The Linear Equations Game

Kandace Norby
Math Activity Report 3 – July 2010
Equations

A title for this activity: Linear Equations Game
Source for this Activity: http://www.educationworld.com/a_tsl/archives/07-1/lesson016.shtml
Subjects: Algebra / Equations
Grades: 6-8

Brief Description: Game cards help pair up students to solve linear equations for the value of a variable.

Objectives: Students practice solving linear equations for one variable.

Keywords: equation, linear equation, variable, algebra

Materials Needed:

• a set of cards with equations written on them (see Before the Lesson below)
• notebooks/paper
• chalk and blackboard, or markers and whiteboard

Link to MN State Standards: http://education.state.mn.us. Grade 6, Algebra, 6.2.1.1

“Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and mathematical problems.”

“Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts.”

The Lesson:

Before the Lesson....

This game is planned for use with 30 students; however, more cards can be made for play in a larger-sized class. Students might help you to prepare the 30 game cards, or the cards might be prepared in advance. Each card should have a letter of the alphabet (in this case, A to O) written on it along with a linear expression; there will be two different cards with the same letter and different linear expressions. For example, see the list below. For the letter A there are two cards:
• one card has A written on it with the linear expression 4x + 2 -8x
• the other card has A written on it with the linear expression 3x Create additional pairs of cards with the following letters and linear expressions.

Card Expression On Card 1 Expression On Card 2 Answer
A 4x + 2 - 8x 3x x = 2/7
B 6 x - 7 0 x = 7/6
C 7 – 10z 17 z = -1
D 6x + 16 2x - 12 x = -7
E 6 - 5x 13x x = 1/3
F 14y +7 -6 y = -13/14
G 8x – 4 -6 x = -1/4
H 7 - 5x -10 x = 17/5
I 6x - 17 9x x = -17/3
J 10x + 7 17 x = 1
K 20x + 10 4 - 10 x = -4/5
L 15p - 5 10p + 10 p = -3
M 11x + 33 55 x = 2
N (6x -5)/2 (3x +6)/2 x = 11/3
O 5x – 3x + 7 -7 + 8x x = 7/3

If you have a class of 30 students, shuffle the set of 30 cards and distribute a card to each student. (If you have fewer or more students, shuffle a set of letter cards for each pair of students.) Allow students who get the same alphabet cards to sit together and solve the equation for the value of the variable. For example, the pair of students who got the two cards with the letter A on them will solve for x in the linear equation

4x + 2 - 8x = 3x

Once students have solved their equations, you might place lettered slips (in this game’s example, one slip with each letter A to O) in a bowl or hat. Draw out a slip and read the letter that is written on it. Invite the pair of students who have that letter on their cards to come up to the board to show how they solved their equation. If they do it correctly they win that round of the game.

Assessment:

Let all student pairs who correctly solved their equations play another round of the game (with new cards or the same ones). With each repeat of the game, you will eliminate more pairs of students. Play until you have a final winner (a pair of champions).

Thus, the game can be used to motivate and provide drill in solving linear equations in one variable.

Below you will find the step-by-step solution to each of the equations.

Card A
4x + 2 - 8x = 3x
4x - 8x - 3x = -2
-7x = -2
x = 2/7

Card B
6x – 7 = 0
6x = 7
x = 7/6

Card C
7 - 10z = 17
-10z = 17 – 7
-10z = 10
z = 10/-10 = -1

Card D
6x + 16 = 2x – 12
6x – 2x = -12 – 16
4x = -28
x = -28 /4 = -7

Card E
6 - 5x = 13x
-5x - 13x = -6
-18x = -6
x = -6/-18
x = 1/3

Card F
14y + 7 = -6
14y = -6 – 7
14y = -13
y = -13/14

Card G
8x – 4 = -6
8x = -6 + 4
8x = -2
x = -2/8 = -1/4

Card H
7 - 5x = -10
-5x = -10 – 7
-5x = -17
x = 17/5

Card I
6x – 17 = 9x
6x - 9x = 17
-3x = 17
x = -17/3

Card J
10x + 7 = 17
10x = 17 – 7
10x = 10
x = 10/10 = 1

Card K
20x + 10 = 4 – 10
20x = 4 – 10 – 10
20x = -16
x = -16/20 = -4/5

Card L
15p – 5 = 10p + 10
15p – 10p = 10 + 5
-5p = 15
p = 15/-5 = -3

Card M
11x + 33 = 55
11x = 55 – 33
11x = 22
x = 22/11 = 2

Card N
(6x-5)/2 = (3x+6)/2
[The numerators are equal as the fractions are equal and the denominators are same.]
6x – 5 =3x + 6
6x - 3x = 6 + 5
3x = 11
x = 11/3

Card O
5x -3x + 7 = -7 + 8x
5x - 3x - 8x = -7 – 7
-6x = -14
x = -14/-6 = 7/3

Submitted By Ms. Madhavi Dhande, Sree Chaitanya Public School in Delhi, India
Education World® Copyright © 2007 Education World


* What introductory information is necessary for children to have prior to starting this activity?

The following information would be necessary before students start this activity: introductory algebra, basic linear equations, multiplication, division, subtraction and addition.

* What grade level/s is appropriate for this activity? Please use appropriate justification for your answers here.

I would definitely teach this activity to the 6th -8th grade students. It captures math concepts that students have worked on and is now ready to advance their thinking to a deeper level with the equations. Also, it allows students to refresh their math skills such as multiplication, division, subtraction and addition by working on these equations, too. This is the stepping stone for students to build upon their skills at this grade level.

* How will you engage students with different learning styles?

This activity is a great way to reach all learning styles. For example, you could pair an advanced student with a lower ability student. The students could learn from each other by teaching or asking questions and getting one-on-one attention. Also, students’ can learn from each other because each pair has to write out the equation on the board and explain how they solved it. This will help every student in the class because they get to see how they solved the problem. This will help the visual learners and auditory learners, too. What’s great about this is that students can write down the math problems that are up on the board and use them as examples on how to solve their own math problem. I really believe that collaboration is essential to learning and this activity allows students to learn from each other and themselves!

* How does this activity connect to the real world for students? Be specific.

Students can use this equation help figure out real world problems. Such as, how they can start saving for a car. For example, a student wants to buy a car for $5,000.00. They can use the following equation to help figure it out: (12x = y) how much is needed to be saved each month to reach their goal purchasing a car. If variable x=$100.00 a month then total saved for the year is $1,200.00. By changing the variable x, they will see the different savings. So if they are saving for a $5,000.00 vehicle, they will understand that it will take them approximately 4 years and 2 months to reach their goal.
* Why is this activity with its concepts important for student learning? Be specific.

This will prepare students for the next level of math classes such as advanced algebra, pre-calculus, calculus and other college courses etc.. It is also a fun way to get students involved and gets hand on participation by seeing students present their problems and explain their problem solving methods. This will help deepen the understanding for students. It also places ownership and accountability on the student for figuring and solving their math equations because they have to present it to the class and explain it.

* What are your comments on this activity? Would you use it in your classroom?

Yes, I would definitely use this activity in my classroom! I think this is a great activity because gets the student physically and mentally engaged in the problem solving process. I love that they have partners who they can bounce their ideas or questions off each other. This can be less intimating for many students who don’t like to raise their hands for help. I also like that students have to teach, explain and present their math problems to the class. This would give the students who like to sit back and day dream during class an incentive to pay attention and figure out the math problems. Lastly, the problems can be made harder to challenge students as they develop the skills to move on to the next level. Even though there is a winner at the end of the activity, all students are winners because they are benefiting from all the discussions and math problems that are displayed and solved on the board.