Math Lab: Turning Calculations into Experiments for Grades 6-12

 

For many middle and high school students, math class feels like a constant march through abstract equations and repetitive problem sets. Meanwhile, science class offers the excitement of hypotheses, data collection, and tangible results.

What if we blurred the lines? By designing math activities as science experiments, we can leverage the inherent curiosity and investigative spirit of adolescents to build deeper conceptual understanding, especially for complex topics in algebra, geometry, and statistics.

The core difference between a math problem and a science experiment lies in the student’s role. In a math problem, the student seeks the known answer. In an experiment, the student seeks to discover a relationship or prove a hypothesis. This shift promotes agency and critical thinking.

Here's how to structure a math concept using the scientific method:

1. Formulate the Hypothesis (The Conjecture)

Start with the formula or principle, but frame it as an unproven idea.

• Standard Math: Find the area of the circle with radius r.

• Math Lab Hypothesis: "The area of a circle is directly proportional to the square of its radius ($A\propto r^2$). We hypothesize that the value of the constant of proportionality is approximately 3.14 (or π)."

2. Design the Experiment (The Data Collection)

Students collect data through physical activity or simulation, forcing them to use measurement and precision.

• Experiment: Students measure the diameter and calculate the radius of several circular objects (lids, coins, plates). Then, they wrap string around the circumference and use a precise cutting technique to estimate the area by filling the circle's shape with squares (or by using a balance scale to measure the weight of the cutout circle relative to a cutout square).

Three Ready-to-Run Math Experiments

1. The Projectile Motion Lab (Quadratic Functions & Physics)

• Concept: Modeling the parabolic trajectory of an object using a quadratic function, $y=a{x}^2+bx+c$.

• Experiment: Students build a small ramp or use a simple launcher to propel a marble or small ball. They mark where the ball lands from different launch heights or angles.

• Analysis: They plot the points of the trajectory on a coordinate plane, use regression (or a graphing calculator/Desmos) to find the best-fit quadratic equation, and then use the equation to predict where the ball will land next. The experiment validates the theoretical model.

2. The Statistical Sampling Trial (Bias and Probability)

• Concept: Understanding sampling bias and the law of large numbers.

• Experiment: Pose a controversial survey question to the class. Students then conduct the survey using two different sampling methods: 1) Convenience Sampling (asking only their friends) and 2) Random Sampling (using a random number generator to select names from a list).

• Analysis: Students compare the final statistics (mean, percentage supporting an idea) from the two groups. They conclude, based on their data, which sampling method produced a more reliable and less biased result.

3. The Exponential Decay of Foam (Logarithms and Exponentials)

• Concept: Modeling exponential decay and solving for variables using logarithms.

• Experiment: Students mix soda or dish soap and water to create a large volume of foam in a clear container. They measure the height of the foam every 30 seconds for 5 minutes.

• Analysis: They plot the data and confirm it follows an exponential decay model $H(t)=H_0{e}^{-kt}$. They then use logarithms to solve for k (the decay constant) or to predict how long it will take for the foam to reach half its original height.

By transforming math problems into labs, we not only make the learning relevant but also teach essential scientific process skills that transcend the math classroom.