# «Phosphate: A Florida Resource Mined for Math A middle school grade level unit created by Donna Ellis Lake Alfred Middle School Polk County, FL 2012, ...»

Using an angle ruler and a protractor, students will practice measuring, constructing, and naming angles. The dragline, a giant excavating machine used by the phosphate industry, will serve as the source of the angles the students will measure.

**Estimated Time:**

One—90 minute class

**Grade Level:**

6-8

**Standards:**

SC.6.N.1.4 SC.6.N.3.4 SC.7.N.1.6 MA.8.G.2.2 MA.8.G.2.3 MA.8.G.2.4

**Materials:**

Angle rulers Protractors Paper Pencils Measure and Draw Angles Practice worksheet What’s Your Angle? worksheet Comparing Angles worksheet

**Procedure:**

1. Show the picture of the dragline. Point out that there are many different angles in the construction of the dragline. Now focus the students’ attention on the boom of the dragline that holds the bucket. This dragline boom that holds the bucket that digs out phosphate is also able to rotate 360°. Discuss how a circle has 360°. Explain that if the boom stops anywhere else in the turn, the measurement of the angle is different. The two tools that we would use to find the measurement of the angle are the protractor or the angle ruler.

2. To use the protractor, place the center circle on the vertex of the angle. The straight line goes along the right ray of the angle. Using the inner scale, read the angle over the line.

3. Provide time for students to practice in class drawing and measuring angles with the protractor using introductory worksheet. Wander around the room and make sure students use the tool correctly. Introduce the names of angles and have students identify the various angles in their exercises. Check for understanding.

4. To use the angle ruler correctly, place the rivet over the vertex of the angle and set the center line of the arm passing through 0° on one side of the angle. Then swing the other arm around until its center line lies on the second ray of the angle. The second arm will pass over a mark on the circular ruler, telling you the degree measure of the angle.

5. Provide time for students to practice in class drawing and measuring angles with the angle ruler beginning with introductory worksheet and then going on to individual practice worksheets.

Wander around the room and make sure students use the tool correctly. Stop, check, and discuss the work often. Check for understanding.

6. Explain how the degrees of the circle now relate to the latitude and longitude of the earth. Use a map to point out the Equator, Prime Meridian at Greenwich, and the North and South Poles.

Describe how pilots and ocean liner captains rely on latitude and longitude to navigate planes and ships.

7. Culminate the lesson with the map activity. Model measuring an angle between three given locations so all can be successful.

**Assessment:**

Successful completion of the worksheet activities.

**Teacher Notes:**

Make copies of the protractor and angle rulers, if needed Make copies of the Measure and Draw Angles Practice, What’s Your Angle?, and Comparing Angles worksheets Make copies of the Answer Keys for the Measure and Draw Angles Practice, What’s Your Angle?, and Comparing Angles worksheets If your budget does not allow you to purchase a class set of protractors and angle rulers, copy the templates included with this unit onto transparency film and have the students cut them out. The two pieces of the angle rules can be connected with a brad.

Measure and Draw Angles Practice Directions: Estimate the measures of the angles of the following pictures showing the draglines from the air and the phosphate waiting to be mined. For the first ray, start at the red dot on the center of the dragline, then go to the tip of the boom. For the second ray, go from the center of the dragline straight across to the star on the phosphate rock. Write your answer on the line below each picture. Check your estimates using an angle ruler.

1. 2.

4.

3.

Identify the angles marked 5-8 on the structure of the dragline and write your answers

**below:**

5. ________ 6. ________ 7. ________ 8. ________

**Now draw angles with the following measurements on the back of the paper:**

Directions for #7-14: Without using an angle ruler, match the angle below with a measure closest to the measure given. Check your answers with an angle ruler.

Directions for #7-14: Without using an angle ruler, determine the letter of the angle below with a measure closest to the measure given. Check your answers with an angle ruler.

3.

_______________

Directions: At the start of each hour, the minute hand of a clock points up at the 12. Determine the angle through which the minute hand passes from the 12 for the given amount of time. You might want to make a sketch to help you illustrate each situation.

