Math Background

Lesson: Expressions and Equations
Developing the Concept

The next step for students in understanding expressions and equations is to complete addition and subtraction operations within parentheses first. Later in their studies, students will learn the complete order of operations (parentheses, exponents, multiplication and division, addition and subtraction), but for now they need to know to do what is within the parentheses first and then to add and subtract from left to right.

Materials: overhead projector or chalkboard

Preparation: none

Prerequisite Skills and Concepts: none

Write (4 + 6) + (2 + 5) on the board or overhead. Have a student read aloud the expression and help identify the parentheses.

  • Ask: Is this an expression or an equation?
    Most students should be able to note that without an equals sign, this is an expression.
  • Ask: How do the parentheses act upon the numbers in this expression?
    They group the numbers inside them. Some students may realize that these numbers will be added together and replaced by their sum.
  • Say: The operation shown inside the parentheses must be done before other operations outside the parentheses when simplifying an expression.
    Point to the operation in each set of parentheses. Have students complete the addition within each set of parentheses.
  • Ask: What can we do to further simplify the expression?
    Rewrite the expression with the sum of the numbers in parentheses. (10) + (7)
    Students should see that they need to add to simplify.
  • Ask: What is the result after all addition operations are completed in the expression?
    Students should realize the result is 17.
  • Say: When we complete all the operations in an expression, we simplify the expression.
    Write 10 + 7 = 17 and have students note that by showing the equality, you have created an equation.

    Now write (x + 4) − 1.

  • Say: This is an algebraic expression. What makes it different than the other expression we just worked on?
    Students should point out the use of x as a variable.
  • Ask: Who can translate this expression into words?
    Students should translate the variable as some number. The expression would read some number plus four minus one, four more than some number take away one, some number added to four less one (or some variation.)
  • Ask: Do we know the value of x?
    The variable x could be any value at this point. Have students substitute various numbers for x and simplify.
  • Say: When we evaluate an algebraic expression, we substitute a number for the variable.
    Write (x + 4) − 1 = 8.
  • Ask: Can a single value of x be determined now?
    Yes, and some students may be able to identify x as 5. Have a student demonstrate how 5 works in this equation.

    Have other students substitute different numbers to demonstrate that only 5 will work in this equation.

    Continue with additional examples of expressions by using different numbers and variables and different combinations of addition and subtraction. Have students test values for x. Then allow students to translate these expressions and equations into words. Students may also begin new expressions by stating them in words and then translating them into numbers and symbols.

Wrap-Up and Assessment Hints
Test student understanding of the equals sign by having them write about the difference between expressions and equations.

Houghton Mifflin Math Grade 5