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I really enjoyed today’s lesson. I’m noticing that the warm-up for the day seems to always somehow be within the classroom that we observe. I had a tougher time following the teacher I observed today but I was still able to jot notes down. I especially enjoyed the area and perimeter lesson taught today and how we could think about this lesson when applying the three-tier system.

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Chapter 4: Be aware that your actions can inadvertently shut down student thinking
and damage self-esteem. "It's easy" and "Let me help you" are two such statements. Think about the message each one sends. If a student is stuck and you say, "It's easy," then you inadvertently say, "You are not very smart or you wouldn't be stuck." Similarly, saying "Let me help you" communicates that you think the student cannot solve the problem without
help.

Chapter 6: Students' backgrounds are not only an important part of who they are as people, but who they are as learners and this background enriches the classroom.

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I LOVED being able to observe the math lesson being taught within the classroom and being able to identify the strategies being used. I have a hard time following along with the videos within the class but if I doodle on my paper I am much better at absorbing the information by listening. I really enjoyed learning about the notice wonder aspect of mathematics and thought it was very useful for students to break down their problems at hand.

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Chapter 2: "One aspect of being mathematically proficient is to rely on one's own justification and reasoning to determine if an answer is correct."

Chapter 3: "Students engaged in these inquiry-based practices are encouraged to ask: Why? What would happen if? What is another way? How does this compare to that way? Will this always work? Inquiry is a disposition of openness, curiosity, and wonder."

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Throughout this class, I learned a lot about “notice & wonder’s” and also learned how to use mathematics for similarities and differences. I also enjoyed how we got to observe popular media within our age group to show different thoughts students have or wondering and what our responses were toward this. I also loved learning about the history of standards and was shocked to hear that there weren’t any before the 1900s.

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"Ultimately, your students need to think of themselves as mathematicians in the same way as they think of themselves as readers."

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Sometimes students are able to multiply fractions but are unaware of what is happening when the multiplication occurs. My biggest takeaway from our last class was using different representations to allow students to make sense of multiplying and dividing fractions. I enjoyed the ruler example to allow students to visually see that when you multiply a whole by a fraction the number becomes smaller. One method that made a lot of sense to be was the area model when multiplying fractions. This is something that can be easily aligned with students' previous knowledge of the area model and using that knowledge to create a visual for multiplying fractions.

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From today's class, my biggest takeaway was that the numerator tells the number of parts and the denominator tells the unit. Keeping this in mind, I was able to gain a better number sense when it came to fractions. I was able to use this number sense to estimate the expected size of the results of fraction equations. I really enjoyed the examples of higher or lower than 1, this allows for students to gain number sense and use the parts and units to make accurate estimations. Students are able to argue their reasoning and work through the problem by making sense of it.

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One major takeaway I took from today's class was the idea of measurement and the different forms it can take. I really enjoyed the book Measuring Penny and how it demonstrates the use of comparing attributes, estimation, different measurement instruments, area, and volume. I could see this being a lesson opener to a measurement lesson. One thing I have always struggled to read quickly and accurately is telling time and I never would have thought of the broken clock in a classroom to be such a large issue but now I can see how it is an issue within mathematics.

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In today's lesson, I was able to view different representations of fractions and how to build students' understandings of fractions using concrete objects. I even was able to perform a fraction assessment with a student. We then were moved into rotations where we could build number sense through a number line, then use our number sense to compare fractions, and then finally be able to use concrete options to demonstrate fractions.

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We were able to look over our diagnostic interview and be able to come up with the planning for the assessment. I was able to come to a determination of my topic as well as the kinds of questions I am going to ask throughout. I was able to view multiple different strategies for multiplication being used such as an array, open array, lattice, partial product, and the standard algorithm.

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I was unable to attend class this session but I was able to learn about the 5 fundamentals for basic fact fluency. I was also able to work on a worksheet determining how to write an equation for different word problems using division and multiplication. After creating the word problem, I was able to group the problems into different categories such as equal groups, area/array, rate, combination, and multiplicative comparison. I struggled with creating an equation for the combination but then I discovered that I was making the word problem much more difficult than it was... which I feel like students might as well.

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I gave my number talk today and was able to get real feedback. I discovered that I am going to keep all of the work on the board so students are able to view it through the progression of the equations. I also was able to learn more about the different ways to word addition and subtraction which is really helpful when creating formal assessments. I also was able to learn, from Scout's presentation, more about grouping students based on math levels has a large impact on students own perception of themselves.

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One big takeaway I had from today's class was being informed about number strings and how that should be implemented when giving a number talk. I wasn't quite sure of what kind of problems I should include and what was too complex or too easy but I learned that using both can be a necessary tactic to reach a middle ground and possible extension.

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How Many Jelly Beans Read Aloud: Link
Would You Rather? Math Routine: Link

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Close, Far, and In Between Activity Sheet 

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Close, Far, and In Between Activity Sheet 

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Today was a very interesting class. I was really looking forward to teaching in Ms. Coyne’s class since I observed her last semester but I was able to do some on the fly teaching with a different topic.

I really enjoyed learning about the bottom-up number chart and now to it within the classroom. I also enjoyed the lesson covering how to teach students the importance of the equal sign and the truth behind it.

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Website

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I really enjoyed today's class. Being able to get an in-person observation of the number talk was extremely beneficial for me. Especially seeing what the teacher does when not everything goes exactly to plan & seeing what to do from there. Learning the 3 act task was more of a struggle for me because did not know certain aspects of labeling certain numbers or the "why" aspect of the division So I wouldn't necessarily know how to teach my students the "why" if I did not know myself.

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Resources:

Blog Post: Why Use 3-Act Tasks?
https://mikewiernicki.com/2014/05/13/why-use-3-act-tasks/

Collections of 3-Act Tasks:

https://gfletchy.com/3-act-lessons/

https://mikewiernicki.com/3-act-tasks/

https://tapintoteenminds.com/3act-math/

https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/edit#gid=0

https://docs.google.com/spreadsheets/d/19sms4MpuAOO71o4qFPJyVKK-OGLnNegMgSL6WAwIdb8/edit#gid=0

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I really enjoyed learning more about the process of diagnostic interviews and being able to implement an in-person trial run. This created a much deeper understanding of the task and understanding of students' knowledge. I was able to see the concepts of diagnostic interviews such as flexibility, accuracy, efficiency, and appropriate strategy selection. Although the thought of going into a lesson without explicit planning was stressful it was nice to know how easy this can be enforced during our future classrooms.

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Math Fact Fluency - Two Prompt Interview Assessment

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Math Fact Fluency - Two Prompt Interview Assessment

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Math Fact Fluency - Assessing During Game Play

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Math Fact Fluency - Assessing During Game Play

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MathFactFluency-Tool 18-Interview Prompts for Assessing Fluency During Game Play

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Same but different / Notice & Wonder Resources 

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Same but different / Notice & Wonder Resources 

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- This website is a curated set of Same But Different tasks for grades PreK-12 across a wide variety of mathematical concepts: Link
- Learn more about the Notice and Wonder routine with great resources from NCTM: Link
- This NY Times Opinion piece relates to the big ideas of math practice 3: Link

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Link