Today in class I was teaching the “Mixing juices” task and found out that kids don’t know about concentrate cans of juice.  This is the part of the task where kids are given a number of cards with various juice mixture recipes.

Kids kept saying they had difficulties, and it sounded weird that after five or ten minutes of talking about, the language kids used didn’t really relate to the problem.  Instead of saying cans of juice, or cans of soda one kid would say “the grey cans” or the “The empty ones.”

After class a student came up to my desk and I was explaining again the task and she legit didn’t undrerstand.  “You know, when you make juice from a can?” I said.  “Like this.”

Then she recoiled back with a look in her eyes that was a mix between disbelief and disgust as she said “I don’t even know what that is!”

Unfortunately, I think students had a similar response to the talk about ratios.  Representations of a rational relationship between juice and water was treated pretty differently by the students in both of my classes, and not just because of the orange juice in a can business.  I think the concept of a rational relationship, the need for it and the usefulness of it, is one that doesn’t make sense.  Scores of kids immediately turned the ratios into fractions, decimals, and percents when thinking about the order the cards would go in, but not seeing how that number makes sense.  One girl in particular took a card 2 juices and 3 cups of water on it and came up with 66%, but on another card 1 juice and 2 cups of water she wrote 33%. I figured this out at the board, 10 minutes after this task was supposed to end and had to tell kids we would come back to this.  In my head I realized that this could have been a rich conversation at the board, or in groups, but I didn’t have the time, I wasn’t prepared for the variety of responses that I would see, and I was worried about what this student would think if we dissected her thinking in front of the class on day 4.  It was pretty rough.