Submitted by Submitted by Jacqui Ochoa, Kurt Walker, and Randy Davis, Trabuco Hills H.S., Mission Viejo, CA. (first published in The Math Projects Journal, Nov/Dec 1997)

One of the reasons students have a tough time learning to solve equations is that many do not really know what the algebraic equations represent. In particular, they do not understand the concept of a variable. We discovered this through a new assignment called the “Student-Generated Word Problem,” The student is asked to: write a word problem that can be solved by using an equation, write and solve the equation relating the solution to the original word problem.

Here are some examples of the traditional problems the students had previously experienced:

Question #1: You have three boxes of pencils and you lose 5 pencils. You then buy another box. If you now have a total of 37 pencils, how many are in each box?
Equation #1: 3x – 5 + x = 37

Question #2: The length of a rectangle is 2 more than 3 times the width. If the perimeter is 36,
what are the dimensions of the rectangle?
Equation #2: 2w + 2(3w + 2) = 36

The students were familiar with a variety of word problems for which they would be asked to write and solve the equations. Our fear was that they would simply copy one and submit it. Here is what we received instead:

Student #1: I have 5 Great Danes and 4 Poodles. I get another Great Dane. How many dogs do I have?
Equation #1: 5g + 4p + 1g
Answer #1: 10

Student #2: I have 4 shirts. I buy three more. I sell ten. I get left with 4 shirts. How did I get 4?
Equation #2: 4s + 3s – 10 = 4
Answer #2: s = 2

In the first example, the student created a logical question that did not need algebra to solve. The second student created an illogical question, then correctly solved an unrelated equation. In both cases, there was no cognitive connection among the word problem, the equation, and the solution. This assignment told us volumes about how little our students really understood algebra, even if they could do algebra.

Consequently, we offered them equations for which they were required to write a problem. Eventually our students developed a stronger understanding as demonstrated below.

Equation: 5x -3 = 3x + 10
Answer: On Monday, Joe bought 5 boxes of apples and ate three on the way home. On Tuesday, he bought 3 boxes and a friend gave him 10 more. He noticed that at the end of each day he had the same amount of apples. How many apples were in each box?

Through these assignments, the students’ understanding of the word problems improved, as did their ability to solve algebraic equations. The Student-Generated Word Problem was not only a powerful assessment tool, it proved to be an effective instructional instrument as well.

Nearly 30 years after creating this activity … Edutopia publishes, “Student-Created Math Word Problems Help Motivate Deep Learning” (Jan 2026)