We can simplify numerical expressions using the order of operations, including parentheses and exponents.
(2x(3-4))²+6 has two sets of parentheses. How would you use the order of operations to simplify an expression like this?
I would use the order of operations to simplify an expression with two sets of parentheses by...
By studying this visual, students might:
- There is one set of parentheses
- The result inside parentheses is raised to a power of 3
- There’s a negative number multiplied in front: −2
- There are multiple operations: addition, division, subtraction
- The steps are labeled with P, E, M, D, A, S
- What happens first, the parentheses or the exponent?
- Why is −2 outside the parentheses?
- Does the exponent apply to everything or just the number inside?
- Can I do addition before division?
- What does PEMDAS stand for?
Extending the Discussion
- After randomly calling on students, if there is anything from this list that was not mentioned, then ask the class, "Did anyone notice...?"
- After students have shared what they notice, ask the class, "Did anyone wonder...?" using the suggestions above or anything else you might think is interesting or relevant to the lesson.
Structured Conversation Prompts
What is order of operations?
The order of operations is...
How is the order of operations related to an expression
The order of operations is related to an expression because...
(2x(3-4))²+6 has two sets of parentheses. How would you use the order of operations to simplify an expression like this?
I would use the order of operations to simplify an expression with two sets of parentheses by...
Example Student Responses to the Observational Question
The order of operations is the way you solve math problems step by step so you get the right answer.
The order of operations is the set of rules that tells you which math operations to do first when solving a problem with parentheses, exponents, multiplication, division, addition, and subtraction.
Responding to Responses
Emphasize and celebrate each student's use of the key vocabulary to support a culture of "no wrong answers."
Structuring Student Conversations
Have students list observations from the visual as a warm-up, then use the Q-SSS-A process to guide small-group conversations. In the slide decks, brackets can be moved to prepare the structured conversation. In the example to the right, students will be instructed: Q-SSS-A.
- To put a thumb up, then lower their hand when they are ready to answer the question
- To share with their elbow/shoulder partner, and that the student with the darkest shoe will share first
- That they will be randomly called on after the conversation
Here is an example of structuring a conversation with Q-SSS-A.
Note: the inferential question is the same as the language objective. It is recommended that students answer the inferential question in a small-group discussion before answering it individually as the closure or exit ticket of the lesson.
Structured Reading
The purpose for reading is to learn how the order of operations helps us solve expressions step by step.
- Parentheses and how they are used
- When exponents are solved
- The order of multiplication, division, addition, and subtraction
- Words that explain why the order matters
- Steps that change the value of the expression
Why is it important to follow the order of operations when evaluating expressions?
It is important to follow the order of operations when evaluating expressions because...
Structuring the Reading
Communicate the purpose of reading to the students and instruct them to make a note every time they see something on the PAT ("Pay Attention To") list. How you have students note items on the PAT list is up to you. This could include:
- Putting an asterisk in the margin
- Underlining text that supports the PAT list
- Putting a comment in the margin
Follow the reading with the post-reading discussion. Structure this discussion using the Q-SSS-A process just like the structured conversations in this lesson.
Note: you might find the relational question is better discussed before or after the reading. This depends on whether the relational question is directly related to the reading or might make connections across units.
Differentiating the Reading
You will notice that three different reading passages are provided with this lesson. Look at the shapes in the top-left of each passage to determine the grade level.
In a class with students at diverse reading level proficiencies, you can give the appropriate reading passage to different students, while having all students follow the same PAT list and post-reading discussion.