Expressions and Equations / Using Structure to Solve Equations

Understanding

Students develop an understanding of the logic of equation solving by recognizing the overarching structure within the equation.

What to look for

In the equation 2(x + 4) = 32, students can recognize that the value of x + 4 is the answer to the question "2 multiplied by what number is 32?

Sample Assessment

The solution to the equation -3x - 29 = -5 will also be the a solution to which of the following equations?

a. 3x = -24
b. 3x = -24
d. 3x - 30 = -6
c. 3x - 30 = -6

Answer: a. 2x = -24 and d. -3x - 30 = -6

The Big Idea

Visualizing the arithmetic structure of expressions in an equation can help in thinking about how to find the solution for the equation- a value or values that will make the equation true.

What are the students doing?

Students highlight portions of linear equations and give a value for the highlighted expression that makes the equation true.

What is the teacher doing?

The focus is on thinking carefully about the structure of the equation and using that structure to create simpler sub equations that develop the logic for solving equations.