Using Diagrams to Model and Solve Equations

A step-by-step guide to using diagrams to model and solve equations

Modeling and solving equations using diagrams can be a visual and effective method for understanding mathematical concepts. Here is a step-by-step guide for students.

1. Identify the equation: Start by writing down the equation that you want to solve. Make sure it is a simple equation that can be solved using diagrams.
2. Draw a diagram: Draw a diagram that represents the equation. For example, if the equation is x + 2 = 5, you can draw a number line with 5 on one side and x + 2 on the other side.
3. Label the diagram: Label the diagram with the values from the equation. For example, in the number line, you would label 5 as “5” and x + 2 as “x + 2”.
4. Compare the values: Compare the values on each side of the equation and determine if they are equal. In this case, 5 and x + 2 are equal.
5. Solve for the unknown: If the values are equal, then you can solve for the unknown value, in this case, x. To do this, you can subtract 2 from both sides of the equation, resulting in x + 2 – 2 = 5 – 2, which simplifies to x = 3.
6. Check the solution: Finally, check the solution by plugging the value of x back into the original equation and making sure both sides of the equation are equal. In this case, x + 2 = 3 + 2, which equals 5.

By following these steps, you can use diagrams to model and solve equations visually and effectively.

Using Diagrams to Model and Solve Equations – Example 1

Graph the diagram that represents the equation, \(s-14=6\).
Solution:
The equation represents that if you have a number, s, and subtract 14 from it, it is equal to 6. Or if you have a number, s, it is equal to the sum of 6 and 14, \(s=6+14\).

Using Diagrams to Model and Solve Equations – Example 2

Graph the diagram that represents the equation, \(2f=12\).
Solution:
The equation represents that if you have a number, f, and multiply 2 by it, it is equal to 12. Or if you have a number, f, it is equal to the multiplication of 2 in f, \(2f=12\).