4.2: Variables on Both Sides
This activity is intended to supplement Algebra I, Chapter 3, Lesson 4.
ID: 11131
Time Required: 1520 minutes
Activity Overview
In this activity, students will encounter various scenarios involving perimeter of polygons. The students will write equations and solve them in order to answer the questions provided.
Topic: Solving Equations with Variables on Both Sides
 The student will use algebraic expressions to form equations relating two different perimeters to each other.
 The student will solve equations with variables on both sides.
 The students will use the App4Math to check their answers.
 The student will answer a deeperlevel inquiry question regarding the relationship between two regular polygons and the difference in their perimeters for different lengths of sides.
Teacher Preparation and Notes
 Teacher preparation must include having students set up and solve equations with variables on both sides. These equations include the Distributive Property.
 Students should also be encouraged to show their work, whether it be on paper or in the document itself. If the teacher prefers paper, then use a prepared handout labeled by tab number to correspond to the tabs in the .tns file.
 Be sure the App4Math is installed on all calculators.
 To download the App4Math application, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=11131 and select "App4Math.8xk" to download.
Associated Materials
 Student Worksheet: Variables on Both Sides, http://www.ck12.org/flexr/chapter/9613, scroll down to the second activity.
 App4Math Application
Introduction to App4Math
You may want to take a few minutes introducing App4Math to your students.
A few quick notes:

x,y,z , etc. can be entered using the alpha keys or by repeatedly pressingX,T,θ,n .  Use
2nd [MATH] for the equals sign.  The up and down arrows can be used to cycle through previously written equations. This will help eliminate a lot of repeated key entry.
Have the students use the app4math to check if
Now have them check to see if
Problem 1 – A Square and a Rectangle Have Different Perimeters
Student should observe the labels for the length of the sides, and be certain to understand the translation from the text on the left side to the labels. Then, students are to write expressions for the perimeter of the square and of the rectangle. (Sample answers: Perimeter of the square:
Students will use the perimeter expressions to create and solve an equation that shows the relationship between the perimeters of the figures. (Answer: a.
Students should use the App4Math app to check their answer.
Problem 2 – An Equilateral Triangle and a Square with Different Perimeters
Students should again observe the labels on the polygons, and be sure that the labels agree with the written description. Then, students will write expressions for the perimeter of the square and triangle. Then, students will create an equation show the relationship between the perimeters and solve the equation to find the length the sides of the triangle and square.
Student worksheet solutions

Side of the triangle is
x and side of the square is2x+1 . 
The perimeter of the square is
4(2x+1) . 
The perimeter of the triangle is
3(x) . 
4(2x−1)=3x+19 
x=235 ; side of square is515 cm or10.2 cm  The correct App4Math screen is below.
Problem 3 – A Hexagon and an Octagon with Sides that are Related by a Scale Factor
Student worksheet solutions

x 
6(2x) 
8(x) 
12x=8x+20 ,x=5 , hexagon side length=10
Problem 4 – An Equilateral Triangle and a Rectangle that Share a Common Side
Student worksheet solutions

3x+9=14+2x, x=23
Problem 5 – A Regular Decagon and 15gon
Student worksheet solutions

Because the side lengths for both polygons all equal
x , the perimeter of the15− gon will be longer by the length5x because it has five more sides.
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