We can identify and explain the absolute value of a number and how it relates to its opposite.
Why do you think an absolute value cannot be negative?
I think an absolute value cannot be negative because...
By studying this visual, students might:
- The absolute value symbols are shown as two vertical lines around a number.
- All absolute values on the number line are positive.
- The absolute value of both a positive and negative number is the same.
- Numbers like –.3 and .3 have the same absolute value.
- The number line is used to measure distance from zero.
- Why is the absolute value of a number always positive?
- Can zero have an absolute value?
- What do the vertical bars in |--5| mean?
- Why do opposites have the same absolute value?
- Is absolute value the same as taking away the negative sign?
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 an absolute value?
An absolute value is...
How is an absolute value different from an opposite number?
An absolute value is different from an opposite number because...
Why do you think an absolute value cannot be negative?
I think an absolute value cannot be negative because...
Example Student Responses to the Observational Question
An absolute value is how far a number is from zero.
An absolute value is the distance a number is from zero on the number line, and it is always positive.
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 figure out what absolute value means and how a number line and the idea of distance can help us understand it.
- What absolute value means
- How a number and its opposite are shown on a number line
- How far numbers are from zero
- How absolute value is written in math
- How absolute value compares to negative and positive numbers
How does thinking about distance help you explain why the absolute value of a number is always positive?
Thinking about distance helps explain why the absolute value of a number is always positive 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.