Original Discipline: Basic Algebra
The Student Struggle
Students often experience anxiety when approaching algebra word problems. Even when they understand mathematical operations, they may struggle to translate a written situation into an equation.
Some students immediately search for numbers and formulas without first understanding the problem. Others hesitate because they are afraid of choosing the wrong approach.
Intended Learning Outcome
Students will be able to interpret a word problem, identify relevant quantities and relationships, develop an appropriate mathematical model, and explain the reasoning behind their solution.
Thinking Students Practice
Primary Capacity: Transfer & Application
Students apply familiar mathematical concepts to situations presented in written language rather than as straightforward equations.
Secondary Capacity: Metacognition
Students examine how they approach unfamiliar problems, recognize where they become stuck, and identify strategies that help them move forward.
The Learning Activity
Students work through an unfamiliar word problem using a structured reading process before attempting calculations.
Instead of immediately identifying an equation, they first describe the situation, determine what needs to be found, and identify the relevant mathematical relationships.
Students then work together to develop a solution, explain their approach, and compare alternative strategies.
The emphasis is on understanding how a mathematical model is constructed rather than simply arriving at the correct numerical answer.
Try This With Your Students
The Community Event Budget
The Scenario
Your student organization is planning a community event.
A local company charges a $75 setup fee plus $12 for each table rented.
Your organization has a total budget of $255 for tables and setup.
Your challenge is to determine how many tables you can afford and explain how you reached your answer.
Your Challenge
Step 1: Understand the Situation
Read the problem without attempting calculations.
Explain in your own words:
What is happening?
What are we trying to determine?
What information is important?
Step 2: Identify Relationships
Read the problem again.
Identify which cost stays the same and which cost changes depending on the number of tables.
Explain how those costs relate to the total budget.
Step 3: Build a Mathematical Model
Create an equation representing the situation.
If you are unsure how to begin, imagine that someone tells you the organization can rent 10 tables.
How would you check whether that answer fits the budget?
Use that process to help construct your equation.
Step 4: Solve and Explain
Determine the maximum number of tables the organization can afford.
Explain what each part of your equation represents and how you know your answer is reasonable.
Step 5: Compare Approaches
Discuss your solution with another student or group.
Did you begin in the same way? Did you use the same equation or strategy?
Share Your Thinking
Write a short explanation addressing:
Which part of the problem was most difficult to understand?
What helped you move from the written description to an equation?
How did you check that your answer made sense?
Which strategy would you use the next time you encounter an unfamiliar word problem?
Remember: The goal is not simply to find an answer. It is to understand how to turn a situation into a mathematical model and explain why that model works.
Making Student Thinking Visible
Students submit their equation, solution, and an explanation of how they interpreted the problem.
The instructor looks for evidence that students understand the relationships among the quantities rather than simply substituting numbers into a familiar formula.
Students' reflections provide additional information about which problem-solving strategies they understand and when they recognize the need to adjust their approach.
Adapt This Scenario
The underlying instructional approach is to separate understanding a problem from selecting a solution method.
Healthcare: Students identify relevant information in a dosage calculation or resource-allocation problem before performing calculations.
Business: Students interpret a pricing or budgeting situation and develop an appropriate financial model.
Information Technology: Students translate a client's technical requirements into measurable constraints before recommending a solution.
Science: Students identify variables and relationships in a scientific problem before selecting formulas or calculations.
Across disciplines, students learn to interpret a problem, identify what matters, choose an approach, and explain their reasoning.
Original AI Prompt and Faculty Revisions
The faculty contributors asked an AI system for strategies to help community college algebra students overcome anxiety about word problems and improve their ability to solve them.
The AI-generated response suggested several approaches, including number substitution, a three-read protocol, collaborative whiteboard work, and recognizing common problem structures.
The contributors noted that they particularly liked the three-read protocol and collaborative whiteboard approach.
This library version develops those ideas into a short, student-facing activity. The community event budgeting problem is a new illustrative example, not a problem included in the original submission.
The original contribution documents discussion of the strategies but does not include evidence of their subsequent classroom implementation.