1-106th grade math

Variables and Expressions

Objective

• To evaluate expressions having as many as 3 variables.

• Why? To master one aspect of Algebra and Functions in 6th grade math (and beyond) of whole numbers and decimals. Evaluating variables and expressions is a key component in Algebra and other higher math.

California State Standards AF 1.2: Evaluate an algebraic expression for a given

situation, using up to three variables.AF 1.3: Apply algebraic order of operations and the

commutative, associative, … properties to evaluate expressions…

MR 1.2: Formulate and justify mathematical conjectures based on a general description…

Vocabulary• Variable- A letter used to stand for a number in an expression or equation.

2x; 6 + x; …• Expression

- A mathematical phrase made up of a combination of variables and/or numbers and operations. Expression with variables are also called algebraic expressions. Expressions with variables must have a number to substitute the variable and then solve.

• 5n, n = 4. 5 x 4 = 20; 4x – 7; (5 x 2) – 6/3; … • Equation– A number sentence stating that two expressions are equal.• 3 + 5 = x; 8x = 32; …

How to Evaluate Expressions Using Variables

1) Substitute the named numbers for the named variables.

2) Solve by using Order of Operations.

3) Remember: Parentheses are solved first. Exponents are next. Multiplication and division are next (from left to right). Addition and subtraction are last (from left to right).

4) Show all steps and Check your work.

A) 3x + y; x = 5 and y = 6= 3(5) + 6= 15 + 6= 21

B) 2a + (5b – 4c); a = 15, b = 16, c = 0= 2(15) + (5x16 – 4x0)= 30 + (80 – 0)= 30 + 80= 110

Try It!Evaluate each expression for a = 10

and b = 51) a + b 2) a x b

3) a – b 4) a ÷ b

1) 10 + 5= 15

2) 10 x 5 = 50

3) 10 – 5 = 5

4) 10 ÷ 5= 2

Evaluate each expression for x = 10, y = 7, z = 2

5) 2x + 3y

6) 4x – 5y + 4z

7) 6y ÷ 3z8) (x + y) – 2z

5) 41

6) 13

7) 7

8) 13

Objective Review

• You can now evaluate expressions using several operations with whole numbers and decimals in the correct order.

• Why? You have now mastered another aspect of Number Sense in 6th grade math (and beyond) of whole numbers and decimals. Order of Operations is a key component in Algebra and other higher math. Order of Operations rules tell you how to evaluate any expression with or without parentheses.

Independent Practice

• Complete problems 10-22.

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 25-34.

• If still more time, work on Accelerated Math.