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Volume, measurement, problem solving, connections

Overview

Too often students see volume only as a formula in which they "plug in" numbers. Doing problems that can be visualized in the real world can help students see what volume is all about. In this problem, small groups of students work together to measure the room, find volumes, and determine the amount of root beer in a huge tank. The group then prepares a presentation to show the class their findings.

Learning Objectives:

• Use unit analysis to compute with measurements.
• Develop the concept of volume.

The "Hook"

You LOVE root beer!  Lots and lots of root beer!  You love it so much that you want to build the largest cylindrical tank that would fit in this classroom, fill it with root beer, and bottle it for all the students.

The Investigation

Question - answer individually before any work is done:

Before you do any calculations, make a prediction as to which cylinder would hold the most root beer and how many 2-liter bottles could be filled from that cylinder.  After students have made their predictions they are ready to investigate (see Activity Sheet).

Students work together in groups (2 to 4) to solve the problem and prepare a presentation of their findings (The teacher can decide if this presentation is to be oral, written, or both). 

Explain the possibilities you tried and your results.  Which cylinder would hold the most?  If all of that root beer were put in 2-liter bottles, how many bottles would be needed?  Be able to completely explain your method. 

What? You don't like 2-liter bottles?  OK! How many 12-packs of cans could be filled? It is important that students understand each step they take to solve the problem and can explain their reasoning.

Teaching Tips

• Students need more than textbook experience.
• Having a skeleton cubic meter and cubic centimeter in the classroom will help students understand that there are more than 100 cubic centimeters in a cubic meter.  Likewise, working with a cubic yard, cubic foot, and cubic inch will make the concept come alive.  Students can make these items for the classroom.
• Students need to explain every step of their work; they must demonstrate that they completely understand what they are doing.
• Another problem you can pose that involves the concept of volume: How many basketballs would fit in this room? Many students want to divide the volume of the room by the volume of the basketball to find the number of basketballs.  They need to take into account how the basketballs would fill the room.  Sorry, I cannot give you an answer to this problem for your particular classroom. 
• Have the entire class listen carefully to other students' explanations to determine if their method makes sense and is reasonable.
• Having students estimate their solutions before they do the investigation will strengthen their concept.
• You may want to have a 12-pack of cans and a case of 2-liter bottles available for students to measure.
• Through this problem, students will learn the value of unit analysis - using the ratio of equivalent measurements.  This strategy works for any measurement conversion.
• Students will need to find a conversion factor to change cubic measurement to liquid measurement.
• The orientation of the largest cylinder is often with the circular bases on the floor and ceiling; however since classroom sizes vary greatly, all possible cylinders need to be checked to determine which contains the most root beer.
• There is no one answer for this problem because each classroom is different.
• I did not include the conversion from cubic measurement to liquid measurement on the worksheet because that would be a clue for the students, and I want them to determine that they need to find that.

Citation

From the teaching files of Marilyn Link.