LEARNING EXPERIENCE

Overview

This experience was prepared for an eighth grade math class. It lets the students create their own circle graphs by hand and with the aid of a computer spreadsheet program. It can be adapted to any grade learning similar concepts. This experience can be used in a number of ways. (Refer to Reflection) Two forty-minute class periods with students doing finish up work on their own should be sufficient. If the computer-generated graph were also developed it would require an additional period. (Dependent, of course, on the availability of computers.

Learning Context

Prior Knowledge:

1. Facts about circles.
2. The relationships between percents and fractions.
3. Use of protractors and compasses.
4. Microsoft Excel (or similar spreadsheet program with graphing capabilities)

Connection to instruction:

This exercise ties together percent calculations, circle activities and graphing.

Connection to Learning Standards

1. MST 1- Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.
   -Abstraction and symbolic representation are used to communicate mathematically.
   -Critical thinking skills are used in the solution of mathematical problems.
2. MST 2- Students will access, generate, process, and transfer information using appropriate technologies.
   -Information technology is used to retrieve, process, and communicate information and as a tool to enhance learning.
   -Knowledge of the impacts and limitations of information systems is essential to its effective and ethical use.
3. MST 3- Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
   -Students use number sense and numeration to develop and understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.
   -Students use mathematical operations and relationships among them to understand mathematics.
   -Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
   -Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.
4. ELA Standard 1- Students will read, write, listen, and speak for information and understanding.
   -As listeners and readers, students will collect data, facts, and ideas; discover relationships, concepts, and generalizations; and use knowledge generated from oral, written and electronically produced texts. As speakers and writers they will use oral and written language to acquire, interpret, apply, and transmit infor mation.

Procedure

The teacher will help students to recall the procedure for determining percentages. Using the think aloud process the teacher will demonstrate using student input. The teacher will remind the students that their percentages, ideally, should equal 100%. However, it must be pointed out that if any rounding is necessary, the total will only be close to 100%.

The students will now calculate percentages from the data.

The teacher will assess accuracy of technique and calculations through observation.

The teacher will help students recall facts about circles. (i.e. How to construct them with a compass, that there are 360 degrees, etc.) The teacher will show examples of pie graphs and discuss the makeup with the students.

The teacher will help students to recall setting up and using proportions. Using the think aloud process the teacher will demonstrate finding how many degrees of the circle each percentage calculated above will be. The teacher will remind the students that their degrees should equal 360 degrees. However, it must be pointed out that if any rounding is necessary, the total will only be close to 360 degrees.

The students will now calculate the number of degrees each percentage will be.

The teacher will assess accuracy of technique and calculations through observation.

The teacher will model creating a pie graph using a protractor to measure the angles.

The students will now create their pie graphs using their earlier calculations using the following criteria: 1) The graph should be neat.

1. The graph should be labeled clearly and correctly.
2. The graph should be titled appropriately.
3. The graph should be colored neatly so they are appealing to the viewer.

The students will then enter the information into a spreadsheet program with graphing capabilities (Microsoft Excel). After entering the data and the appropriate functions to determine the percentages and degrees, the students will create a computer-generated graph to display the data.

The students will write a paper explaining any differences between the two graphs. It should include an explanation of why these differences may have occurred. It should also include any difficulties they encountered in completing this project.

A comparison between the two graphs will be the object of a class discussion.

Instructional/Environmental Modifications

The students can be paired to complete the activity if necessary. The work can be set up in a worksheet form for students who may have trouble completing the whole project.

Material and Supplies

Chalkboard, overhead or whiteboard for teacher demonstrations

Compass

Protractor

Pencils

Paper

Crayons, markers or colored pencils

Computer Spreadsheet program with graphing capabilities

Assessment Tools and Techniques

Teacher observation will be used to assess progress. Calculations will be checked at each step. Rounding practices will also be checked where necessary. The final graph will be graded by the following rubric that the students will be aware of before they begin.

See attached.

Time Required

Two forty-minute periods with students doing some finishing work on their own should be sufficient for the student-created graph. Another forty-minute period would be needed for the computer graphing exercise. (Of course this depends on the accessibility of computers.)

Student Work

The accompanying student work is from this experience where the students were directed to determine a future career goal and find a reasonable starting yearly salary. The students then determined monthly income. The allowed for social security (7%) and income tax (12%). They then approximated how much they would spend on such things as rent, transportation, food, etc. They determined set amounts and the percentage of the total monthly income. They than did the calculations and determined the number of degrees so the data could be turned into a pie graph. They entered the data into the spreadsheet program entering the necessary formulas to refigure their calculations. They compare their outcomes and create a graph.

Reflection

All the topics and calculations in this experience are required techniques and have basis in the learning standards. This experience can be used in a variety of ways. The teacher can give the data to the students, they can obtain data from another source or they can collect the data through a survey of their own.

Rubric for Student-generated Graph

Rubric for computer generated graph