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.
Read Horns to Toes and In Between by Sandra Boynton. (You can find an amusing version of the book on YouTube 17 .)
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)?
1.
Record the number of eyes based on the number of people in Table 2.1.2.1.
| Number of Monsters, \(M\) | 1 | 2 | 3 | 4 | 5 | 6 | \(M\) |
| Total Number of Eyes, \(E\) | \(E =\) |
2.
Graph the data in Table 2.1.2.1 using Figure 2.1.2.2. Label the horizontal axis, Number of Monsters, and the vertical axis, Total Number of Eyes.
(a)
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).
(b)
Choose a reasonable scale for the vertical axis. Explain why the scale is reasonable.
(c)
Describe the shape of the graph.
(d)
Why do you think the graph has the shape it does?
3.
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
4.
Choose a body part that humans have more than 2 of. Repeat Student Page Exercise 2.1.2.1, Student Page Exercise 2.1.2.2, and Student Page Exercise 2.1.2.3 for the body part you choose. You are welcome to look up numbers on the Internet if you don't know them.
5.
Graph number of people versus total number of the chosen body part on the axes above in Figure 2.1.2.2. What do you notice?