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Linear Equations Game

Subjects

  • Algebra

    Grades

    • 6-8
    • 9-12
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    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[shopmaterials]

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

    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 games 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

    05/02/2007

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