Goal-directed Instructional Design Plan - Introduction to Algebra and Geometry
Introduction to the Laws of Exponents
Author - Deborah Johnson
1.
A problem or a need:
The problem of practice in my Introduction to Algebra and Geometry classroom is that there
is a varying degree of student understanding when simplifying exponents. The goal will be
to use a goal-directed instructional design plan that provides students with differentiated
instruction through the use of technology as students explore how to simplify exponents
using the Laws of Exponents.
2.
A real-world performance:
It is important for my students to be able to take mathematical situations and learn how to
break the problems into a series of logical steps to be solved. This process of simplifying
exponents can be transferred into the real-world as students are in careers that require
taking complex situations, identifying the key elements, and then recognizing a process to
solve the problem.
3.
An instructional objective:
In the assessment, students should be able to:
a.
b.
4.
Demonstrate the ability to simplify expressions containing integer exponents
(perform a skill)
Recall facts about the laws of exponents (ex: subtract exponents when dividing
expressions with the same base, add exponents when multiplying expressions
that contain the same base, etc.)
A set of essential content:
In addition to an ability to perform basic arithmetic, students will need to understand the
underlying definition of exponents to understand the laws of exponents. This skill will be
evaluated as students use the online applet to simplify a number of expressions containing
integer exponents, as well as a final test at the end of the unit.
Students will also need problem solving skills to be able to differentiate the different
components within each expression and decide upon the order to solve the problem. Based
upon the need, some students will rely on the guidance of technology to initially learn this
process.
5.
An evaluation consisting of a test or observation:
Students will initially be evaluating their progress through the guidance of the applet, which
indicates whether their answer was correct. Should a student find an error, the applet
guides them through the thinking process and highlights the misconceptions.
Upon completion of the lesson, students will be able to demonstrate their knowledge of the
material through demonstration of skills on a test.
Michigan State University, Educational Technology Programs
http://edutech.msu.edu
6.
A method to help participants learn:
Lesson 1:
1. Students review the basic definition of an exponent by completing a K-W-L warm-up
activity. After discussing the graphic organizer with an elbow partner, students will
complete an “expansion” activity to discover the different “Laws of Exponents” and
make conjectures about the relationship amongst the exponents. Students can
complete this activity by choosing from two different options: A. On a piece of
paper, “draw out” the expansion of the different exponential problems being
simplified. B. Using cube manipulatives for each variable, physically count out the
different scenarios being represented in the problem. Ask students to make
conjectures about what they are discovering as they complete this task.
2. Whole-class discussion finalizes student discovery and defines the Laws of Exponents
(Product of a Power, Power of a Power, etc). Have students fill in the “rules” in their
own words into a graphic organizer. Ask students to additionally include an example
for each Law of Exponents.
Lesson 2:
1. Using the Math Interactives applet, ask students to begin on the “Explore It” tab of
the lesson. This part of the lesson will provide an additional way to continue student
exploration about the meaning of the Law of Exponents. Students may use the “Print
Activities” lesson to guide their thinking about the lesson.
2. Upon completion of the “Explore It” tab, students will then have the opportunity to
complete the “Use It” tab. In this tab, students will explore simplifying expressions
that contain integer exponents. Students will be guided through the program at
their own pace and skill level, receiving appropriate feedback when solutions are
incorrect. Inform students that their end goal will be to complete all four sections of
the applet. Instruct students that they should print their final answers to
demonstrate mastery of the goal. This will be their personal method for monitoring
progress. The teacher will continuously monitor and engage in further feedback with
students, as the need is presented.
To accommodate DHH and ESOL students (based on my students for 2010-2011 school
year), there are several online resources that students can use in addition to the Math
Interactives lesson resource:
Specifically for my ESOL students and struggling readers:
 Natural Reader is a free download that will read-aloud any text on the computer.
Students could have the directions to the problems or the text explanations read
to them verbally to further cement understanding.
 Holt Multilingual Glossary is a free glossary that is provided by my student’s
textbook publisher. If my students type in the word that they do not recognize,
it will then provide a definition in both English and their chosen other language.
This particular Math Interactives program uses a lot of text to explain student mistakes,
which will accommodate my DHH students. The above glossary, however, will also be
useful for my DHH students since they often have gaps in vocabulary. The glossary
provides many visuals in addition to the definition.
Michigan State University, Educational Technology Programs
http://edutech.msu.edu
●
Motivation:
○
Meaningfullness
Through the use of expansion (drawing), discovery, and then application on the
applet, students are able to see value in the process of moving from conceptual
learning to instrumental learning. The applet provides a level of instant feedback,
helping struggling students to gain confidence as well as learn from mistakes. In
addition, the applets “game” element provides students motivation to simplify all of
the problems.
○
Pleasant consequences
Since mathematics often reflects “solving a problem” the activity will allow students
to feel the confidence of being successful in analyzing multiple situations and finding
the desired result. Compared to paper-and-pencil practice, the student will feel
instant success in achieving the goal of understanding how to simplify exponents.
○
Novelty
In the particular math applet, increased engagement can arise as they find various
“bones” through a paleontological dig. Each time that a student finds a “bone,” they
are asked to solve an exponent problem using the various laws. This can provide
incentive for students to complete the problems.
●
Socialization
Students can engage in elbow-partner discussion as well as a whole class discussion
about the Law of Exponent discoveries found from expanding exponents.
●
●
Audience
○
Age
o 8th Grade Students
○
Demographics of Students
o Regular Education Students
o Deaf and Hard of Hearing Students
o English Speakers of Other Languages
○
Skill level
o Basic Algebra Foundation
o Varying levels of technological skills
○
Prerequisite knowledge
○ Varying levels of technological skill
Technology Needs
o
o
o
Class Set of Computers for 30-45 minutes
High-Speed Internet
Math Interactives applet
Michigan State University, Educational Technology Programs
http://edutech.msu.edu