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Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 1.0 Knowledge of Algebra, Patterns, and Functions

Topic B. Expressions, Equations, and Inequalities

Indicator 1. Write and identify expressions

Objective b. Determine the value of algebraic expressions with one unknown and one operation

Assessment limit: Use +, - with whole numbers (0-1000) or ×, ÷ (with no remainders) with whole numbers (0-100) and the number for the unknown is no more than 9

Clarification

An expression is a relationship between quantities. Quantities may be numbers or variables. A variable is a letter or symbol which represents one or more numbers. An algebraic expression is a mathematical relationship that uses numbers, variables operation symbols.
For example:
Numerical Expressions:

3 + 6     21 ÷ 7     4 × (6+2)     8 - 5     9/4

Algebraic Expressions

a + 5     b - 7     c × 2     d ÷ 4     5c

To evaluate an algebraic expression:

  • Replace the variable with a given number and
  • Simplify the expression by completing the computation

Classroom Example 1

Evaluate a + 3 for a = 7

Answer: Replace the variable a with 7 and complete the computation     7 + 3 = 10

Classroom Example 2

Evaluate an expression that matches a problem situation.

Problem Solving Algebraic Expression Evaluation

The after school club has 24 students. The teacher puts the students into teams. Let t equal the number of teams formed. How many students are on each team?

24 ÷ t

Evaluate the expression for t = 4 and t = 8.

Answers:
24 ÷ 4 = 6
24 ÷ 8 = 3

A package of juice contains 6 juice boxes. Let p equal the number of packages of juice boxes. How many total juice boxes are there?

p × 6

Evaluate the expression for p = 3

Answer:
3 × 6 = 18

Jill has a bag of apples. Jill eats two apples. Let b equal the number of apples in the bag. How many apples are left?

b - 2

Evaluate the expression for b = 14 and b = 18

Answers:
14 - 2 = 12
18 - 2 = 16

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