Evaluating and Writing Algebraic Expressions

1. Evaluating and Writing Algebraic Expressions Mrs. Ash

2. Day 1 Learning Target: I can evaluate algebraic expressions for specific values of variables. 

3. Team member #2 please get: • A dry erase board and marker for each person in your group • One rag per table

4. What is an Algebraic Expression? • An expression consists of a combination of numbers, operation symbols, and grouping symbols such as parentheses ( ).  An algebraic expression is an expression that contains one or more variables, but NO equals sign! • Expressions: Algebraic Expressions 3 + 4 3 (c + 8)6 – 2 2 a (6 + 3) -19 – x

5. What is a variable? A variable… • Is a letter or symbol that represents an unknown number. • Can be any letter. • When the same letter is used more than once it represents the same value

6. The parts of an expression separated by the operation symbols are known as terms. • Terms may have a variable. • Variables may have a coefficient.A coefficient is a number getting multiplied by a variable. • Terms without a variable are known as constants.

7. Let’s Try! Given the expression below: • How many terms are in the expression? • Underline each coefficient. • Circle each constant. • Put a box around each variable 5x + 3 – 2x

8. Now we are ready to evaluate Algebraic Expressions. How do you think this is done? For example, if you are given the expression r + 5 and I tell you that r = 5, what steps would you take? 1.) Rewrite the expression replacing the variable with its value 2.) Follow order of operations to simplify and evaluate the expression 3.) Circle final outcome.

9. Remember!In expressions, there are many different ways to write multiplication • 1) ab • 2) a • b • 3) a(b) or (a)b • 4) (a)(b) • 5) a x b We are not going to use the multiplication symbol any more. Why?

10. Division, on the other hand, is written as: 1) 2) x ÷ 3

11. Let’s Practice! Evaluate each expression when a = 12 • a + 3 • 17 – a

12. Evaluate the following when n = 4 • 9n (what operation does this mean when a number is right beside a variable? Look at your notes if you don’t know) 2) 40 / n

13. Now, let’s try two operations! • ) 7x + 4 for x = 6 2.) 8y – 22 for y = 9 3.) + 8 for x =4 4.) y + 3z for y = 5 and z = 6

14. Time to apply what we’ve learned! • Team member # 4 please return dry erase boards, markers, and rags.

15. Day 1 Learning Target: I can translate written phrases into algebraic expressions.

16. When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions. For example, Katie and Aaron both donated canned foods for the Holiday food drive, but Aaron donated five times the amount Katie did. The amount Aaron donated can be found using the expression 5x . What would x represent? What word(s) tell you to multiply?

17. In order to translate a phrase into an algebraic expression, we must first review some synonyms for the basic operations.

18. Remember! • Multiplication expressions should be written in side-by-side form, with the number always in front of the variable. 3a 2t 1.5c0.4f • Division expressions should be written using the fraction bar instead of the traditional division sign.

19. Addition phrases: • 3 more than a number t • the sum of 10 and a number • a number increased by 4.5

20. Subtraction phrases: • a number y decreased by 4 • the difference between 10 and a number • 6 less than a number

21. Multiplication phrases: • the product of 3 and a number • twice the number n • 4.2 times a number p

22. Division phrases: • the quotient of 25 and a number • the number y divided by 2 • 2.5 divide g

23. Let’s try it! • Write an algebraic expression for1) mincreased by 5 2) 8 less than a number x 3) a number r divided by 15

24. 4) 2 7 times the sum of x and t 5) 11 less than 4 times a number y 6) two more than 6 times a number

25. Write a verbal expression for: • 8 + a. 2) 3(x) 3) 2x + 9