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Absolute Value Intro
Absolute value is the distance of a number from zero, which is always positive. The absolute value symbol indicates this distance is being calculated. Absolute value can be used to describe distances on a number line. For example, the absolute values of -5 and 4 are both equal to 5, since they are both 5 units away from zero, but in opposite directions. A word problem example involves a student, Nia, who starts in the cafe and moves between classes, with her total absolute distance traveled being calculated using absolute value symbols.
Absolute Value Intro
- 1. Absolute Value 1 Word Definition Example/Symbol Absolute Value a number’s distance from zero, distance is always measured in positive values Absolute Value Symbol “bracket-like” lines that inform one is calculating distance from zero - 0 3 3 -3 = 3 Agenda
- 2. Intro to AbsoluteValue 1) Explain how far away Carlos’ friends live. 2 Agenda Carlos lives in the green house. Rita Pedro Sam Eve 2 1 -2 -1 1 -1 -2 2 2) Eve and Sam are at -2. Explain how they are positive 2 away from Carlos. When we want to know distance from 0, we use Absolute Value. 2 = 2 -2 = 2 2 = 2 -2 = 2 Absolute values are always positive.
- 3. Absolute Value &the number line -5 -4 -3 -2 -1 0 1 2 3 4 5 3) Create an inequality statement (>, <) that relates the values represented by the green and red dots. 4) What are the absolute values of the quantities represented by the red and green dots? 5) Create an inequality statement that relates the absolute values of the dots. 3 -5 < 4 4 = 4 and -5 = 5 4 < 5 Agenda
- 4. Real world scenario:Hallway at Nia’s School Library Health Spanish Physic 4 s Café Gym Math ELA Biology The Café is in the middle of the school’s hallway. Nia just ate lunch in the Café. After lunch, she attended class 2 rooms to the right of the café (Math). She then went 5 rooms to the left of Math. After this class she traveled 3 rooms to the right. 7) In what room does Nia finish her day? 8) After leaving the café, how many total rooms did Nia either pass by or enter? *Hint - if she passes or enters a room more than once, it should be counted again. 9) Assuming the Café is the number 0, write an equation that represents the answer to #6? 10) Assuming the Café is the number 0, write an equation that represents the answer to #7? *Hint – you will need to use absolute value symbols. Agenda
- 5. Answers: Hallway atNia’s School -5 3 Library Health Spanish Physic 5 s 2 Cafe Gym Math ELA Biology 7) Nia finishes in the café. 8) Nia passes or enters 10 rooms. 9) 0 + 2 – 5 + 3 = 0 (Distance from starting point) 10) (0 + 2 + -5 + 3 = 10 Absolute distance traveled) Agenda
- 6. Answers: Hallway atNia’s School -5 3 Library Health Spanish Physic 5 s 2 Cafe Gym Math ELA Biology 7) Nia finishes in the café. 8) Nia passes or enters 10 rooms. 9) 0 + 2 – 5 + 3 = 0 (Distance from starting point) 10) (0 + 2 + -5 + 3 = 10 Absolute distance traveled) Agenda
Editor's Notes
- #2 (Time on this slide - 5 min) Time passed – 13 Depending on class norms, students can either fill vocab on CW handout or in designated vocab section of their notebooks. Preparation Notes I have chosen not to introduce “or equal to” inequalities in the notes. I feel this will complicate the initial understanding. It will be hinted at in the HW and must be addressed in a future lesson. Contributing to this decision is the idea that these inequalities are actually 2 symbols in 1. I want to stress the inequality aspect alone.
- #3 (Time on this slide - 10 min) Time passed – 23 Tell students that the focus is not on the value at each location, but the distance needed to get to Carlos’ house (zero).
- #4 (Time on this slide - 12 min) Time passed – 35 Shoulder Partner pairings – allow students about 8 minutes before reviewing answers with class.
- #5 (Time on this slide - 10 min) Time passed – 45 Allow groups of 4 to wrestle with this. Provide minimal guidance. If a group member provides a correct solution, ask another group member to explain it to you. This slide is meant to differentiate between the idea of net distance and absolute distance traveled. The equations, compared side by side, should reinforce the story.
- #6 (Time on this slide - 5 min) Time passed – 50 Time permitting…students could present their findings with group. If time is tight, review as a class.