Saturday, March 14, 2026

The famous 3-question diagnostic often used by math educators is the Cognitive Reflection Test (CRT) created by Shane Frederick.

It reveals whether a person relies on quick intuitive answers or careful analytical thinking—something very relevant when diagnosing how students approach math.

Here are the three classic questions.

1️⃣ The Bat and Ball Problem

A bat and a ball cost $1.10 in total.

The bat costs $1 more than the ball.


Question:

How much does the ball cost?

_____

2️⃣ The Machines Problem

If 5 machines take 5 minutes to make 5 widgets,

how long would 100 machines take to make 100 widgets?

____

3️⃣ The Lily Pads Problem

In a lake, a patch of lily pads doubles in size every day.

If it takes 48 days for the patch to cover the whole lake,

how long does it take to cover half the lake?

____

Source: ChatGPT