Forgot password
  • Home
  • Chapter 3 – Option 3 (Action)



 
 

Chapter 3 – Option 3 (Action)

01/25/2019 9:34 AM | Anonymous

Think of an example task from your grade level where this routine would be fruitful for your teaching OR try implementing the routine with your students and tell us how it went. 


If you want to share a task with the group, send a document, photo, or link to atomicbookclub@gmail.com and I will set up a shared google drive folder for the materials.


Comments

  • 01/25/2019 10:36 AM | Cortni Muir
    In my district we use Exemplars (standards based word problems) as a compliment to our math program. I would love to help teachers try to use the Capturing Quantities Routine. We do put some emphasis on locating the important information, but I would rather see us help students really see the relationships between the different quantities presented in the various problems they face. When I launch these kinds of task in classrooms lately, I have been trying to present the task without the numbers to help student make sense of the problem rather than just jumping in to solve the problem. Maybe my next steps could be that besides removing the actual numbers, remove the actual question, making the problem more like problem step for students to look at and anticipate what the question might be.
    I also really like the idea of sentence frames ans sentence stems are being part of the routine to help focus students attention on quantities and relationships.
    The last big take away fro me in chapter 3 is Figure 3.22 on page 71 "Think Like a Mathematician". Having a place for students to reference to help them think mathematically is a great strategy and not something that comes easy to everyone.
    Link  •  Reply
    • 01/28/2019 4:52 PM | Nicole Gilson
      I agree with your take away - I am going to make an anchor chart for this - p. 71 figure 3.22 "Think Like A Mathematician". It is not an easy strategy for most of my fifth graders. It also validates that they are truly mathematicians - each and every one can "think abstractly and quantitatively". I like the idea of presenting the task without numbers and the question. It really opened up dialogue and conversation for my students. They were using context clues - making predictions based on evidence of "quantity" and number relationships.
      Link  •  Reply
  • 01/25/2019 11:53 AM | Todd Butterworth
    I think I'm going to give this idea a shot, although not exactly as written, in my calc class. During this semester we're going to focus on free response problems, which are more in depth and difficult questions (as compared to multiple choice). Last year I would often give the students the problem stem with the instructions for them to create new problems from that stem, but perhaps this year I will go further. Here's my plan...
    1) Give them the problem stem, have them figure out all of the information they now know from the problem stem (similar to capturing quantities).
    2) Have them share with a partner about what they've noticed or found so far. (they could create diagrams as in the routine, but it depends on the question)
    3) Have them create questions that could be asked based on the information they've been given and discuss how they connected their questions to the info given.
    4) Everyone posts questions they have come up with and, in pairs, the students will solve each of the questions on the board.
    5) Discuss how they solved each of their created problems
    6) Do the actual problem in pairs, then discuss how to do the problem and how our initial work allowed us to (hopefully) more easily attack the given problem.

    The idea of sentence starters and frames is a good one and would help, but I think I'll have to develop those as I do more problems with the students.
    Link  •  Reply
  • 01/28/2019 2:51 PM | Laura Larson
    I tried this today in one of my 7th grade classes. We are having them write algebraic equations (not brand new content -- they did some of this in sixth grade), and I thought this might help students with identifying/defining their variables using really precise language. We had previously had a conversation about defining variables beyond just "b stands for books" -- is it all of the books in the world? the books he adds to his collection each month? the number of books he read last week? etc. So they were used to having their variable names nit-picked!

    This was students' first time in my classroom with this routine, although many of them saw it last year in their sixth grade classes. The process took a LOT longer than I budgeted, possibly because we were introducing the routine (including listing features of diagrams vs. pictures), but I will definitely plan for this to take an entire 50-minute block next time. Students also struggled much more than I expected with just pulling relevant quantities from the problem (we used the "Zoe, Minh, and Jake" task from the website).

    Because I didn't want to rush the routine, we didn't actually have the opportunity to create or share diagrams. I am running the routine with a second class tomorrow and I'm curious to see how they run on time. I do think today's group still gained something from doing the routine, but I clearly need to watch my time a bit better. And obviously, both students and teacher will get better at it as we gain experience. The other routines I've tried have not run away from me quite so much!

    If anyone out there has run the routine (or if Amy and/or Grace are eavesdropping...!), any words of advice for what to say when students offer "irrelevant" quantities, like "Jake's age in years" or "length of Zoe's shift in minutes"? I faithfully added them to the list (my hand still hurts, heh), so as not to invalidate the response, but I'd also like to redirect student attention in a more productive way.

    Thanks so much!
    --Laura
    Link  •  Reply
    • 01/29/2019 8:47 PM | Sarah Giaquinta
      I am curious to hear how your second run through of this went with your other class? Did the time work out better? I was just doing another routine in my class today and it took the full 50 minute class. I agree, it will definitely pick up on pacing once they are more familiar with the routine, but I was struggling with how to handle the ideas that students were given that were pretty far off track. So I'm following along here to see if there are any suggestions on how to deal with that :)
      Link  •  Reply
      • 02/14/2019 1:46 PM | Laura Larson
        Hi, Sarah.

        Sorry! Just now revisiting this thread!

