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Chapter 3 – Option 2 (Connection)

01/25/2019 9:33 AM | Anonymous

Use this sentence frame to connect the Capturing Quantities routine to what you already think or do in your teaching practice:


I used to ___________________ and now I ___________________.


Comments

  • 01/25/2019 10:38 AM | Cortni Muir
    I used to have students focus on key word and important numbers to help solve word problems and now I hope to help students develop their skill in identifying quantities and relationships by having students do more of the talking and using tools like sentence starters or sentence frames.
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    • 01/29/2019 8:42 PM | Sarah Giaquinta
      That is one of my goals too! I love that these routines have the students do so much talking. I think I talk too much, and even when I'm trying not to, I find it hard! I was just doing a routine in my class today and my kids kept asking me questions. It is so tempting to answer! After a while, they got tired of me saying, "well what does your partner think?" I'm sure this will get easier with more practice!
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  • 01/27/2019 10:47 AM | Alison Foley
    I used to have students share mathematical thinking by showing completed diagrams/models to the class and now I am going to have students share diagrams without labels so that students can focus on making sense of the quantities and relationships in the problem. By not having the labels, students need to make connections between the various diagrams and the quantities and relationships in the problem to determine if those diagrams accurately show those relationships.
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    • 01/31/2019 8:48 AM | Dave Johnston
      That was a subtle, but brilliant, detail in this routine - recreate a student diagram without labels for discussion. What a great way to prompt thinking.
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  • 01/27/2019 4:42 PM | David Shimchick
    I used to ask students to identify important information in a problem with numbers being essential information to identify (of course.) And I have often asked students what a particular number represents in a given problem because it's essential they know what a number stands for. And now I know to use the term quantity when asking what it is a number represents.

    I used to NOT expect students to represent the relationships between the identified quantities with a diagram and now I will expect them to do that.

    I used to expect students to explain their thinking but I have never provided sentence starters and frames and now I will prepare those as reference slides for students to use so that all students can respond with greater specificity and use more precise mathematical language.
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  • 01/28/2019 3:43 PM | Hala Sahlman
    I used to praise students for identifying numbers as important information within a word problem and now I ask them to identify a quantity that goes with that number. I've found the language of "quantity or label" to be very helpful when teaching students how to dissect word problems. They typically pick out a number, but the trouble comes in (as I'm sure others know) when they need to find a quantity to go with that number, and whether or not it will help in determining the best strategy to use and in turn find the final answer.
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  • 01/29/2019 8:34 PM | Sarah Giaquinta
    I used to have students pull out important information from word problems, both numbers and their meaning, as well as defining variables, but I never thought to take the actual question out of the information given! Now I will give them the information without the question. I love this! In Algebra 2, I spent a lot of time on applications of ideas and concepts, and I always find myself trying to find supplemental problems because the textbook has certain types of problems that they offer up over and over again. I find the students just start to recognize the numbers and types of problem but lose the meaning behind it. I think this is a fabulous routine to help me put the meaning back into what we are learning. Without a focus on the final question and the answer they are trying to find, they will slow down and really be able to get into capturing the meaning of the quantities they are given. This will certainly help them to troubleshoot when given different problems throughout the curriculum, when they have a familiar routine to help them tackle problems.

    As I am writing this, I'm thinking about all of the times I struggle to keep the meaning and value in what I'm teaching. For example, when doing applications of systems of equations, I think students forget that they can think visually- think of their system as the two equations they wrote on a graph, what are they actually doing when solving a system? They forget that they are trying to find what those equations have in common when graphed. This is where the visualizing piece comes in. Do they need to graph it to solve? No, not always, but there is a lot more meaning to the context of the problem if they start to have an image in their head of what they are actually doing. When I first start introducing these topics, we link equations to graphs and add contexts in, but now I really want to have them reinforce those visuals when working on these problems. It is so important for them to make the connections, otherwise everything they learn, they think as distinct pieces, as opposed to just different ways of looking at the same information.
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  • 01/30/2019 7:47 PM | Jennifer Rianhard
    I used to have students circle or highlight important key clues and numbers to help them figure out what the problem is asking them to do and now I will work on having students find the quantities and relationships in math problems. It also stated to display and explain the thinking goal. I’m not sure I ever displayed the goal of a problem to help them identify the quantities and relationships. I have given students some think time after a problem is read, along with the think-pair-share, group discussion, and then back to small groups or individual writing time to reflecting their learning.
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  • 01/31/2019 8:54 AM | Dave Johnston
    I used to emphasize identifying important "information" in a problem 0 which meant, "find the useful numbers and ignore the distracting numbers." Now I understand the importance of looking deeper: What values are in the problem & what do they represent? What values are implied and what to they represent? How do those values relate? This encourages deeper exploration and helps students make meaning.
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    • 02/02/2019 1:46 PM | Grace Kelemanik
      Dave,