Directions: At the start of each hour, the minute hand of a clock points up at the 12. Determine the angle through which the minute hand passes from the 12 for the given amount of time. You might want to make a sketch to help you illustrate each situation.

**Introduction:**

The phosphate industry uses millions of gallons of water each day to transport and process phosphate rock, which is found intermixed in a matrix with sand and clay, into useful fertilizer.

Students will gain practice converting data from a table into a bar graph. The data will show the phosphate industry’s use of water for eight years during the processing of phosphate rock into fertilizer.

Students have previously studied and created bar graphs, so they will have to review the concept.

**Activity:**

After a discussion about the phosphate industry’s need for water, students will read a handout about how much they pumped from 1991-1998. They will then graph the data. Students will then predict water use by the phosphate industry for 1999-2002, and check the accuracy of their predictions against data provided only to the educator. A second bar graph of the later data may be made if desired.

**Estimated Time:**

One—90 minute class

**Grade Level:**

Grades 6-8

**Standards:**

MA.5.S.7.1 MA.6.S.6.1 SC.6.N.1.4

**Objectives:**

The students will…

1. Read the handout Florida Phosphate Industry Water Use, 1991-1998.

2. Make a graph of the water usage of the phosphate industry per day from 1991-1998 from a published table.

3. Make predictions about the phosphate industries water usage from 1999-2002 based on data given from the previous years.

4. Compare validity of water usage predictions to actual data collected from 1999-2002.

**Materials:**

Florida Phosphate Industry Water Use, 1991-1998 Polk County Water Use graphs Graph paper Markers Paper and pencils Pens Computers with Excel® software

**Procedure:**

1. Begin the lesson by discussing the need for fertilizer and that phosphate is the raw material we mine and process into fertilizer. Explain that it is necessary to use a lot of water to transport and process the phosphate into fertilizer.

2. To get the class thinking in terms of large quantities of water, ask them to first visualize a home swimming pool that is 12 ft. wide by 28 ft. long. Its shallow end is 3 ft. deep and its deep end is 8 ft. deep. Have the students estimate how many gallons of water the pool has in it. Answers will vary depending on the length used for the deep and shallow ends, but the best answer is 13,823 gallons.

3. Hand students the Polk County Water Use tables for 1990, 1995, and 2000. Have them compare the water use between the different water users.

4. Now talk about the phosphate industry’s use of water. Back in 1991, for every ton of rock it mined, it used approximately 1,185 gallons of water. Ask “What is their estimate of how many gallons of water are used each day?”

5. Tell the students that the industry pumped over 117 million gallons of water per day in 1991.

Discuss the problems that such a high water usage poses for Polk County and Florida.

6. Hand out copies of Florida Phosphate Industry Water Use, 1991-1998. Have students locate the data, organize it, and display it in a bar chart.

7. The students should explain the trends of water use between 1991 and 1998, and any possible explanation for deviations from the trends (i.e., years that don’t follow the trends).

8. Ask students to predict trends of phosphate industry water use from 1999-2002 (the last year for which the Florida Phosphate Council provided data). Compare their predictions with actual data.

9. If desired, have students make a bar graph of the 1999-2002 data.

Analysis/Conclusion Students will produce the bar graph(s) and all the paperwork for planning and completing the graph(s).

**Extension:**

Have students create the bar graph(s) on the computer using Excel®.

**Teacher Notes:**

Make copies of Florida Phosphate Industry Water Use, 1991-1998 Teacher’s copy of Florida Phosphate Industry Water Use Sheet—Key Make copies of the Polk County Water Use graphs

Phosphate Mining and Processing Phosphate mining and processing requires a lot of water. It is used in the mining pits to make a “soup” or slurry of the matrix dug by the dragline. This matrix consists of about one-third phosphate, one-third sand, and one-third clay. The slurry is then piped to the beneficiation plant, where more water and special chemicals are used to separate the phosphate from the sand. The clayey water that remains is pumped to special settling ponds. As the clay slowly settles, the clear water at the top of the ponds is recovered, stored, and then recirculated to be used once more in the mining and beneficiation process. The phosphate industry sometimes uses treated domestic wastewater in its mines and processing facilities. This helps them save energy and ground water resources, while at the same time helping local governments dispose of their unwanted wastewater. Another way the phosphate industry reduces water use is by collecting rain that falls on its lands.

