This activity from Robert Kaplinsky begins with the following situation:

Frito-Lay produces packages of chips that contain a variety of flavors like the package below.  The circles on the bags’ lower right corner normally displays the quantity of each type of chips.

With 20 bags in the package and four flavors, it would be natural to assume that there would be 5 bags of each flavor. However, that would be wrong.  This is the actual quantity of each type of chips.

“This lesson gives students an opportunity to think about how a company like Frito-Lay determines the quantity of chips they will include in each package and compare that to their own class’ or school’s preferences.  The idea would be to present students with one of the chip packages (with numbers blanked out) and find a strategy for determining how many of each type of chip they would need.  Strategies may include:

• Divide the total number of bags by the number of flavors in the package.  This may lead to a discussion as to how to handle a remainder (i.e. which flavor gets an extra bag or can you split the remainder across the flavors).
• Let people choose their own combination of flavors each time.  This may seem like a good idea in theory but is not practical for a company that mass produces their products.
• Survey their classmates and use the results to distribute the bags according to their classmates’ preferences.

The hope is that after students have a conversation about each strategies’ pros and cons, they will conclude that surveying their classmates will enable the fairest results.”

College and Career Readiness Standard:

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. (Medium Emphasis)

Students may have to demonstrate an understanding that statistics involves conclusions about a population based on the results obtained from a random sample of the population. Questions assessing this standard often take the form of “Which sample will best represent the population?” or “Which conclusion can be drawn from this sample?” 

In addition to the above standard, these standards are also explored in this activity:

• CCSS 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
• CCSS 6.RP.3c – Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
• CCSS 7.RP.2 – Recognize and represent proportional relationships between quantities.
• CCSS 7.RP.3 – Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
• CCSS 7.SP.1 – Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
• CCSS 7.SP.2 – Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.