Numerical Expressions


Learning Objective

Students will interpret numerical expressions without solving them and write simple expressions.


Grade Levels



Common Core Standard

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. 


Materials Needed

Dog Market Worksheet

Blank Paper




  • Review the commutative property of multiplication and the order of operations.
  • Teach students that expressions are a series of numbers and symbols, such as +, -, x, and ÷, without an equal sign.
  • Write the expression 4 (3 + 2) on the board.
  • Tell students that when that expression is worked out it is called an evaluation of the expression.
  • The expression equals 20, therefore 4 (3 + 2)= 20 is the equation.
  • Tell students that the expression 4 (3 + 2)= is 4 times larger than the expression (3 + 2).
  • Let students know that today they are going to evaluate the relationship between expressions and write their own expressions to evaluate.

Explicit Instruction/Teacher Modeling

  • Write the steps “double four and then add 30” on the board.
  • Ask students to write an expression for the steps above.
  • They should write (4 x 2) + 30 or 4+4+30.
  • Write the expression "3 (5x5)" on the board.
  • Ask students to describe, in writing, how the expression relates to (5x5).
  • They should write that the expression 3 (5x5) is 3 times larger than the expression (5x5).
  • Choose volunteers to create their own expressions like the two you just modeled and explain them.
  • Guide students through the process of evaluating their expressions orally.

Guided Practice/Interactive Modeling

  • Allow students to form pairs or small groups. Explain to students that responsible dog owners must do many things to care for their dog, including buy them items they need.
  • Pass out the Dog Market worksheet.
  • Advise students that they should work with a partner or group to write an expression and evaluate the expressions.
  • Remind students to refer back to their notes from the models you provided.

Independent Working Time

  • Pass out blank paper.
  • Tell students that they are going to work alone to create their own expressions and evaluate the relationships between the numbers just like they have been practicing.
  • Students may need an example to get them started. Example: Write an expression in words, such as "divide 60 by 5, and then subtract 10." Students should write (60 ÷ 5) – 10 and go on to write that the expression (60 ÷ 5) – 10 is 10 less than (60 ÷ 5).

Review and Closing

  • Write the following expression on the board: (100 ÷ 5) x 0.5.
  • Have students identify the expressions and equation.
  • Then have students evaluate the expression without calculating it: (100 ÷ 5) x 0.5 is ½ of (100 ÷ 5).
  • Ensure that students can create a word problem or steps for this equation: divide 100 by 5 then multiply by a half.