Buying Books
Goal: Think like a mathematician! Learn to look for repetition in your calculation process then generalize the regularity.
If Juan buys his books on-line, he gets 15% off the price of each book. However, he must pay a $12 shipping charge on each order. He wants to decide whether to buy his books on-line. For each amount that he spends on books below, will he save money by buying them on-line?
- $50
- $150
- $75
- How much money does Juan need to spend on books so that the cost would be the same whether he bought the books on-line or not?
Source: CME Algebra 1 textbook http://cmeproject.edc.org/
Back to Recognizing Repetition Tasks
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This was my third lesson with beginning third graders. I modified the numbers to make the calculations easier, and the teacher and I showed them how to find ten percent (vs. 15%) since they had not be exposed to percentage in the second grade curriculum. The time they were more used to the routine as I had used the power point slides in exactly the same way as the other two times. The outcome for this one surprised me in that I had expected the problem to be challenging because we didn’t use cubes, but two students who didn’t seem to understand the first two lesson tasks were able to get all the way to the generalization, and a couple of students I thought were getting it were unable to generalize at the end even when they had figured out the generalization on the first two lessons. I still had about a third of the class that was still confused at the end. Again, I think I will use tasks that only require one step at this developmental level. I tried this with my fourth grade girl and she was able to verbalize the generalization clearly after a short while. After trying this routine, I feel that I have the rhythm of the routine better but I am still struggling how to best draw out students’ thinking during the share parts of the lesson. This is the part that I need to continue to focus on during planning. I also struggled with being able to listen to every group long enough to see how they were thinking. I am going to use this routine a few more times, and then I can imagine that I would be able to learn the other routines more easily. I already used the three-reads with the students that I tutor, and found that one to be quite straightforward to implement. I think I will still have trouble with the share part of the lesson with these third graders until much later in the school year.