Order of Operations with Exponents
Est. Class Sessions: 1Developing the Lesson
Review Order of Operations. Begin the lesson by reviewing the order of operations and the use of parentheses with students. Write the following six number sentences on a display.
6 + 5 × 4 + 3 = 29
6 + 5 × 4 + 3 = 47
6 + 5 × 4 + 3 = 77
7 + 6 − 5 × 4 = 32
7 + 6 − 5 × 4 = 11
7 + 6 − 5 × 4 = −7
Have students work in partners to discuss which sentences are true. If a sentence is not true, ask student pairs to come up to the display and add parentheses to make it true.
Then direct students' attention to Question 1 on the Order of Operations with Exponents pages in Student Guide. Parentheses can change the meaning of a number sentence by changing the order of the operations. For example, students may add a set of parentheses to Ming's number sentence to make it true. Ming's number sentence would then read:
(1 + 3) ÷ 2 + 4 = 6
Operation Target. Introduce the game Operation Target. Students might be familiar with this game from Grade 4. The rules are included in Irma and Jacob's dialog bubbles in the Student Guide. More detailed directions are on the Operation Target Master. Ask students to use the target numbers in Question 2 to explore the order of operations and the game rules. Collect student responses to each target number on a display. All the target numbers in this question have more than one possible solution. As students share their solutions, ask them to explain how they know each number sentence is true.
For Question 3, students find the largest and smallest whole number using the digits 1, 2, 3, and 4.
Add Exponents to Order of Operations. Use Question 4 to introduce exponents into the order of operations. Jackie wrote a number sentence for the target number 6 that included an exponent. As a result, Mr. Moreno adds exponents to the order of operations list.
For Question 5, students check if number sentences are true, keeping in mind the order of operations. Shannon and Ming wrote true number sentences. Roberto did not. Students need to add parentheses to Roberto's number sentence to make it true.
42 ÷ (1 + 3) = 4
Ask students to use the target numbers in Question 6 to explore the order of operations with exponents and parentheses. For Question 7, students write a number sentence for a different target number that they choose themselves. Ask pairs to trade targets and write a number sentence for that target. Ask them to check each other's number sentences.
Ask students to complete Check-In: Question 8–9 independently.
