Lesson 1 6 Algebra: Variables and Expression Students will be able to evaluate algebraic expressions. P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions. P7 P9 Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified. Recognize a variety of uses for variables. Lesson objectives Teachers' notes 1
Get Ready for the Lesson A pattern of squares is shown: 1) Draw the next three figures in the pattern. 2) Find the number of squares in each figure and record your data in a table like the one below. Figure 1 2 3 4 5 6 Number of Squares 3 4 5 3) Without drawing the figure, determine how many squares would be in the 10th figure. Check by making a drawing. 4) Find a relationship between the figure and its number of squares. 2
Get Ready Answer: 1) 2) Figure 1 2 3 4 5 6 Number of Squares 3 4 5 6 7 8 3) 12 squares 4) The number of squares is 2 more than the figure number. 3
Quick Review Evaluate each expression: 1) 6 + 2(4 1) + 4 x 9 2) 28 (3 1) 2 3) 13 + 12 17 12 48 7 5 4
Vocabulary: Variable a symbol that represents an unknown quantity. Algebra the branch of mathematics that involves expressions with variables Algebraic Expression an equation that contains variables, numbers, and at least one operation. Coefficient the numerical factor of a multiplication expression that contains a variable. variables coefficients 6d + 4e algebraic expression 5
REMEMBER In algebra, the multiplication sign is often omitted. 6d 9st mn 6 times d 9 times s times t m times n 6
"Equations with Variables" 7
Notes and Examples! EXAMPLE 1: Evaluate n + 3 if n =4. n + 3 = 4 + 3 Replace n with 4. = 7 Add 4 and 3. 8
Check Your Progress Think Pair Share Evaluate each expression if c = 8 and d = 5. a) c 3 a 5 b) 15 c c) c + d C b 7 13 9
Notes and Examples! EXAMPLE 2: Evaluate 8w 2v if w = 5 and v = 3. 8w 2v = 8(5) 3(3) Replace w with 5 and v with 3. = 40 6 Do all multiplication first. = 34 Subtract 6 from 40. 10
Notes and Examples! EXAMPLE 3: Evaluate 4y 2 + 2 if y = 3. 4y 2 + 2 = 4(3) 2 + 2 Replace y with 3. = 4(9) + 2 Evaluate the power. = 38 Multiply then add. 11
Check Your Progress Think Pair Share Evaluate each expression if a = 4 and b = 3. d) 9a 6b d 18 e) ab 2 e 6 f) 2a 2 + 5 The fraction bar is a grouping symbol. Evaluate the expressions in the numerator and denominator separately before dividing. f e Hint 37 12
Real World Example Use the formula below to find Latrina's minimum training heart rate if she is 15 years old. (a represents age.) 3(220 a) 5 123 13
Check your Understanding Evaluate each expression if a = 3 and b = 5. 1) a + 7 2) 8 b 3) b a 4) The standard formula for finding your maximum heart rate is 220 a, where a represents a person's age in years. What is your maximum heart rate? Evaluate each expression if m = 2, n = 6, and p = 4. 5) 7m 2n 6) 15 m 3 7) 3p 2 n 14
test practice Which expression could be used to find the cost of buying b books at $7.95 each and m magazines at $4.95 each? A) 7.95b + 4.95m B) 7.95b 4.95m C) 12.9(b + m) D) 12.9(bm) 15
CHALLENGE of the DAY Name values of x and y so that the value of 5x + 3 is 18 greater than the value of 2y + 14. Answer 16
Complete Lesson 1-6: "Practice" worksheet. 17