Goal: Think like a mathematician! Read the problem multiple times.
A prince picked a basketful of golden apples in the Enchanted Orchard. On his way home, the prince came to a troll who guarded the orchard. The troll stopped him and demanded payment of one-half of the apples plus 2 more, so the prince gave him the apples and set off again. A little further on, he encountered a second troll. The second troll demanded payment of one-half of the apples the prince now had plus 2 more. The prince paid him, and set off once more. Just before leaving the Enchanted Orchard, a third troll stopped him and demanded one-half of his remaining apples plus 2 more. The prince paid him and sadly went home. He had only 2 golden apples left. [How many apples had he picked?]
Source: Kelemanik, Lucenta, Janssen Creighton, Routines for Reasoning Fostering the Mathematical Practice in All Students, Portsmouth, NH: Heinemann, 2016
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This was the second task that used for The Three Reads Routine in my 7th grade special education classroom. After reflecting on the first task we had completed, I noticed that students hadn’t really understood the concepts of relationships within a word problem. I felt this problem would allow me to focus more on the idea of relationships (and patterns). My students still had a hard time with relationships and I really had to lead them to see that each time he ran into a troll was related to the previous troll because it changed the number of apples he had. I was also surprised that after the second read a few students misunderstood how many apples the Prince was giving each troll and reported that the important information was that the Prince gave each troll 2 more, but left out the one-half. After discussion and the an extra read before the third, they were able to identify this information and the relationship and pattern. It really stuck out to me how lost students can get in the words and how effective this technique is.
I chose the Golden Apple and Troll toll problem to use with 2 students who participate in Intensive Mathematics class. We only got through this routine 2x because the language-demand of the problem was considerable. The kids latched on to the quantity 2 for the apples and needed prompting to consider the 1/2 that was also given as the troll tolls. With considerable discussion and time, the kids were able to grasp the critical information from the text and begin to paraphrase the problem. This is difficult for them in reading work, as well as mathematics. They would benefit from continued work with this routine.