Download Lesson 1-10a

1-10
6th 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 = 5
1) 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 ÷ 3z
8) (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 1022.
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 25-34.
• If still more time, work
on Accelerated Math.