Exploration: Volume, Shape and Container

Presented by Dr. Uccellini

5th Grade Enrichment Support Field Trip

9/08/17

In this experiment, the students poured “cups” of colored water into differently shaped containers (graduated cylinders, flasks, vases, etc).  They collected data on the height of the water (in centimeters) for each additional cup poured into the container.  The data was plotted on an x-y axis with the number of cups poured on the X-axis and the height of the water on Y-axis.  For example, the ordered pair (5,7) means that five cups of water were poured into the container and the height of the water was 7 centimeters.

 

The students were to look for the relationship between the shape of the container and shape of the graph.  Some observations that were made by the students were:

1.  If the container was wide the level of the water rose slowly. 
2. If the container was narrow the level of the water rose faster.
3. In the case of the graduated cylinder, the level of the water rose by the same amount for every additional cup.

The final activity was for the students to draw the graph for cups of water poured into a new container (flower vase) that they did not previously measure.  They then explained how they used their observations from the five different containers that they had previously measured to come up with the graph of the new container.  Measurements for the new container were made and they compared their graphs to the actual graph.

Concepts and Skills

Deductive Reasoning

Deductive Reasoning is a type of reasoning which goes from general to specific. Deductive reasoning is based on premises and if the premises are true, then the reasoning will be valid.

Examples:

-In mathematics, If A = B and B = C, then A = C.

-Since all humans are mortal, and I am a human, then I am mortal.

-All dolphins are mammals, all mammals have kidneys; therefore all dolphins have  kidneys.

-Since all squares are rectangles, and all rectangles have four sides, so all squares have four sides.

Inductive reasoning

Inductive reasoning is a logical process in which multiple premises, all believed true or found true most of the time, are combined to obtain a specific conclusion. Inductive reasoning is often used in applications that involve prediction, forecasting, or behavior.

Example:

Every tornado I have ever seen in the United States rotated counterclockwise, and I have seen dozens of them.

We see a tornado in the distance, and we are in the United States.

I conclude that the tornado we see right now must be rotating counterclockwise. 

Graphing on the X and Y axis

Coordinates - A set of two numbers that indicate where a point is on a graph. The first number indicates the x-axis and the second number the y-axis. Other names include ordered pair and numbered pair.

Meter Stick

A meter stick is a meter long, and it will be marked off in decimeters (there are 10 of these per meter), centimeters (10 of these per decimeter and 100 per meter) and millimeters (there are 10 of these per centimeter and 1,000 of these per meter). As the markings get thinner and closer together, they indicate smaller measurements. Usually, decimeters are boldest, followed by centimeters and then millimeters. Decimeters and centimeters will be numbered, but millimeters likely will not.

Place the meter stick against the object you wish to measure. The end of the meter stick that has the lowest numbers (most start with 1 centimeter) should be your beginning point of measurement and will be placed at the end of the object. Note how far up the object extends on the meter stick.