Using Models to Solve Equations

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Presentation transcript:

Using Models to Solve Equations

An equation is a statement that says the value of one expression is equal to the value of another expression. Solving equations is the process you used to determine the value of the unknown that makes the equation true. This is called the solution.

Using Models to Solve Equations – Balance Scale Model – page 319 Herman is in the last round of the spell-a-thon in his school. A contestant receives 3 points for every word spelled correctly. Herman has 42 points. How many words has he spelled correctly? Let h represent the number of words Herman has spelled correctly. Then, the number of points is 3 times h, or 3h. Since Herman has 42 points, the algebraic equation is 3h = 42. Use a balance-scales model to represent this equation. On the left side, show masses to represent 3h. On the right side, show a mass to represent 42. Since there are 3 identical unknown masses in the left pan, replace 42 g in the right pan with 3 equal masses. Each mass is 14 g. So, each unknown mass is 14 g. h = 14 Herman has spelled 14 words correctly. Check: 3h = 42 3(14) = 42 42 = 42 The solution is correct.

Tile Method The solution is j = 8. Jodee is also a contestant in the spell-a-thon. A contestant receives 3 points for every word spelled correctly. Because of a technical penalty, Jodee loses 5 points. She now has 19 points. How many words has Jodee spelled correctly? Let j represent the number of words Jodee has spelled correctly. Then, the number of points she receives is 3j. When the penalty is considered, the number of points is 3j - 5. So, the equation is: 3j – 5 = 19 The solution is j = 8. Jodee has spelled 8 words correctly. Check: 3j – 5 = 19 3(8) – 5 = 19 24 – 5 = 19 19 = 19 Solution is correct.

X X Draw the equation and then solve: 2x + 4 = 8 Remove 4 blank squares from both sides. Now there are 2 identical unknown masses on the left side and need to arrange the weights into 2 equals groups. x = +2

Draw the model then solve x +4 = -7 x = -11 x – 3 = -6 x = -3 -1 +x -2x +2 -5 = 3x -2 +3 -2x +2 = -4x -4 x = -3 x = 1.25

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