Student Page 2.1.2 The Eyes Have It
Because variables are so important in our work with algebra, it is helpful to further develop our facility with their use. In this activity, you will study the relationship between the numbers of monsters and the corresponding numbers of eyes (each monster has only two eyes) through tables, graphs, English sentences, and algebraic equations.
How many eyes do 3 monsters have? 4 monsters? 7 monsters? All the monsters in the book? Any number of monsters (with 2 eyes each)?
Record the number of eyes based on the number of people in Table 18.104.22.168.
|Number of Monsters, \(M\)||1||2||3||4||5||6||\(M\)|
|Total Number of Eyes, \(E\)||\(E =\)|
Starting at 0 where the two axes meet, number the tick marks on the horizontal axis increasing by 1 each time for each dark vertical line (every other tick mark).
Choose a reasonable scale for the vertical axis. Explain why the scale is reasonable.
Describe the shape of the graph.
Why do you think the graph has the shape it does?
Describe the relationship between the number of monsters and the total number of eyes the monsters have. Here is one way to phase into the use of variables:
The number of Eyes is two times the number of Monsters.
Number of Eyes = 2 × number of Monsters
E = 2 × M
E = 2M
Choose a body part that humans have more than 2 of. Repeat Student Page Exercise 22.214.171.124, Student Page Exercise 126.96.36.199, and Student Page Exercise 188.8.131.52 for the body part you choose. You are welcome to look up numbers on the Internet if you don't know them.
Graph number of people versus total number of the chosen body part on the axes above in Figure 184.108.40.206. What do you notice?