# Shopping with Mixed Numbers

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By: Mary Kienstra on: February 2, 2016 in: Engagement, mixed numbers *
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The Farm stand! That’s where you use mixed numbers. Finally, a way to multiply mixed numbers with a real world feel. This week my students went shopping with mixed numbers in their farm stands. At first they were totally confused… but then, they started to think about what makes sense, and everything changed.

The farm stand idea hit me as I was looking over the weekly grocery advertisements. Whole sections of the ad were dedicated to showing the cost per pound of all kinds of fruits and vegetables. That would be perfect – my students could “buy” a mixed number amount of each and then determine the cost. Shopping with mixed numbers — just what they need.

The first thing my students did was to create the farmstands. They worked in groups with the advertisements to create posters aka farmers’ booths. Each poster included the fruit or vegetable name, a picture, and the price per pound. The chatter was interesting as they discussed what was a fruit or vegetable and why.

We placed the posters on the floor around the room, each with two dice – a typical one with numbers 1-6 and a fraction one. As students visited each farm stand, they rolled both dice to determine the number of pounds they would buy there. They used an organizer to keep track of their purchases and to show their work.

At first, the students were confused. They knew the dice revealed the amount of pounds they would “buy” and they knew the price, but they were unsure how to figure out the cost of their “purchase.” At this point we stopped and talked about WHAT MAKES SENSE. This was the real value of this lesson.

Once the focus changed to what makes sense, my students had no problem figuring out the costs. If the price of bananas is $0.29 per pound and you buy 2 1/2 pounds, it must be between $0.58 and $0.87. They started thinking instead of just doing math; they were ready to go. Some were most comfortable changing their mixed numbers to improper fractions and multiplying that way. Some wondered if they could round $0.59 per pound to $0.60. My response, “What makes sense?” Isn’t that what math is all about?