Can you spot trends in this table? Why do you suppose water use in a particular year might be significantly higher or lower than for the previous year?

Try your hand at making some predictions. How much water do you think the phosphate industry used in 1999, 2000, 2001, and 2002?

Other Users of Groundwater in Polk County The phosphate industry is just one of many users of groundwater in Polk County. To compare all groundwater users in our county and see how much was used in 1990, 1995, and 2000, see the accompanying bar graphs. Note that mining is not a separate category, but is included in the same category as all other industries and businesses in the county.

Trends Note the large drop in the amount of groundwater pumped from 1991 to 1992. Why was this?

Answer: The industry continually incorporates technological advances into its operation.

Among these are the ability to utilize water more efficiently and to recycle greater percentages of the water it needs for its processes. Significant advances were incorporated during this time period.

Groundwater gallons per day pumped increased in 1993 compared to 1992 and in 1996 compared to 1995, increased a little more in 1997, then began to drop again. Why was this?

Answer: For 1992-93, lower rainfall amounts required more groundwater to be pumped to meet industry needs. For the years 1995-1997, a possible explanation is that there may be a time lag after rainfall is collected for use before it becomes available for processes. Therefore the industry must continue pumping groundwater until it has caught up with the time lag.

Note the drought in 2000, and how it increased groundwater pumpage as well as gallons of water per ton of rock. Compare this to 2002, a very wet year. This is contrary to the likely prediction for the larger trend of decreasing pumpage to continue. The lesson is that there are other factors that influence trends that make the future hard to predict.

**Introduction:**

In Florida, ammoniated phosphate fertilizer is the primary product manufactured. Ammonia provides nitrogen and is added in varying amounts to create different types of fertilizer.

Diammonium phosphate, or DAP, is the most commonly produced fertilizer product (about 65% of the total in 1998). Next is monoammonium phosphate, or MAP, at 14% of the total in 1998.

MAP and DAP are similar, but MAP has a lower concentration of nitrogen.

Triple superphosphate, or TSP, comes in next at 8% of the total product manufactured in 1998.

TSP is made by reacting phosphate rock primarily with phosphoric acid rather than sulfuric acid, resulting in a more concentrated product.

Animal feed supplements made up 6% of the products manufactured by the phosphate industry in 1998. Animal feed phosphates are defluorinated because fluorine can cause adverse health effects to animals eating it.

There are several main finished products that phosphate is proceed into after it is mined out of the ground in Florida. The data offers a chance for students to practice converting numbers to percentages and creating circle graphs.

Students should already familiar with rounding integers and percentages.

**Activity:**

Students will use their inquiry skills to analyze data about phosphate mining finished products, convert that data to percentages, and use a percent protractor to create a circle graph to represent the data.

**Estimated Time:**

One—90 minute class

**Grade Level:**

6-8

**Standards:**

MA.5.A.2.3 MA.6.A.5.1 SC.6.N.1.4 LA.7.1.7.8 LA.7.2.2.2 MA.7.S.6.2

**Objectives:**

The students will…

1. Know the main finished products of the phosphate industry.

2. State the purpose of a circle graph, in their own words.

3. Convert given data into percentages.

4. Show their work in making conversions.

**Materials:**

1998 Major Finished Products of the Florida Phosphate Industry Paper and pencils Ruler Percent Protractor Colored pencils Black pen.

**Procedure:**

1. Hand out the 1998 Phosphate Industry Finished Products fact sheets. Discuss the finished products the phosphate industry produces and the need for fertilizer to increase food production to feed our growing population.

2. Review and discuss procedures for rounding. Demonstrate rounding to the nearest thousand with the first finished product. Allow time for the students to round the data to the nearest thousand.

3. Review and discuss procedures for calculating the data in the table to percentages. Allow time for students to convert the amounts to percentages.

4. Model using the Percent Protractor to make a circle graph using different data. Have students make their own circle graph using the phosphate industry finished product data.

5. Allow time for the students to make their key, or legend, describing what the segments of the circle represent, and to write a summary of the purpose of the circle graph.

**Analysis/Conclusion:**