Free Chances: A Simple Formative Assessment Strategy for Math
What if one of the most useful assessments you gave your students wasn't graded?
Free Chances are one of my go-to formative assessment strategies in math. They're short, ungraded assessments designed to give students a low-pressure opportunity to make mistakes while giving teachers a quick snapshot of what students understand and where they need help.
The idea is simple:
Give students a chance to show what they know before the learning is finished, then use what you learn to adjust your instruction.
Here's how I use Free Chances in my math classroom.
What Is a Free Chance?
A Free Chance is a short, ungraded formative assessment that focuses on the foundational skills students are currently learning.
I typically give students about 5 to 10 minutes to complete one at the end of class. It might contain only two questions, or perhaps four.
The goal isn't to measure everything students know. It's to identify common errors and misconceptions while there's still time to do something about them.
I tell students that this isn't a grade. In fact, I sometimes tell them I don't even care if they put their name on the paper.
That message matters.
We're reinforcing the idea that math class is about learning and growing, not simply collecting grades. Mistakes aren't something students need to hide. They're information that can help us figure out what to work on next.
Why Use an Ungraded Assessment?
It's easy for assessment to become synonymous with grades.
But formative assessment serves a different purpose.
Instead of asking, "What grade did this student earn?", I'm asking:
"What does this student understand right now, and what should I do next?"
That distinction changes how I approach the assessment.
When students know a paper is being graded, their attention can shift toward getting the answer right. With a Free Chance, the pressure is removed. Students can try, make mistakes, and show us where their thinking breaks down.
And that's exactly what I'm looking for.
When Should You Give a Free Chance?
I typically give a Free Chance somewhere between Day 2 and Day 4 of a unit, with Day 3 being the most common.
There are two competing considerations:
Students need enough time to actually learn and practice the concept.
Teachers need enough time remaining in the unit to respond to what they discover.
If you give the assessment too early, students may simply haven't had enough exposure to the material.
If you wait too long, you may discover a problem after students have already built additional learning on top of a faulty foundation.
The sweet spot is early enough to adjust instruction, but late enough to give students something meaningful to assess.
For longer units, I may give a second Free Chance. But I don't want to overuse them. Students should see these as useful opportunities to learn, not just another assessment routine.
What Should You Put on a Free Chance?
Keep it short, focused, and approachable.
I typically use what we call 80-level problems in our Standards-Based Grading system. These are foundational skill-level problems rather than the most challenging problems students will encounter in the unit.
That's intentional.
I'm not trying to find out whether students can solve the hardest problem in the chapter. I'm looking for common errors that could interfere with their learning as we move forward.
For example, if we're working with equations, I might include problems that reveal whether students understand how to:
Set up an equation correctly
Use inverse operations
Combine like terms
Maintain equality when solving
The questions should give you enough information to identify where the process breaks down without turning the assessment into a full test.
How I Grade a Free Chance
I don't.
That's the point.
Instead, I quickly look through the stack to find patterns.
My process is intentionally simple:
Look at each student's Free Chance.
If everything is correct, set it aside.
If something is incorrect, keep it for a closer look.
Sort the incorrect responses by the type of mistake.
Identify the two or three most common errors.
Keep an example of each common error.
Use those errors to plan the next day's instruction.
The whole process can take less than five minutes once you get used to it.
I'm not trying to analyze every individual response or assign a score. I'm looking for the big picture:
What are several students doing incorrectly?
That's the information I need.
Turn Mistakes Into Your Next Lesson
This is where Free Chances become much more than an assessment.
The results should change what you do next.
Suppose students are solving angle-pair problems, and the Free Chance reveals that several students are setting up the equations incorrectly.
I don't want to simply tell them, "You need to set up your equations correctly."
Instead, I can build the next day's warm-up around the actual mistake.
For example, I might:
1. Show the common mistake.
Have students analyze an incorrect solution and figure out what went wrong.
2. Practice the specific skill.
Give students several angle-pair situations where they only need to write the equation, no solving yet.
3. Reverse the thinking.
Give students an equation and ask them to create a diagram that would produce it.
4. Put it all together.
Finally, have students set up and solve several problems from start to finish.
Notice what happened: the formative assessment directly shaped the next lesson.
Without the Free Chance, I might have continued teaching the unit assuming students were ready to move on.
Instead, I discovered exactly where I needed to slow down.
The Vision Behind Free Chances
For me, Free Chances are about more than a particular assessment strategy.
They're one small way to communicate a larger vision for math class:
Learning takes time. Mistakes are part of learning. And grades don't need to be attached to every opportunity to show what you know.
Students need opportunities to practice, struggle, make mistakes, receive feedback, and try again without feeling like every attempt will affect their grade.
Teachers need opportunities to see what's happening beneath the surface of student work.
Free Chances give us both.
They're a simple formative assessment strategy, but the real power comes from what happens after the assessment.
Don't just collect the mistakes.
Use them to decide what students need next.
Try a Free Chance in Your Next Unit
For your next math unit, choose two to four foundational problems that target the most important skill students are learning.
Give students about 5 to 10 minutes. Don't grade it. Look for patterns. Find the two or three most common mistakes.
Then build your next warm-up around what you found.
That's the whole idea:
Assess. Notice. Adjust. Keep learning.
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