Blueberry Cereal and Ratios

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One of my classes is in the midst of a unit on ratios.  Students have been exploring equivalent ratios and using visual models to compare them.  For the most part, it has been a great journey and students are making connections.

One of the common themes of this unit is for students to apply their understanding of ratios in real-world settings.  On Thursday, I introduced an activity about cereal and flavors.   This was my first time using this task so I wasn’t quite sure of what to expect.  Basically, students are given four different cereal recipes.  Each recipe has a certain number of cups of blueberries and cornflakes.

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The ratio is different for each cereal.  For example, cereal A has 1 cup of blueberries and 2 cups of cornflakes.   Students are then asked questions related to doubling, halving, making additional cups, and finding equivalent ratio recipes.   Students seemed to struggle at first and then created models, mostly tape diagrams, to find solutions.  Questions about making a certain cereal taste more like another were also part of this task.  Students had to stretch their understanding of ratios and apply it here. What I found was that some students struggled through this process.  Through the struggle, they moved towards using pictures/models to help themselves.

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This was where I stayed back and let students work.  That was tough. At times, I asked students questions to help move them towards validating their reasoning.  The application piece of taking ratios and using that understanding to see whether a cereal would taste more like blueberries or cornflakes was challenging for students.  They had to perceive the problem in an abstract sense, and then bring justification to why it would taste a certain way.

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One of the more open-ended problems involved a taste test.  Students were asked to create a cereal with a  stronger blueberry taste than all the other cereals.  The kicker was that the new cereal couldn’t have more blueberries than cornflakes.  So, students were required to analyze all of the ratios and create a new ratio where the blueberry taste was more evident.  I observed that students tackled this problem in a couple different ways.  Some students perceived the problem as adding more cups of blueberries than any of the other cereals.  This caused an issue as the ratio wasn’t dependent on the amount of cups, but the actual ratio.

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Compared to what?

This was a red flag to me as students were looking at the value, not necessarily the ratio.  Other students took each ratio from the initial cereals and converted them into fractions.  They then created a fraction that was closer to one compared to the other cereal. This was used in their justification.

This task seemed like a worthwhile activity.  I’m looking forward to what tomorrow brings.

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