Grade Level: Twelfth grade

Materials: Graphing Paper, Metrozoo Brochures, Markers, Rulers, Conversion Table (American to Metric - for teacher), Handouts with Description of Assignment, Assessment Worksheet.

Objectives: To understand the connections between Algebra & Geometry. To illustrate the reality of the two topics in everyday life and how they could be employed to solve problems. The students will use their knowledge of Algebra and Geometry to solve a real life dilemma at the Miami MetroZoo.

Mathematical Concepts: Volume & Area Formulas, Metric Conversions, Algebraic Equations using Linear Algebra

NCTM Standards: Problem Solving, Communication, Algebra, Geometry, Reasoning, Connections, Number Relationships, Number theory, Computation and Estimation.

Procedure: ( 1 ) Review last class's lecture on formulas for volume and area. Also review how to solve for two or more variables.

( 2 ) Assign the students to groups of three or four to work together and explain the dilemma.

The class must empty the baby whale pool at Metrozoo but cannot waste a drop of the water. Hence we must contain the water another way.

( 3 ) Handout the class activity sheets to the groups ( see attached ).

The pool is circular in shape. Its depth is twenty feet and its diameter is one-eighth of a mile.

There are three cylinders.
(A) 10 ft diameter and 8 ft tall
(B) 8 ft diameter and 8 ft tall
(C) 12 ft diameter and 5 ft tall.

Find the volumes, in m^3, of the cylinders and the pool. Consider these three situations, first.
(1) Use at most one Type A cylinder.
(2) Use no Type B cylinder.
(3) Use at least one cylinder of each type.
(4) Groups are to take 40 minutes to work on the class activity sheet.
(5) In the last 10-15 minutes of class, discuss group results. As a teacher be sure to consider the following list.

Things to Notice: did they realize the pool is also a cylinder instinctively or did they use trial and error? are the conversions clear or are there many questions? do they seem interested or is this simply busy work? is the book a constant referral or do they remember?
(6) As homework, students will individually answer the 3 Assessment questions on the bottom of the Class Activity sheet.

References: Curriculum and Evaluation Standards for School Mathematics: NCTM. (1989).

Fundamentals of Mathematics. Saunders College Publishing: New York. (1995).

Contributors: Corrina Hubbard
Carol Marinas, Barry University, Mathematics Dept., Beverly Grimm, McArthur High School, AP Biology and Research, Marilyn Levinstein, McArthur High School, Algebra II and Trigonometry, Judy Vathauer, Barry University, Dept. Secretary, Tisha Brown, Barry University

Conversion Table (English to Metric)

1 inch = 2.54 centimeters

1 foot = 0.3048 meters

1 yard = 0.9144 meters

1 mile = 1.609 kilometers

Volume of a Cylinder = (pi) (h) (r^2)

CLASS ACTIVITY

DILEMMA: The class must empty the baby whale pool at Metrozoo but cannot waste a drop of the water. Hence we must contain the water another way.

The pool is circular in shape. Its depth is twenty feet and its diameter is one-eighth of a mile.

There are three cylinders. (A) 10 ft diameter and 8 ft tall (B) 8 ft diameter and 8 ft tall (C) 12 ft diameter and 5 ft tall.

Find the volumes, in m^3, of the cylinders and the pool.

Consider these three situations, first.

(1) Use at most one Type A cylinder.

(2) Use no Type B cylinder.

(3) Use at least one cylinder of each type.

Finally, construct illustrations to scale of the pool and cylinders without the water.

ASSESSMENT

1. THE LION'S CAGE MUST BE THIRTY METERS SQUARED IN BASE AREA TO PASS THE SOCIETY FOR THE PREVENTION OF CRUELTY TO ANIMALS STANDARDS. LEO'S CAGE IS EIGHTEEN FEET DEEP AND 288 INCHES LONG. FIND THE BASE AREA AND DETERMINE IF LEO GETS TO STAY IN HIS CAGE.

2. THE SILO THAT STORES THE COW AND PIG FEED IS TWENTY FEET HIGH AND SEVENTY-TWO INCHES ACROSS. DETERMINE THE AMOUNT OF FOOD THE SILO HOLDS, THAT IS, THE VOLUME OF THE SILO.

3. IF THE COWS CONSUME THREE METERS CUBED AND THE PIGS CONSUME TWO AND A HALF METERS CUBED, HOW LONG CAN THE SILO FEED THEM, IF THEY EAT ONLY ONCE A DAY?