Topic: Percent and Applications: Circle Graph

Grade: 8-9

Prior knowledge: Students should be able to use a proportion to find a percent of a number, also should know how to calculate percents.

Materials: Compass, protractor, worksheets provided by the teacher, rule, pen, pencil, paper, blackboard, overhead projector and field trip to Bayside mall.

Objective: The student after a demonstration on circle graphs, should be able to make, read and interpret a circle graph.

Mathematical Concepts: Percents, proportions, circle, degrees, angles.

NCTM Standards:
Standard#1: Mathematics and problem solving; formulate problems from situations within and outside mathematics.
Standard#2: Mathematics as communications.
Standard#4: Mathematical connections; apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, business, science, etc.
Standard#5: Number and number relationships; understand and apply ratios, proportions, and percents in a wide variety of situations, represent numerical relationships in one and two dimensional graphs.

Procedure: One week prior to class, teacher will review percents and will assign a field trip to Bayside mall. The class will be divided into small groups of 3 -4 students, and will deliver a preprinted worksheet as follows:

CATEGORY                 COST IN $       PERCENT           

CLOTHING (1 T-shirt)                                       

SHOES  (1 pair of                                          
tennis)                                                    

MUSIC (2 CD's)                                             

READING (1 book)                                           

FOOD (lunch for one                                        
person)                                                    

Each group will be assigned a nominal budget of $200.00 to be spent only in the above mentioned categories, students will be able to buy the type and brand of their preference, but must obtain all the indicated items. Students are to fill the cost and percent columns with the actual dollar cost and percent.

(We are assuming that students already know how to calculate percents).

Next class, teacher will review the worksheets, and will call one group to the blackboard to explain what they bought, how much it cost and to show how they obtained the required percents.

The teacher will proceed with the class selecting at random one group's worksheet. To simplify we will assume that the worksheet will look as follows:

CATEGORY           COST IN $     PERCENT         

Clothing = 1       $37.00        18.5%           
T-shirt                                          

Shoes = 1 pair of  $68.00        34.00%          
tennis                                           

Music =  2 CD      $30.00        15.00%          

Reading = 1 book   $39.00        19.5%           

Food(lunch for 1   $26.00        13.00%          
person)                                          

The teacher will write a proportion to find the number of degrees that clothing represents in a circle, teacher will mention that there are 360 degrees in a circle.

18.5 / 100 = X1 / 360

Where X1 represents the number of degrees for clothing in a circle.

360 represents the total number of degrees in a circle.

And 18.5 / 100 represent the amount of dollars spent on clothing related to 100%.

To find X1, student should multiply and divide the above referenced terms in such a way that X1 should be left by itself: (18.5 x 360) / 100 = X1. (We are assuming that the student already knows how to solve this expressions). The teacher will find that the clothing percent of 18.5% occupies 67 degrees on the circle (X1 = 67). On the overhead projector, the teacher will draw a 3 in. radius circle using a compass. Then will draw a radius from the center of the circle and with the protractor will measure a 67 degree angle. The section made represents the percent spent in clothing.

The teacher will write the next proportion to find the number of degrees that shoes represents in a circle, and will obtain the following expression: 34 / 100 = X2 / 360 and will obtain that X2 = 122 degrees.

Making center on the same circle drawn before, the teacher will measure an angle of 122 degrees from the last line drawn for the prior category and will continue doing the same for the next categories.

Music 15/100 = X3/360 X3 = 54 degrees.

Reading 39/100 = X4/360 X4 = 70 degrees.

Food 26/100 = X5/360 X5 = 47 degrees.

The circle graph will look as follows:

THE SUM OF ALL THE DEGREES OBTAINED SHOULD EQUAL 360 DEGREES.

The teacher will explain that 18.5% represent the amount of money spent on clothing, the 67 degrees represents the amount of circle graph clothing cost will occupy. Percent compares to 100%, the degrees compare to 360 degrees.

A circle graph pictures the way data are related, the sum of the percents equals 100, the sum of angles equals 360.

Reference:

Contributor: Major: Martiza Simauchi