Final answer:
The beaker is the piece of glassware that would not give critical measurements in a laboratory setting.
Step-by-step explanation:
In a laboratory setting, the piece of glassware that would not give critical measurements is the beaker. While it is commonly used in labs for a variety of purposes, beakers are not designed for precise volume measurements. They have markings for approximate volume measurements but are not as accurate as other glassware like a volumetric flask or a graduated cylinder.