The Thirsty Crow
Objective: Generate and use real data to demonstrate a linear function with a table, graph, words and a rule (function). In 4th & 5th grades, a table, a graph and a word description of how the marbles affect the water level is sufficient. Students in later grades will generate a rule.
Materials: marbles, bottles with straight (perpendicular) sides, centimeter rulers, graph paper, water (Note: A class set of bottles & marbles are available from PRIME)
Procedure:
· Watch http://www.youtube.com/watch?v=XtnG37texEI&feature=youtube_gdata_player
· This is a video of Aesop’s Thirsty Crow fable in which a thirsty crow raises the water level in a bottle so that he can drink it.
· After briefly discussing the video for clarity, distribute bottles and marbles to groups of 3-4 students. The bottles should be filled with water at varying levels (each bottle will be slightly different). Do not give the students enough marbles to raise the water to the desired height. Students should be able raise the water 2-3 centimeters only. In this way, they will have to decide on a number of marbles per centimeter of rise in the water, or amount of rise per marble, forcing them to use mathematics.
· Instructions for students: “Let’s pretend that this is the bottle that the crow found. He needs the water level to rise to 10 cm from the rim of the bottle. Can we predict how many marbles he will need?” The distance from the rim of the bottle down is needed to avoid the rounded “shoulders” of the bottle, which would change the function.
· The students’ challenge: Gather data regarding the water level and number of marbles dropped into the bottle. Represent your data in a table, in a graph, in words, and then as a rule (not necessary in 4th & 5th grades).
· Have students create graphs, tables and words. It may be easiest to start with a table. Prompt students to think about where the graph should start on the y-axis. Many students will start at 0. However, the height of the water in the bottle at the start is the y-intercept, and should be represented as such on the graph. Then, have groups present their finished products.
Discussion questions:
Why don’t all of the graphs have the same y intercept?
What do you notice about the slopes of the graphs?
What would need to change for the y-intercept to be higher? Lower?
What would have to change for the slope of the line to be greater (steeper)? Lesser (less steep?)
The challenge:
Gather data regarding the water level and number of marbles dropped into the bottle. Represent your data in a table, in a graph, in words, and then as a rule.
The Thirsty Crow Functions
(Sample data collected at PRIME 2 Workshop)
Group #1
x = # of marbles
15 marbles = 1 cm of height
Group #2
= x = # of marbles
For every 4 marbles, the water rises .2 cm
Group #3
x + 10 = y x = # of marbles
8 marbles raise the water .5 cm
Group #4
m + 10 = h m= # of marbles
Group #5
y = + 12 x = # of marbles
18 marbles raise the water 1 cm.