 5

12. 2-2 Variables and Expressions Evaluate each expression to find the missing values in the table. Check It Out: Example 1C n n ÷ 6 - 4 60 48 36 6 4 2

13. 2-2 Variables and Expressions Evaluate each expression to find the missing values in the table. Check It Out: Example 1D b 3  (2 + b) 3 6 9 15 24 33

14. 2-2 Variables and Expressions You can write multiplication and division expressions without using the symbols  and . Instead of... You can write... x  3 x  3 35 ÷ y x(3) 3x3x 35 y When you are multiplying a number times a variable, the number is written first. Write “3x” not “x3.” Read 3x as “three x.” Writing Math

15. 2-2 Variables and Expressions A rectangle is 4 units wide. How many square units does the rectangle cover if it is 3, 4, 5, or 6 units long? Additional Example 2: Evaluating Expressions with Two Variables Make a table to help you find the number of square units for each length. 3 x 4 = square units 20 16 lwl x w 3412 44 54 64 The rectangle will cover 12, 16, 20, or 24 square units. 4 x 4 = square units 5 x 4 = square units 6 x 4 = square units 12 16 20 24

16. 2-2 Variables and Expressions Complete the table. Check It Out: Example 2A z 8  z + 2 7 9 11 58 74 90

17. 2-2 Variables and Expressions A rectangle is 7 units wide. What is the area of the rectangle if it is 8, 9, 10, or 11 units long? Check It Out: Example 2B 7 · 8 = 56 square units; 7 · 9 = 63 square units; 7 · 10 = 70 square units; 7 · 11 = 77 square units

18. 2-2 Variables and Expressions A rectangle has a length of 13 units. The perimeter of a rectangle is twice its width plus twice its length. Complete the table to find the perimeter of the rectangle if its width is 5, 6, 7, or 8 units wide. Check It Out: Example 2C w l = 13

19. 2-2 Variables and Expressions Check It Out: Example 2C Continued w 2  13 + 2  w 5 36 units 6 7 8 38 units 42 units 40 units