Beginning Algebra: Visualization

Lesson: Rules of Exponents Visualization

Essential Understanding:
Use a visualization practice to remember the rules for exponents.

Visualization picture and explanation handout.

Instructional Format:
Teacher-led instruction

Student practice Vocabulary for a Word Wall:
exponent, base, scientific notation, monomial

Prior Knowledge/ Possible Warm-up Activities:
Students need to be introduced to the rules of exponents.

Time needed:
20 minutes for introduction to pegging/20 minutes for visualization exercise.

(I use an exercise in pegging to help students before this visualization. It isn't completely necessary, students can just look at the picture and make the connections as listed.)

1. I either review pegging with the students or introduce pegging. Pegging is a method to help the brain attach meaning and connections to new material by using material that people already know. In order to memorize pegging with beginning students I start with the numbers 1-10. When I have the students learn the numbers and items, they have to do the hand motions as well. I usually have the students practice in partners and learn the numbers and their "peg" by heart before moving onto a visualization.

  The pegs for the numbers 1-10 are the following:

Number #1 "Sun "there is only one sun. (hand motion is a circle using both hands up over the head)
Number #2 "Eyes" because there are 2 eyes. (hand motion is two fingers up to the eyes, then turned out)
Number #3 "Triangle" because it has three sides. (hand motion is both hands up with index fingers and thumbs making a triangle)
Number #4 "Stove" because it has 4 burners. (hand motion is one hand moving across all 4 burners)
Number #5 "Hand" because there are 5 fingers. (hand motion is waving goodbye)
Number #6 "Sticks" because it rhymes. (hand motion is miming picking up sticks)
Number #7 "Dice" because of lucky number 7. (hand motion is miming shaking and rolling dice)
Number #8 "Octopus" because it has 8 tentacles. (hand motion is four fingers on each hand spread out and swimming)
Number #9 "Line" because it rhymes. (hand motion is drawing a straight line in the air)
Number #10 "Hen" because of big fat hen. (mime flapping arms like a chicken)

2. Once students know their "pegs", I show them this visualization picture and explain how each part of the picture attachs to the peg and to the picture. I have the students practice the pegs outloud and say the picture and rule together many times. Then I hand out the explanation for students to have a copy for their own reference.

3. Show different problems concerning exponents and have the students process through the pegs to access the rule and then solve the problem.

Assessment (Acceptable Evidence):
Any Test/Quiz on exponents 

Attached worksheets or documents:
Visualization Picture Description (pdf)

Cautionary notes/ misconceptions:
I use pegging often with students to help them remember new information. It is an efficient method for learning new information and can be used in any subject area. There is also a visualization exercise that I have created for Solving Systems of Linear Equations (Visualization Systems [pdf]).


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