a. The ratio of shaded to unshaded in Set A is 1:2. The ratio of shaded to unshaded in Set B is 2:3.

b. The ratio of shaded to total in Set A is 1:3. The ratio of shaded to total in Set B is 2:5.

c. The number of shaded circles in both sets is the same.

However, Set B has a greater portion of the whole shaded than Set A, that is 2/5 as compared to 1/3. How do you know that 2/5 is greater? One way is to give the two fractions common numerators. Since 1/3 is equivalent to 2/6, compare 2/5 and 2/6. Two parts of five is greater than two parts of six, so 2/5 is greater than 2/6 [and therefore greater than 1/3].

Another way to think about it is to look at the ratio of shaded to unshaded circles in each set. Using a common number of shaded circles, you find that for every two shaded circles, Set A has four unshaded circles, whereas Set B has only three unshaded. Therefore, the ratios are 2:4 and 2:3, respectively. If we wrote these as fractions, we'd see that the numerators are equal. This means we can say that 2:3 is greater than 2:4.

A third way to compare the sets is to use a common number of unshaded circles. For every six unshaded circles, Set A has three shaded circles. Whereas in Set B, for six unshaded circles, there are four shaded circles. Since there are more shaded circles for every six unshaded in Set B, this set has a greater portion of shaded circles. This approach is similar to finding a common denominator.

  Communicate about the Shaded/Unshaded Circles problem