Less Is More: Scaffolded Math Problems

Typically, a math problem is presented as a long and fairly complex situation. First, the student has to read the text (which can be a challenge in itself), and then analyze it to figure out what information is needed to solve the problem.

In a scaffolded problem, the situation is much more stripped down. The student has to ask the teacher for the specific information needed and explain why they need it. If their reasoning is sound, the teacher gives them a mathematical clue.

A scaffolded problem isn’t just an application of mathematical concepts. Drawing on everyday life, it encourages students to develop new problem-solving strategies. Step by step, students piece the problem together—figuring out what information they need, calculating with it, then figuring out what they still need next.

For example: let’s say someone in a student’s family wants to plan a trip to Europe. To figure out the cost of the trip, the student would need to track down the necessary information. This means finding things like airfare, the number of hotel nights, and the distances between destinations. Scaffolded problems place students in exactly this kind of scenario. It teaches them to think about what information they need, rather than having it provided in advance. 

The benefits to scaffolded problems include:

• Encouraging students to collaborate and communicate—they have to discuss and agree on which information they need. 
• Reducing cognitive load—there is little reading and no initial data to work with.
• The concept is easier to grasp and closer to a real-life problem-solving situation. 
• Engaging students in learning through problem-solving.
• Giving teachers an opportunity to probe students’ thinking and understand their mathematical reasoning.

A scaffolded problem takes some preparation, but with the right approach, it can be a genuinely rich math-learning experience.

Before the activity, cut out the clues into individual strips. Each clue should have the same number of strips as there are groups in the class (each group should receive one copy of each clue).

Here’s how a scaffolded math problem typically unfolds in the classroom.

1. Read the situation to the students
   • Explain the situation to the whole class.

2. Divide students into groups of 3 or 4
   • Group those with a similar math level together—this helps ensure that all students get a chance to contribute.
   • Provide work materials (whiteboards or large sheets of paper, markers, math workbooks, tokens, base ten blocks, etc.)

3. Explain how the activity works
   • Students work together to figure out what information they need to solve the math problem. 
   • One student per group comes to the teacher to tell them what information their group needs and explain their reasoning.
   • Each time a group gets a new piece of information, they regroup, figure out what else they need, and go back to the teacher as needed. Step by step, the full picture of the problem comes together as they collect more and more clues.
   • Once they have all the clues they need, each group puts all the data together and attempts to solve the problem.

4. Get feedback from the students
   • Take a moment to gather students’ thoughts on the activity and collect all the clues.