Constructing the Idea of Absolute Value
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Using the NROC absolute value game, “Absolutely
,” students construct the meaning of the absolute value symbol. They then collaborate to create a set of class notes and hypothesize about how the symbol effects solving for X in an equation.
• Find the absolute value of numbers.
This 55minute high school level lesson introduces absolute value using “Absolutely,” a game from NROC's Algebra 1--An Open Course, Unit 2, Lesson 2, Topic 1: Absolute Value. The students act as collaborative investigators to solve the mystery of absolute value. The class activity is followed up with a written assignment to assess understanding.
10min— Warm up your class with a reminder about negative numbers.
- Give them a few problems to solve as bell work, or see if you can use Socratic Questioning to lure them into explaining negatives to you.
10min— Introduce the new symbol | |, but not what it means. Tell the students it’s up to them to figure out how it works.
- As a framing device, the lesson can be built up as an archeological investigation in which the symbol, |x|, has been found as part of a machine left by a vanished civilization. The students must discover what this key symbol means!
15min— Now that students know their goal is to find them meaning of |x|, have most of your students work in pairs at computers playing the "Absolutely" game and noting what they find.
- If using the framing device, you can claim that there’s a number code that needs to be figured out and tested to unlock a tomb, but you’ll only have one chance to get it right! Put on the board a few absolute value problems, the answers to which will be the code.
15min continued— Meanwhile, have a few students collecting information to make a set of class notes on the white board.
- They are your “Field Researchers.”
- “Absolutely” has students order integers (with or without absolute value symbols) from least to greatest by flipping around pairs of numbers mounted on gears. It provides deeper understanding than a standard introductory lecture on absolute value because of the higher level of cognitive engagement and the immediacy of feedback in the game situation.
5min— When ready, the note takers should present the class notes to the people who were at the computers. Everyone copies the notes into their own notebooks.
- They are the “Senior Investigators” creating “Research Notes.”
- Clipboards and white lab coats can be fun to use.
- Encourage revision and neatening of the notes. This is an opportunity to teach good note organization skills.
5min—Name the symbol.
- Present this as a consultation between the field teams and the senior researchers to ensure consistency before attempting the key code.
- Encourage more revision and feedback from the field teams.
5min— As a class they should now discuss the answers to the key code problems. It’s up to you whether you give them some sort of prize when they get it right, but use their answers as a wrap up for the class being sure to summarize the absolute value findings.
- The class should propose a name for the symbol they now understand so well.
- Reveal the symbol’s established name is absolute value and discuss its use.
- If time: Invite students to hypothesis about how |x| + 7 = 10 will be solved.
5min— Homework – Students must write a paragraph explaining what the |x| means and including a few examples of their own making.
- Prompt: Your research has gained national attention and you need to write a one paragraph summary (at least 7 sentences) for newspaper publication explaining your techniques and findings. An original example must be included.
- Extra Credit Extension: |x| has been found in expressions and equations in nearby tombs. In a second paragraph, develop a hypothesis about how |x| + 7 = 10 will be solved OR how a negative number placed in |2x| + x would be evaluated.
- For the negative number review, the distance you walked to school can be a good example. Have +1 mile represent the distance to school and -1 mile represent the distance home. Overall, if you’re trying to figure out where you are at the end of the day, you’d add the positive mile and negative mile together to get 0 miles away from home. For tomorrow’s warm up or as part of class wrap up, you can introduce the idea that if you wanted to find the total distance walked (not just where you ended up), you’d do 1 + |-1| since direction wouldn’t matter.
- Keep things fun! Props like clip boards or a few lab coats can help your researchers get into their roles.
- If short on time, omit the “Key Code” questions or move them to homework.
- To encourage time on task, you can have each senior investigator working on separate boards with their teams of field researchers. Class notes are then moved to a single white board as part of a peer review process. The most successful research group will receive National Science Foundation funding (or be first dismissed from class)!
- Choose students who are not shy and who might have trouble with sitting still as your senior researchers. Advanced students also often like the Senior Researcher roll.
- You can also have two folks working at the boards as “Research Recorders” that your senior researchers report to if you need to have roles for more students.
- Pair a student who is likely to struggle with a stronger, helpful student.
If notes are kept in a binder by each student, just mark them with a plus, check, or minus in a brightly colored pen as you circle the room. Later, a TA or you can count up the total number of pluses, checks, or minuses to calculate an overall grade for the notebook. Commonly, plus is 100%, check is 75%, minus is 50%, and 0 (earned if nothing is there or the students significantly disrupted) is 0%.
Alternately, if using a 10 point scale and collecting the notes and the homework paragraph the next day as a single assignment the following rubric can be used:
Notes and Paragraph Rubric
- 5pts – Class notes are neat, complete and clear. Points can be lost from this section if student was disruptive the previous day.
- 3pts – The paragraph explaining absolute value uses complete sentences that successfully communicate the meaning of |x|.
- 2pts – An original example is included and is correct.
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