Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Teaching Math Home   Sitemap
Session Home Page
CommunicationSession 02 Overviewtab aTab btab ctab dtab eReference
Part B

Exploring Communication
  Introduction | Problem: Shaded/Unshaded Circles | Solution: Shaded/Unshaded Circles | Talking About the Problem | Representing Fractions with Rods | Other Denominators | Modeling Operations | Try It Yourself: Cuisenaire Rods | Problem Reflection | Summary | Your Journal

Shaded/Unshaded Circles #2

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.

Next  Communicate about the Shaded/Unshaded Circles problem

    Teaching Math Home | Grades 6-8 | Communication | Site Map | © |  
Home | Video Catalog | About Us | Search | Contact Us | Site Map |
  • Follow The Annenberg Learner on Facebook

© Annenberg Foundation 2013. All rights reserved. Privacy Policy.