Systems+of+Equations



Students: EmilyRose Sherman, Tiffanie Meridth, Megan Gosnell, Matt Lininger Inspector X and Y  **Introduction:** This game provides students the opportunity to practice their skills in solving linear equations using single or multiple variables. This game is intended to be adjusted to meet the needs of multiple grade levels, accommodations for struggling students, and higher level learners are provided throughout the lesson plan. It is intended to be played with 2 players of similar abilities to incorporate competition and speed. This game may be used for warm-ups, practice activity, and formative assessments. **Objectives:** I can solve systems of linear equations by using substitution, elimination, or graphical representation.

8. Analyze and solve pairs of simultaneous linear equations. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6
 * Standards**: CCSS Expressions and Equations 8.EE

**Instructions:** Level: 8-10 Skills: Solving Systems of Liner Equations

Players: 2 of equal skill level

Materials: 1 Deck of Cards/group, Ace-King (Ace=1, Jack=11, Queen=12, King =0), Black cards are positive and red cards are negative numbers, calculators (for checking answers only), paper, pencil

Getting Started: The goal of the game is to be the first player to 10 or have the highest points at the end of the time limit set by the teacher. To begin, both players must record the following game board to work with throughout the game:

number of card x + number of card y = number of card

2x-11/4=1 2x=15/4 X=15/8 or 1 7/8 ||  -36y=9 y=-1/4 Check Answer 2(15/8)+11(-1/4)=1   30/8+-11/4=1    30/8-22/8=1    8/8=1 or 1=1  ||
 * Player’s One’s Cards ||  Player Two’s Cards  ||
 * 2,11,1 ||  6, -3, 12  ||
 * Player one then Player two chooses three cards. Laying them in order the cards were chosen. Then the players records and solves for x and y. The first player to solve correctly earns one point. Handicap-If at any time in the game a player is ahead by 3 points they the other player receives a 5 second head start to solve the problem. ||
 * 2x+11y=1 ||  6x-2y=12  ||
 * 2x=1-11y ||  6(1/2-11/2y)-3y=12  ||
 * X=1/2-11/2y ||  3-33y-3y=12  ||
 * 2x+11(-1/4)=1
 * note there are several different methods to solve systems of equations. You may use which method you feel is the quickest for you.

The player who finishes first gets one point. However, both players must complete the finish the system to determine if the answer the first player done is correct. If the players disagree on the correct answers, both players will check their answers. The person who came up with the correct answer receives the points. (If the player that was done first answer ends up not being the correct answer, the point will go to the other player if his or her answer was correct.

Variation I: All cards are positive

Variation II: Tournament style. Teams which finish early may face the winner and losers of another team. First to five wins or to time limits set by the teacher.

Variation III: Struggling students: Students will be matched with similar abilities. Students which are struggling solving systems of linear equations may use one the following game board for linear equations.


 * 1) number of card x+ number of card = number of card
 * 2) number of card x + number of card = number of card x + number of card
 * 3) number of card x + number of card = number of card x

Or using the original equation. Player one draws one card. That card is the “x” value. Player 2 draws 3 cards and enters the numbers into the equation. Players then solve for “y.”


 * cards may be remove from the deck to create simpler problems which only use single digit numbers.


 * Questions:** Does it matter which variable you solve for first? Explain

Does it matter which equations you solve for first? Explain

How can you check your work?

When would use systems and equations in your everyday life? How can this process make your everyday life easier?
 * Possible teaching strategies**: Different ways to solve Systems of equations: Substitution Method, Elimination Method, Graphical Method.
 * Comments on teaching your lesson:** When teaching how to solve linear equations, I found students achieved a higher comprehension level when I had students come up to the board and solve the systems then had those students lead groups or help their neighbors. This provided more possibilities for the students to learn the information in different ways. If your students do not have the concepts of linear equations fully mastered. This game has provided multiple techniques to accomplish that and help the students work at their own level.

Currah, J. & Felling J. (2001). Radical math. Edmonton, Alberta: Box Cars & One-Eyed Jacks.