Øriginal Distance: Absolute Value and Additive Inverse

Students enter the room silently and complete their do now.  They are given 3 minutes to answer all questions independently and silently, and then they are sent to work anywhere in the classroom in groups of 2 - 4. Student's may choose their own group members. Once all students have formed their groups, the student with the most siblings will share the first answer on the Do Now. Each of the other students in the group will share their answers in clockwise order (2 mins). I will choose one student to write all of the answers on the board for groups to double check.

After 2 - 3 minutes of reviewing in groups, students are instructed to return to their original seats and use their vocabulary index cards (Additive inverse and absolute value) to complete their Cornell Notes. They are encouraged to share what they wrote with their partners. One student is selected to write their notes on the smart board. If students finish early they are encouraged to work on the example problems with their group members.

While students word independently I will be checking in with students who seem to be struggling and giving them any extra time or explanation needed to understand the key ideas of this lesson:

• the absolute value is simply the distance any number is from zero; a common misconception is that the absolute value is a synonym for the additive inverse (i.e. the abs. value of 5 is 5, not -5)
• it is always reported as a positive number
• the additive inverse of a number is the opposite of a number
• when you combing two opposites, or two additive inverses, you get zero

Examples 4-6 are a good opportunity to challenge students at a higher level. I do not review all of these problems. I choose one depending on what I feel the class can handle and encourage them to discuss the rest of the problems with their group members or in their journal later in the lesson.

During this section of class students are practicing MP8 by repeatedly answering the same question, "what is the distance between...?" This practice also helps them employ MP2 when they answer the last question, "what is the distance between x and zero?" because students have to reason abstractly about ANY number and its distance from zero. MP1 is in use as students are challenged through questioning to consider the meaning of absolute value versus the definition of an additive inverse.

Students will make two concentric circles. They will rotate so that students have a new partner after each rotation asking and answering questions.

1. Students stand in two concentric circles, facing a partner. The inside circle faces out; the outside circle faces in.
2. The students on the outside circle will have dry erase boards and the students on the inside will have question cards.
3. Students with question cards ask, listen, then praise or coach. Students on the outside with dry erase boards answer out loud if it is only an absolute value question (i.e. ) and they use the dry erase board if the question asks them to draw the solution. (i.e.  Draw a picture to show your answer). Students with the question cards get green cards to give to students answering questions if they are correct. These green cards can be turned in for achievement points. 12 questions correct = 3 achievement points; 6 questions correct = 2 achievement points; 3 questions correct = 1 achievement point
4.  After each question, students in the outer or inner circle rotate to the next partner. (Teacher may call rotation numbers, “Rotate three ahead”, or switching of roles “Switch circles!”)

After students practice for 15 minutes, they take a seat and I close with review of the word "opposite" and higher level questions involving negatives and absolute value.

-(-3) says the opposite of negative three

thus, -(-3) = +3

-(abs val)(-3) says the opposite of the absolute value of -3

thus, -(abs val)(-3) = -3 

Students receive journals after they were checked over the weekend. They are directed to complete today's journal entry before going back to look at what I wrote in their past entries. If there is time, they may ask for further clarification  on anything I wrote in response to last week's entries.

Describe and correct the error in evaluating the expression:

  |-17|=-17

Write ONE of the following at the bottom of your journal entry for today.

J I really understood this idea…

K I have a few questions about… before I can say I understand

L I don’t even know where to start on …