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.

Standards & Objectives

Academic standards
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different...
Recognize and represent proportional relationships between quantities.
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and...
GLE 0706.2.3
Develop an understanding of and apply proportionality.
GLE 0706.2.4
Use ratios, rates and percents to solve single- and multi-step problems in various contexts.
GLE 0706.3.5
Understand and graph proportional relationships.
GLE 0706.4.2
Apply proportionality to converting among different units of measurements to solve problems involving rates such as motion at a constant speed.
GLE 0706.4.4
Understand and use ratios, derived quantities, and indirect measurements.
SPI 0706.1.3
Recognize whether information given in a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.
SPI 0706.2.6
Express the ratio between two quantities as a percent, and a percent as a ratio or fraction.
SPI 0706.2.7
Use ratios and proportions to solve problems.
SPI 0706.3.4
Interpret the slope of a line as a unit rate given the graph of a proportional relationship.
SPI 0706.3.5
Represent proportional relationships with equations, tables and graphs.
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For...
Recognize and represent proportional relationships between quantities.
Use proportional relationships to solve multi-step ratio and percent problems.
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
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: 
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


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