# The Curious Saguaro

Subject:
Math
Lesson Duration:
60 Minutes

### Objective

How can you use an algebraic equation to solve the age of a saguaro? The objective of this lesson is to help students learn about the components of algebraic expression and how they can use that to solve the problem.

### Background

The saguaro cactus is the largest cactus in the United States, and will normally reach heights of 40 feet tall. The tallest saguaro cactus ever measured towered over 78 feet into the air. The saguaro cactus grows as a column at a very slow rate, with all growth occurring at the tip, or top of the cactus. It can take 10 years for a saguaro cactus to reach 1 inch in height. By 70 years of age, a saguaro cactus can reach 6 and a half feet tall, and will finally start to produce their first flowers. By 95-100 years in age, a saguaro cactus can reach a height of 15-16 feet, and could start to produce its first arm. By 200 years old, the saguaro cactus has reached its full height, reaching upwards of 45 feet tall. Some saguaros have been seen with dozens of arms, while other cactus never produce a single one. Why this happens remains one of the desert’s mysteries.

### Preparation

Print out the student worksheet under Materials.

### Materials

Explains the relationship between the growth of saguaros and its living environment.

Saguaro Height-to-Age Table

Grandpa Saguaro Age Worksheet

### Lesson Hook/Preview

Watch Section 17 video to give students an idea about how saguaros are doing at the Park. The video should give the students an idea on the living environment of saguaros at the Park.

### Procedure

#1: Ask students if they are familiar with the saguaro cactus. Follow up with how many arms, fruits, and/or flowers they think a saguaro can have.

#2: Allow the students to read the information about saguaros and how they grow.

#2B: See Growth and Age under Materials.

#3: Given that Anna’s grandfather is close to eight and a half feet tall, how old do the students think Grandpa Saguaro is?

#4: Brainstorm with students several ways they can approach the problem. For example, if they are given a data, how can they use a graph to find the age of a saguaro given its height? What kind of graph would be appropriate for this? This would be a great refresher if they have finished learning about different kinds of graphs or if they are about to learn it.

#5: Discuss what an algebraic equation is and how to solve problems using it. Give a couple examples.

#6: Allow the students to read over the problem, discuss with a partner or in a group, and answer it. How old is Grandpa Saguaro?

#7: End with the idea that saguaro height-age relationship differs depending on the growth environment.

### Vocabulary

Coefficient- often found infront of a variable. Example: 3x where 3 is the coefficient.
Constant- a number that does not change its value i.e. it stays the same
Expression- it contains numbers, variables, and operators. Example: 3x + 2

### Enrichment Activities

Using the Saguaro Data Guide, create an algebraic expression that’ll determine the average number of flowers that grow on top of a saguaro branch.

Using the formula provided, calculate the age of a saguaro when it is 12, 17, 24, and 30 in. tall. Compare your answer to the chart provided under Additional Resources.

• X = 10(-0.609+.884*SQRT(1.493+2*log(Y)))
Where "Y" equals stem height in centimeters and "X" equals age in years.
The formula written above is derived from the study, The Saguaros of "Section 17" in Saguaro National Park. This equation is applicable only for saguaro cacti less than 2.2 meters, or approximately 33 years. After this age, saguaros change growth form and rate.