Ready-to-use classroom activity
Students create their own problems or questions based on given content, developing deeper understanding through reverse engineering.
Grade range
Works across
Activity style
Classroom walkthrough
One concrete example you can borrow, adapt, or teach as written.
Example lesson context
Gather these before class.
What to have ready before students begin.
Create a set of shape cards with rectangles and squares of different dimensions. Develop problem posing templates with sentence starters and structure. Prepare example problems that show different ways to ask questions about area and perimeter. Design a quality criteria checklist for evaluating created problems.
A classroom-ready sequence from launch to follow-up.
Introduction to problem posing (5-7 minutes):
Explain that mathematicians don't just solve problems—they create them
Discuss how creating problems helps deepen understanding
Show examples of different types of area and perimeter problems
Review core concepts (8-10 minutes):
Brief refresh of area and perimeter formulas and relationships
Practice a few example problems that illustrate key concepts
Highlight connections between area and perimeter (e.g., shapes with same area but different perimeters)
Guided problem creation (10 minutes):
Model the process of problem posing using a simple rectangle
Demonstrate different question types you could ask:
Calculation problems: 'Find the area of this rectangle.'
Comparison problems: 'Which shape has the greater perimeter?'
'What if' problems: 'What happens to the area if I double the length?'
Reverse problems: 'The area is 36 square units. What could the dimensions be?'
Use think-aloud to model the thought process for creating good problems
Problem posing practice (15-20 minutes):
Distribute shape cards and problem posing templates
Students create at least three different problems about their shape
Each problem should be different in type or complexity
Students include answer keys for their problems
Teacher circulates to provide guidance and feedback
Problem evaluation (5 minutes):
Review the problem quality criteria:
Clear wording with specific information needed
Mathematically accurate and solvable
Appropriate challenge level
Creative or interesting approach
Students self-assess their problems using the checklist
Problem exchange (10-15 minutes):
Students swap problems with a partner
Try to solve each other's problems
Provide feedback using evaluation form
Discuss any unclear wording or challenges
Revision and finalization (5-7 minutes):
Students revise their problems based on feedback
Create final versions for class problem collection
Extension: Create a class problem solving book with student-created problems organized by type and difficulty.
Adjust the activity without losing its core purpose.
For struggling students, provide more structured templates and simpler shapes. For advanced students, encourage creating multi-step problems or those involving irregular shapes. For visual learners, emphasize drawing and diagramming in problem creation.
Use these signals to assess understanding.
Evaluate created problems for mathematical accuracy, clarity, creativity, and appropriate challenge level. Assess students' ability to solve peers' problems as evidence of concept understanding. Note which problem types students gravitate toward creating, as this reveals comfort levels with different concepts.