Standard Understand the concept of a unit rate $a/b$ associated with a ratio $a:b$ with $b \neq 0$, and use rate language in the context of a ratio relationship. <span class='clarification'>For example, “This recipe has a ratio of $3$ cups of flour to $4$ cups of sugar, so there is $3/4$ cup of flour for each cup of sugar.” “We paid $\$75$ for $15$ hamburgers, which is a rate of $\$5$ per hamburger.”</span><span class='footnote'>Expectations for unit rates in this grade are limited to non-complex fractions.</span>

Mangos for Sale

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Alignments to Content Standards: 6.RP.A.2

Student View

Task

A store was selling 8 mangos for \$10 at the farmers market.

Keisha said,

“That means we can write the ratio 10 : 8, or \$1.25 per mango.”

Luis said,

“I thought we had to write the ratio the other way, 8 : 10, or 0.8 mangos per dollar."

Can we write different ratios for this situation? Explain why or why not.

IM Commentary

The purpose of this task is to generate a classroom discussion about ratios and unit rates in context. Sometimes students think that when a problem involves ratios in a context, whatever quantity is written first should be the first quantity in the ratio a:b. However, because the context itself does not dictate the order, it is important to recognize that a given situation may be represented by more than one ratio. An example of this is any problem involving unit conversions; sometimes one wants 3 feet : 1 yard and the associated unit rate 3 feet per yard and sometimes one wants 1 yard : 3 feet and the associated unit rate $\frac13$ yard per foot.

A similar task that provides students an opportunity to choose between the two different ratios and associated unit rates based on their usefulness is in development.

Solution

Yes, this context can be modeled by both of these ratios and their associated unit rates. The context itself doesn’t determine the order of the quantities in the ratio; we choose the order depending on what we want to know.