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I realized how important visual models are to the development of understanding.

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I realized how important visual models are to the development of understanding.

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I wish this was something my students had.

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Mustafa's explanation of the 4:3 problem was simple and elegant. Much better than my failed attempt. It made me thing some more about the ideas.

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I loved Naseem's graph to explain one of the questions. I hadn't really looked at it that way before.

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Good to think about the differences between ratios and fractions. They are often treated or thought of as the same....but good to discuss and think about ways they are different.

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I realized that talking with Cindy itself gave me a lot of insights into how literature works in our teaching role. Thanks to all for the great conversation

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I realized that talking with Cindy itself gave me a lot of insights into how literature works in our teaching role. Thanks to all for the great conversation

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was good to know how students progress from additive toward multiplicative thinking

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was good to know how students progress from additive toward multiplicative thinking

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Shocked how difficult it was to solve problems like a 5th grader.  

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Shocked how difficult it was to solve problems like a 5th grader.  

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Learning different representations...double number line

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It's great to see how the proportional reasoning cluster progresses through the grades and to know what the kids should have BEFORE they get to me and where they are GOING.

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It's great to see how the proportional reasoning cluster progresses through the grades and to know what the kids should have BEFORE they get to me and where they are GOING.

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realizing the importance of ratio reasoning in HS math.
Take-Away- I liked the medication problem, and will use it next time I cover that material.

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Multiplicative vs additive reasoning, great ideas.

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Multiplicative vs additive reasoning, great ideas.

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Good to talk with other PreCalc teachers for ideas of how to approach factors and graphs, etc. Also interesting to see the graphical though on how things were getting more expensi

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It is nice to spend time thinking about rigor.

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It is nice to spend time thinking about rigor.

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Drawing what you see in a problems ,Multiplicable vs additive Thinking , Ratios and Fractions , Learning Target/Cluster and application.

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Loved how Irma started......we teach STUDENTS not standards!

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Loved how Irma started......we teach STUDENTS not standards!

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Great to see the depth proportional reasoning has within so many mathematical concepts. Really shows the need to continue building these connections vertically and horizontally.

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I noticed our students are not at the level they should be. We were advised to slow down to go fast, which makes sense. It is helpful for them to understand the path that they should have taken to ease the learning.

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I think it is always an oh wow moment when we as teachers realize that tasks do not have to be "amazing" and can still be conceptual and involve application. Just because the task seems simple, it can still involve conceptual, procedural, and application.

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Oh wow. Looking at how tasks align with Mathematical practices. Also shifting my own thinking from formulaic to visual and be okay with not knowing. Mary Guzman

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Oh wow. Looking at how tasks align with Mathematical practices. Also shifting my own thinking from formulaic to visual and be okay with not knowing. Mary Guzman

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Whole depends on scale factor for ratios but factors always have the same whole!

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The progression of proportional reasoning standards was helpful!

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The progression of proportional reasoning standards was helpful!

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Today's mind bomb brought to you by #sleepdeprivation : Most of my mathematical thinking is merely patchwork designed to bridge gaps in my understanding of mathematics.