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While refelcting on our last class, I was particularly focused on the importance of estimation when it comes to fractions and their operations. When I was going through school and learning fraction I dont think estimation was even mentioned. Its so important for students to learn how to estimate so they can create a sense of the meaning behind each operation. Wihtout this tool students wont have an expectation of what the operation will do to the fractions being used. This is a hard skill to learn epecially when working with multiplication and division so using the concrete pictoral models and manipulatives is a good way to build students number sense with these operations. Once students can estimate they can make infrences with fractions and their values. I think this is a useful tool for students to learn early on and I wish I wouldve learned it beucase I still have trouble knowing the outcomes of some fraction equations.

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While reflecting on todays class, we mostly spent our time working on operating with fractions. One of the big take aways I had after working with this content is that fractions should be introduced in many different forms not only just written and pictured but different types of written and picture forms as well. One of the activities that I enjoyed was the gardening together activity. I think this activity would be particularly useful to do in the classroom becauase everyone creates/draws there garden out differently even though they are using the same fractions. I think this would give students a unique perspective on the different ways fractions can b edepicted even though they are represnting the same amount.

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Reflecting on class today I keep thinking about my own personal relationshop with fractions which was and is still not (math 151 and 152 did help some) great. When I think about the way i learned fractions I think of mostly fraction circles and finding the common denominator. I dont feel like I ever had a great foundational understand of what a fraction actually was an in result what a nurmerator/denominator was representing. That being said, I love being able to find new strategies that actually break down fractions in a way students will be able to gain a deep understanding from. All the different ways fractions are represented are super important to show so students dont only think of fractions in the shape of a circle, which can be so confusing. My other big take away is that using estimations and reasoning in fractions is super important as a way to develop that number sense/reasoning.

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While in class today something new I hadnt thought about deeply before is the idea that statistics is a concept that should be taught in primary grades and is a super important skill. I had never thought about statistics in the way of analyzing data, I usually associate it with big scary college math that I dont understand. But formulating questions, collecting data, analyzing data, and interpretting results are all important skills that are crucial for moving forward in STEAM content. I was super impressed with all the hands on examples of statisitic lessons that could be done with even really little kids. This also gave me ideas on how i could incorporate this contnet in special education classrooms.

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While reflecting on class today I recalled working with my student on doubles facts. To begin we wrote down our doubles facts on the appropriate paper, my student was slow coming up with the answers and often had to count on his hand. Next time I would probably providing the double facts first and then have the student come up with the answer rather than providing the number/answer and have them tell me the double facts. After, I worked with my student to fill in the bingo sheet with numbers 0-20 (skip counting by 2). We pulled cards and covered the doubles facts until the board was covered. The most interesting part of this work session with my student was observing how he broke apart doubles facts. He was fluent breaking up the facts under 10 but 10 and up he would break it apart using the 10. For example he would break up 12 as 10+2 instead of 6+6. I wonder if this is becuase they are working with ten in the classroom.

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Today in class I had practice with my number talk where I learned that it is a lot harder to clearly transcribe someones mental math than i thought. Im glad i had the practice with my number talk though, and i got some great feedback! A big aha moment I had with todays content was when we were looking at hundreds charts. I had always vieweed numbers charts going from up to down and had never worked with a bottoms up chart. It was defientely weird trying to navigate the bottoms up chart but realize now that it is probably easier for students when using the charts to add and subtract since they would be moving up and down respectively. I also liked the idea of describing subtraction and addition as the distance between numbers on the chart.

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Today in class I foudn that the truffle problem super enlightining. I enjoyed doing this problem becuase it allowed me to put myself in the shoes of my students who are learning to work with blace value and base tens. I can oftenfind mysefl frustrated with students not easily picking up on this concept or even confused by the mistakes they are making. After working this problem and can now feel more empthatetic by why we need to spend so much time on this concept. Its a completely new system for the students!

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I had a great time working 1 on 1 with a student today. I did struggle with keeping my student on task and math focused..but im sure that would be easier if I was in my own classroom, they were probably really excited! Thinking about fluency, my student was defintely in phase 1 of mastering basic facts as she was either wrong or had to create math drawings and then 'count all' to get her answer. She did show some fluecny what it came to the addition of doubles "5+5" and was excited to show that she know those. We didnt get to the game but I appreciated that using games is a great way of practicing fluency. I wasnt able to fit a game into my VDW lesson but plan to try one for my student interviews! I love that it gets students engaged and target a specific strategy!

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Today in class I loved learning about the 3-act tasks. I enjoyed these tasks becuase of the practical application and events that the students could see and relate to. I beleive that this type of connection with the problem creates a more meaningful relationship between the student and the work. More so than reading a word problem that has no relvacny to the student. I also love that these problems are accessible to all students on some level because they start with notice and wonder. The opportunities for extension in these problems is pretty endless as the activtiy is student led, so the studens can continue to figure out different parts of the problem (looking back to the notice and wonder list) once they answer the main question. And finally, I love how the problem revists the intial video through answering the main question, I bet students love this!

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Reflecting on class yesterday I am realizing the importance of the 'after' part of an effective lesson. I believe the class discussion/after part of the lesson is something that would have been completely altering to my math experience because I never got the closure of discussion after closing a lesson. This is so important because it's a time students can come together and discuss what did and did not work, and I love the summarizing of main ideas that can help identify solutions for future problems. This is something I wish I had in class because there were many times that I would know how to do a problem in class but then when I came back to it in homework or on another assignment I would be completely lost again because I didn't really understand the components.

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One take away I had from this class was watching the ted tallk by Dan Meyer where he discussed the idea of students needing to understand how to formulate the problem and not just solve it. I appreciate this idea becuase I agree that knwoing how the formula is created and why it works is just as (if not more) important than just using the formula and getting the solution. Having students generate all the steps that are usually given in a multi part word problem allows students to explore and fully understand all components of a problem.

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Im excited for the semester ahead! thank goodness we are in the class (fingers crossed it stays that way!) Glad I foudnd someone from Boston to clue me in on the teaching certificate process up there!