Lesson plan

Pre-algebra Problems with Order of Operations

Algebra concepts can be challenging for students in upper elementary and middle school. This lesson introduces students to the idea of a missing or unknown number while also considering the order of operations.
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Students will be able to create numerical expressions containing multiple operations and a missing variable, and solve for the unknown number.

(5 minutes)
  • Write '10 - __ = 6' and have students discuss how to solve for the unknown number.
  • Engage students in a math talk about how they got their answer. Encourage students to explain their thinking, and welcome multiple strategies.
  • Inform students that when they solve for a missing number in a math equation, they are beginning to learn about algebra, an area of math that will be an essential part of their lives as mathemeticians in fifth grade and middle school.
(10 minutes)
  • Remind students that an equation is a mathematical statement where both sides of the equal sign are balanced or the same.
  • Have students turn to a partner to review the acronym PEMDAS. Confirm their responses by recording PEMDAS, along with its meaning on a piece of chart paper: P (parenthesis), E (exponents), M (multiply), D (divide), A (add), S (subtract).
  • Tell students that today they will practice solving for an unknown number in a math equation, and also learn how to create such an equation.
  • Show the following problem on the board: 5 x (3 - __ ) = 10
  • Say to students: 'Using PEMDAS, I know I need to solve the parenthesis first, but there's an unknown number. I see that 5 multiplied by the unknown number must equal 10. Therefore, the number in the parenthesis' must equal 2 because 5 times 2 is 10. In order to get 2, I have to place 1 in the blank space. The unknown number is 1.'
(15 minutes)
  • Divide students into 5 groups, and distribute a piece of chart paper to each group with one of the following problems on each piece of paper. (31 – __ ) ÷ 5 + 2 = 6 (19 – 7) ÷ + 11 = 14 ** 20 x 2 - 7 + = 43 90 ÷ (3 + __ ) - 5 = 5 64 - __ x 2 ÷ 8 = 6
  • Instruct students to work together to solve for the unknown number, showing the steps, and using the order of operations as well. Tell groups that they must each be able to justify their answer orally.
  • At the bottom of the chart paper, they are to create a new math equation with a missing number, and share their thinking of how they created the problem.
(15 minutes)
  • Distribute an index card to each student, and have them write their name and a math equation with an unknown number.
  • Remind students to keep the order of operation in mind when they design their equation.
  • Circulate the room to check their equations, and offer assistance as needed.
  • Once all students have finished, tell them that they will do a math mingle. Students are to walk around the classroom with a pencil, a clipboard with scratch paper, and switch index cards with another student.
  • Model to students how you switch cards, and attempt to solve for the missing number, using the scratch paper on the clipboard. Students should solve each others' equations at the same time. The student must then confirm if they got the right answer or not. Then, students keep the card that was given to them by their classmate and continue the process with another student.
  • Allow time for students to solve four or five equations.

Support: what to change

  • Allow students to work in partners to complete the independent work.

Enrichment: what to change

  • Advanced students and early finishers could practice their PEMDAS skills with a fifth grade worksheet on order of operations (see suggested media).
(5 minutes)
  • Write the following problem on the board, and have students orally explain how they would solve it: (59 - 29 + 6) ÷ = 4. They may use these sentence stems for support. First, I _____. Then, I _____. ** I know my process and answer are correct because ___.
(5 minutes)
  • Engage students in a discussion about their impressions of pre-algebra concepts with the following question as a guide: How does pre-algebra connect to math concepts you already know?

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