Goal: Think like a mathematician! Identify quantities and relationships in problem situations.
We don’t know Nuna’s age, but we know that in 30 years she will be three times as old as she is now. [How old is Nuna?]
Source: Impact Mathematics Algebra and More Course 2
Back to Capturing Quantities Tasks
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This was the last task that I used with my small group, 7th grade special education group. The previous tasks were Quinn’s Garden, Fruit Salad, and Parkview Elementary, which were all easily represented by fraction models. Students automatically tried to create fraction models for this problem and got very stuck. It was interesting that they all automatically plugged in 10 for her age now and were convinced they had solved it. They all claimed that if she was 10 now, she would be 30 in 30 years and that was 10 *3. We re-read the problem and they quickly realized that if she was 10 now, she would be 40 in 30 years and the light bulbs went on! I praised the students for using the “plug-in” method and how 10 is an easy/landmark number to work with and encouraged them to keep working using that strategy with other numbers. Students were then able to create tables and graphs to represent information and work towards the correct answer- I still can’t get all of them to NOT solve the problem, even if I don’t post question!
I used this task as the second time focusing on the capturing quantities routine with my small group. It was a nice challenge for my 4th grade students. I told the students that they did not have to solve the problem, which instantly relived a lot of anxiety. I reminded them that we were looking for important quantities and their relationships within the problem. The students worked in pairs and talked through the problem. This was the routine that I forgot to do the meta reflection at the end because I ran out of time. I might actually go back to this task again with my whole class in order to see some reflections. My gut is that the students found this task hard, but can understand why it is important to look for the connections within the quantities in the problem.
This was my third task with the fifth grade class I worked with; for reference the first two were Ice Cream & Soda, and Quinn’s Garden. In retrospect, I would have started with Quinn’s Garden because it was accessible math but also lent itself to more quality diagrams that truly showed relationships than the Ice Cream and Soda task. For this task, again, I did not show the question – as people have mentioned above, it may have been anxiety provoking for some students and also that wasn’t the purpose of what we were doing. We were able to name the quantities and relationships relatively well but when it came time for the diagram, many students got stuck. So I ended up grouping them with the help of the classroom teacher so that groups were truly heterogeneous. This helped spark it for most students. They worked together and almost every group had at least one student with a beginning idea that could get them started. Again, because of our students’ background in bar models, which they used for multiplicative comparison in 4th grade, most of the diagrams resembled a bar model. They persevered through the challenge and once they did, I revealed the question. Of course, they had already answered it through their diagrams.