Bean Counting and Ratios

By using this activity, students achieve a sense of equivalent fractions, which leads to a better understanding of proportions.  Students build ratios from the bean activity then converts the ratios to a decimals. Allows students to use tangible items to build ratios and convert ratios to other rational numbers.

Weblink address (URL): 
Bean Counting and Ratios

Standards & Objectives

Learning objectives: 

By the end of this lesson, students will:

  • Recognize equivalent ratios.
  • Determine good and poor estimates.
Essential and guiding questions: 
  • How did your results for the trials (your experimental values) compare to the expected value? Why do you think these differences occur between an experimental value and the expected value?
  • Say you have a sample that contains only marked or only unmarked beans. How would that affect the inference you make about the population the sample was taken from?
  • Explain the method(s) you used to fill in rows 7—10 on the Activity Sheet.

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 
  • How can you use this concept of equivalent ratios to determine how many beans are in a cup if you don’t know how many I give you at first?
  • Distribute another set of cups, and tell students how many beans are in them. Ask them to use sampling to determine how many of the beans in the cup have been marked.
  • A factory puts 150 raisins and 100 peanuts in each package of peanuts and raisins. In a sample with 75 pieces, how many pieces do you expect to be raisins? How is this question different from the other questions we have explored in this activity?

Helpful Hints

Materials:

  • 'Bean Counting' Activity Sheet A or 'Bean Counting' Activity Sheet B 
  • Calculator
  • Paper cups
  • Beans (white beans are recommended)

References

Contributors: 
Leslie Wolfe
Originator: 
Ayers Institute for Learning & Innovation