Question

is the cookie split fairly? adam and his sister bethany have to split the last chocolate - chip cookie in the cookie jar. they often get into an argument about who is getting the bigger piece. they start to wonder: what methods are there to make sure a cookie is split equally? 1. without doing any calculations, which method(s) of cutting the cookie do you think would give adam (a) the same size piece as bethany (b)? method 1: method 2: method 3: 2. to test the fairness of each method, you will be able to use protractors, rulers, string, and extra images of the cookies if you find them helpful. a. method 1: are adam and bethany’s pieces the same? how do you know? yes, adam and bethany’s pieces are the same, using a ruler choose only one of the three measuring tools (protractor, ruler, string) to prove that you are correct. which measuring tool did you choose and why? b. method 2: are adam and bethany’s pieces the same? how do you know? choose only one of the three measuring tools (protractor, ruler, string) to prove that you are correct. which measuring tool did you choose and why? c. method 3: are adam and bethany’s pieces the same? how do you know? no they pieces are not the same choose only one of the three measuring tools (protractor, ruler, string) to prove that you are correct. which measuring tool did you choose and why?

Explanation:

Step1: Analyze Method 1

In Method 1, the cookie is divided into four equal - parts by two perpendicular lines. Using a ruler, we can measure the lengths of the boundaries of the pieces for Adam and Bethany. If the lengths of the corresponding boundaries of their pieces are equal, and considering the symmetry of the division, the areas of their pieces are the same.

Step2: Analyze Method 2

In Method 2, the cookie is divided into non - congruent sectors. Using a protractor, we can measure the central angles of the sectors corresponding to Adam's and Bethany's pieces. Since the central angles of the sectors are different, the areas of their pieces (which are proportional to the central angles in a circle) are not the same.

Step3: Analyze Method 3

In Method 3, the cookie is divided into two non - congruent parts. Using a string, we can trace the perimeters of Adam's and Bethany's pieces. By comparing the lengths of the perimeters, we can see that the shapes are not symmetric and the areas are not equal.

Answer:

1. Method 1 would give Adam the same size piece as Bethany.

2.
a. Yes, using a ruler. We can measure the lengths of the boundaries of the pieces. Since the cookie is divided symmetrically by two perpendicular lines, if the lengths of the corresponding boundaries of their pieces are equal, the areas are the same.
b. No, using a protractor. Measuring the central angles of the sectors of their pieces shows that the central angles are different, so the areas are different.
c. No, using a string. Tracing the perimeters of their pieces shows that the shapes are not symmetric and the areas are not equal.