      You reflection reminded me of my favorite question to help students "look deeper" into the numbers. Is that number a value for a quantity, i.e. is it telling you how much or how many of something you have or is it describing a relationship, i.e. comparing two things? And, if the number is describing a relationship, what are the quantities that are being related or compared? My two cents.
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      • 02/08/2019 8:26 AM | Dave Johnston
        I agree 100%. I love how each routine is very intentional in developing student thinking. I am also beginning to understand how often I gloss over problem solving steps that I am taking for granted in my own thought process. (For example, students may need to draw much more literal diagrams than what I had in mind... students are not yet distinguishing numbers for quantity from numbers for comparison... students do not inherently notice "hidden" numbers and relationships in problems.)
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    • 02/02/2019 1:46 PM | Grace Kelemanik
      Dave,

      You reflection reminded me of my favorite question to help students "look deeper" into the numbers. Is that number a value for a quantity, i.e. is it telling you how much or how many of something you have or is it describing a relationship, i.e. comparing two things? And, if the number is describing a relationship, what are the quantities that are being related or compared? My two cents.
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  • 02/03/2019 11:29 AM | Allison Day
    I used to encourage kids to “draw pictures” and now I encourage them to draw diagrams. This was very enlightening to look at the difference between a picture and a diagram. It is important for students to know what kinds of information that a diagram communicates versus a picture. It conveys concepts, relationships, how something works etc. Elementary students often draw pictures of what the labels are in the problem. For example, the problem in the book is about flowers and students would draw red and purple flowers. Encouraging students to draw diagrams will help them make more sense of the problem. This may be challenging for students at first, however, I think the question on page 50 in the book that talks about the relationships between quantities, “How much bigger/smaller is one quantity than another” is a good scaffold to help students. Looking at the problem, and thinking about the diagrams you will encounter before having students solve the problem will help the teacher develop guiding questions to help students create and improve the accuracy and precision of their diagrams.

    I used to focus on the numbers in a story context and now I focus on the quantities and relationships. This has really impacted my teaching and coaching in a positive way. It is important to know the difference between a number and a quantity. This difference unveils to students and teachers that a quantity doesn’t have to have a number, a quantity can be unknown. When teaching, I have students think about what can be counted and measured in the word problem. This can be done with simple, larger numbers, or no numbers at all. For example, second grade students have been working on unknown start problems. We discussed whether the unknown is a quantity. Using manipulatives to solve these problems helped students argue their answer to this question. Another change I have made to my practice is instead of circling the numbers in a story problem, I encourage students to write a list of the quantities next to it. Using this as formative information, I can see what students are understanding and missing. It has led to some great discussions and students are more aware of the missing quantities. This has helped them to make sense of the problem and persevere in solving it.
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  • 02/05/2019 6:40 PM | Michele DeMaino
    I used to think that students needed a set series of steps for solving a word problem. For example, I know some elementary schools were using the CUBES strategy where they circle certain numbers, underline, box, eliminate and solve (I believe those are the steps.) So in years past I used to try using the CUBES strategy with students because I felt like they needed some kind of tool. I realized this never worked and it still didn't help students understand the problem they were working on. Now I have had the chance to have some professional development on how to use this routine and was able to recently observe this routine in action in an 8th grade classroom. I agree with the comment from Grace that the routine will take longer when starting but once students are used to the routine it will end up taking less time. But this routine seem to really help students understand the quantities and the relationships in the problem first. And since there is no question stem, students can't just try to solve it quickly like some students like to do. Students were talking so much about the quantities and relationships. I would like to try a Capturing Quantities soon with our 6th graders and see how they do with it.
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  • 02/06/2019 1:24 PM | Anonymous
    I found the "important takeaways" comment "Students are accustomed to looking for key numbers in a problem....", and this is helpful for me. Rather than trying to stop that from happening (which is something I have tried to do), I like the idea of being able to "build from that habit". Something I used to do was try to get students (and their teachers) to now focus on the numbers and now I will support students (and their teachers) to focus on quantities.
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  • 02/10/2019 3:50 PM | Walter Pohle
    I used think that underlining/highlighting key words in a word problem helped the students understand the problem and determine what operation to use to solve the problem. Now I have a better understanding of how the students will gain a deeper understanding of the mathematical relationships found in a word problem by using the 5 steps of the Capturing Quantities Routine.
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  • 02/19/2019 3:20 PM | Sara Kaminski
    I used to encourage students to read the WHOLE problem first, and highlight or circle "important numbers and information" as well as the problem itself. Now I will cover up/remove the QUESTION from a problem in order to encourage students to consider the QUANTITIES (what can be counted/measured) and their values.
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  • 02/24/2019 11:43 AM | Kerin Derosier
    During our 7th grade Algebra unit I used to focus on students being able to identify linear and proportional relationships in an equation, table, an graph through memorization of characteristics of both... and now I am really focusing on teaching them the relationship between the two "variable" quantities. I am finding that they are able to identify both linear and proportional better by understanding not only how x relates to y but also being more specific with what the quantities are.
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