We can simplify numerical expressions by following the correct order of operations.
What would happen if there were no rules for the order of operations in mathematics?
If there were no rules for the order of operations in math, I think...
By studying this visual, students might:
- Numbers are grouped in different ways using parentheses
- Multiplication appears before addition in the problems
- The operations are performed in a specific sequence
- The expression on the left is solved without parentheses
- The visual uses arrows to show the step-by-step process
- Why do we need a specific order of operations?
- What happens if I solve the steps out of order?
- Why do parentheses come first?
- Are there situations where the order changes?
- How can different looking problems have the same answer?
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?
Order of operations means...
How is order of operations related to parentheses?
Order of operations is related to parentheses because...
What would happen if there were no rules for the order of operations in mathematics?
If there were no rules for the order of operations in math, I think...
Example Student Responses to the Observational Question
Order of operations means the steps I follow to solve math problems.
Order of operations means the specific rules I use to simplify expressions so everyone gets the same answer, like solving inside parentheses first.
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
Let’s read to learn how the order of operations helps us solve math problems step by step.
- What the order of operations is
- What steps are followed in the order of operations
- How parentheses affect the steps
- A math example that uses the order of operations
Why do you think it’s important to have a rule like the order of operations in math?
It’s important to have an order of operations 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.