# 7.11, 7.12, 7.13 - Write Algebraic Expressions

7.11  The student will evaluate algebraic expressions for given replacement values of the variables.

7.12  The student will solve two-step linear equations in one variable, including practical problems that require  the solution of a two-step linear equation in one variable.

7.13  The student will solve one- and two-step linear inequalities in one variable, including practical problems, involving addition, subtraction, multiplication, and division, and graph the solution on a number line.

### BIG IDEAS

• I can determine the total cost of a family trip to the movies when the number of people and the cost of tickets varies for each age group, and I can figure my total score on a video game where different tasks give different points.
• I will always get the same result as everyone else when evaluating an expression by following the set of rules called order of operations.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - 7.11 Understanding

·  To evaluate an algebraic expression, substitute a given replacement value for a variable and apply the order of operations.  For example, if a = 3 and b = -2 then 5a + b can be evaluated as:
5(3) + (-2) and simplified using the order of operations to equal 15 + (-2) which equals 13.

· Expressions are simplified by using the order of operations.

· The order of operations is a convention that defines the computation order to follow in simplifying an expression. It ensures that there is only one correct value. The order of operations is as follows:

- First, complete all operations within grouping symbols¹. If there are grouping symbols within other grouping symbols, do the innermost operations first.

- Second, evaluate all exponential expressions.

- Third, multiply and /or divide in order from left to right.

- Fourth, add and /or subtract in order from left to right.

¹ Parentheses ( ), brackets [ ], and the division bar should be treated as grouping symbols.

· Expressions are simplified using the order of operations and applying the properties of real numbers. Students should use the following properties, where appropriate, to further develop flexibility and fluency in problem solving (limitations may exist for the values of ab, or c in this standard).

·  An equation is a mathematical sentence that states that two expressions are equal.

· The solution to an equation is the value(s) that make it a true statement. Many equations have one solution and can be represented as a point on a number line.

· A variety of concrete materials such as colored chips, algebra tiles, or weights on a balance scale may be used to model solving equations in one variable.

· The inverse operation for addition is subtraction, and the inverse operation for multiplication is division.

· A two-step equation may include, but not be limited to equations such as the following:
2x + = -5;  -25 = 7.2x + 1;  = 4;  x – 2 = 10.

· An expression is a representation of quantity. It may contain numbers, variables, and/or operation symbols. It does not have an “equal sign (=)” (e.g.,, 5x, 140 - 38.2, 18 ∙ 21, 5 + x).

· An expression that contains a variable is a variable expression. A variable expression is like a phrase: as a phrase does not have a verb, so an expression does not have an “equal sign (=).”
An expression cannot be solved.

· A verbal expression can be represented by a variable expression. Numbers are used when they are known; variables are used when the numbers are unknown.  For example, the verbal expression “a number multiplied by 5” could be represented by “n ∙ 5” or “5n”.

· An algebraic expression is a variable expression that contains at least one variable (e.g., 2x – 3).

· A verbal sentence is a complete word statement (e.g., “The sum of twice a number and two is fifteen.” could be represented by “2n + 2 = 15”).

· An algebraic equation is a mathematical statement that says that two expressions are equal
(e.g., 2– 8 = 7).

· Properties of real numbers and properties of equality can be applied when solving equations, and justifying solutions. Students should use the following properties, where appropriate, to further develop flexibility and fluency in problem solving (limitations may exist for the values of ab, or c in this standard):

### ESSENTIALS

• How can algebraic expressions and equations be written?
Word phrases and sentences can be used to represent algebraic expressions and equations.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·7.111  Represent algebraic expressions using concrete materials and pictorial representations. Concrete materials may include colored chips or algebra tiles.

·  7.124  Write verbal expressions and sentences as algebraic expressions and equations.

·  7.125  Write algebraic expressions and equations as verbal expressions and sentences.

·  7.133  Write verbal expressions and sentences as algebraic expressions and inequalities.

·  7.134  Write algebraic expressions and inequalities as verbal expressions and sentences.

### KEY VOCABULARY

verbal expression, algebraic expression, verbal sentence, equation, variable, evaluate, sum, integer, consecutive, order of operations, operation, term, translate

Updated: Nov 20, 2018