        My second run went MUCH better, or at least more smoothly. To handle the times when students were going off-track, I referred back to the slides, which I noticed afterward had the question "what are the IMPORTANT quantities...?"

        As I shared with the students, there are limitless quantities that might relate to Jake (for example), but we want to list the ones that are mentioned in the problem stem, or which seem important to the relationships in the problem stem.

        Hope you have success! I'll definitely be doing this one again soon.
        --Laura Larson
        Link  •  Reply
    • 01/31/2019 9:40 AM | Michele Hanly
      I can imagine that it would take a full class to introduce this routine to your students. Time will always be a factor; there is just not enough of it! You might want to write the steps of the routine on a poster and put it up so students can refer to it themselves. Maybe it will help make the process go faster.
      Link  •  Reply
  • 01/28/2019 4:47 PM | Nicole Gilson
    Reading this chapter was eye opening. I was guilty of teaching students the strategy of highlighting the numbers and underlining the question. My other take a way was to give more time on the "thinking" part of think-pair-share. I was too quick to turn and talk. Many students in my class need that extra time to process and rely on their partner doing the heavy lifting. So, I tried the steps with a word problem today. Students are learning to add fractions with unlike denominators using an area model. They are comfortable with the model and many are figuring out the denominator quickly. I modeled the "thinking" of the situation and was sure to not include the question. I also used the sentence "stems" to scaffold the process. I kept focusing on the words quantity and amount- the idea that quantity is connected to value. "What can I count or measure in the situation?" I also pushed students to look for relationships between the numbers ex. 2/10 and 3/4 - we discussed estimating and many knew the answer should be larger than the whole. Students drew diagrams ranging from area models to bar models to fraction bars. When they paired and shared their thinking they seemed to take off from their. The individual write time was very productive. They did a great job reflecting on their thinking using the sentence starters as scaffolding. I will definitely use these suggestions in future lesson.
    Link  •  Reply
  • 01/31/2019 9:24 AM | Michele Hanly
    Recently, I was working with a younger student on a word problem that used percentages. It became clear to me that he was struggling to comprehend the overall picture of percentages. So, I drew two circles in an effort to help him make the connection between the total amount in the problem and 100 percent. It took a bit of discussion but it helped. Now that I have read about the "Capturing Quantities Routine" I can see that drawing a diagram is just one of the steps. In the future, I will be sure to use all five of the steps. As a side note, I think that some students may like the pie chart while others might use a square or a rectangle for their diagram.
    Link  •  Reply
  • 02/01/2019 8:46 AM | Marianne Springer
    I am going to try this routine on Monday as my AP Statistics students start working with sampling distributions. They have read an introduction that contains specific statistics vocabulary and relationships among the components, but the specifics will still be quite unclear to them. I am hoping that this routine will help them to start this unit off at a good conceptual level. I had to modify the vocabulary in the routine to fit this particular application, however, I plan to include all of the steps in the process. I will post again with results.
    I will start with the following problem stem:

    Suppose that I had a large container of M&Ms. There are 1,000 M&Ms in the container which have been mixed thoroughly. There are 200 blue M&Ms in the container.

    I have each of you take a SRS of 20 M&MS as follows:

    You reach in without looking and select 20 M&Ms. You quickly record the number of blue M&Ms. Then, you return your M&Ms to the container, we mix them up thoroughly, and the next student repeats the process.

    You each calculate the proportion of blue M&Ms.
    Link  •  Reply
    • 02/04/2019 11:57 AM | Marianne Springer
      I guess this is how I publish a follow-up comment, as a reply to myself. So this went reasonably well in my two classes, but the time required was the whole 50-minute class period. The AP Statistics students jumped straight to calculating probabilities using information from the previous unit and other probability studies instead of focusing on the specific quantities that could be directly counted or measured first. They were also stumped by the diagramming part at first, but I did get viable diagrams to use in each class eventually. A few students struggled with the sentence starters, but for others, they gave a good way to organize their thoughts. I think some of the wording of the sentence starters will need to be different for more advanced math content like this. I struggled mostly with the timing--some students needed more individual think time than others and after presenting the process, the extroverts wanted to start sharing with partners, and the class, prematurely. Both classes are small. I'm struggling to envision this routine with my Algebra classes of 26 and 30 students respectively, especially since the room is configured with groups of 3 students/table.
      Link  •  Reply
  • 02/08/2019 7:14 AM | Leah Frazee
    In our first-credit bearing in the math department at CCSU, we use the approach described in this chapter to help our students make sense of algebra problems. We give them question stems and ask them to reason about the quantities before they are given a question. This is really quite difficult for the students at first—it takes several weeks for them to get used to answering quantity questions rather than solving for a numeric value. However, we have found that this quantitative reasoning is very important for moving into an understanding of functions. Being able to reason about functions as a relationship between two quantities helps our students make sense of function notation and their actual numeric answers. One thing I would like to incorporate into this course more is diagrams that allow students reason about the quantities rather than simply a representation of something physical in the problem. I will continue to think about how this can be done.
    Link  •  Reply

The ATOMIC Mission is to ensure that every Connecticut student receives world-class education in mathematics by providing vision, leadership and support to the K-16 mathematics community and by providing every teacher of mathematics the opportunity to grow professionally.

Powered by Wild Apricot Membership Software