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I have enjoyed this class so much! I have learned more than I thought I ever would! I am also now way more confident in math and in teaching math!

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3 Takeaways
1. Math content and the way math is being taught is always changing.
2. The way math is taught is not helping students retain the information.
3. Give students time to struggle and think and make sure they know it is okay. As the teacher take a step back when it comes to teaching math.

2 wonderings
1. Why do they think making the standards higher is going to help the students get better at math?
2. How do I become more familiar with the new math language?

1 Aha moment
1. The way I was taught math is the reason I do not remember a lot of it. I relied on the textbook and the teacher t give me the formula or tell me how to do the problem. I never learned how to be a patient problem solver.

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Basic Fact Instruction Video, Chapter 9 & Chapter 1 

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Basic Fact Instruction, Chapter 9 & Chapter 1- 9/5

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Basic Fact Instruction, Chapter 9 & Chapter 1- 9/5

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Basic Fact Instruction Video, Chapter 9 & Chapter 1 

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3 Big Takeaways
1. You need to have intentional practices problems after the lesson for your students. Do not just hand them random practice problems/worksheets. Make sure your students know the intention behind the practice. Your intention may be different for the same lesson every year.
2. Students backgrounds and culture can affect how they learn. I always knew students' backgrounds can have an effect in the classroom but I did not realize how intentional and aware you have to be of the student's culture when teaching. "How we do math is culturally determined."
3.There are certain process when teaching lessons and you cannot pass over any of them or your students will miss out on something valuable. You have to be intentional with every step of your lesson. Including your goals, students' needs, selecting the task, assessments, before during and even after the lesson. They all go hand in hand.
2 Wonderings
1. What if during your number talks, you have certain students who are not ready for number talks and practice because they do not understand the strategy? What should you do?
2.How do you incorporate practice of previous lessons into your future lessons? What are some examples? How do I make time?
1 Aha Moment
In the podcast they talked a lot about math talks. I never realized how much you can do with math talks and how intentional they can be. I always imagined them as a way to see students' strategies for math problems. After listening to the podcast that you can be intentional about the problems you give and discuss and also the order you give them to deepen and expand students' thinking's.

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We need to develop our Number Sense and Foundational facts!!!!!

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3 Big Takeaways
1. Language plays a big role in students understanding place value. Our English language does not help with this. When you are first teaching place value to students you can say numbers like 11 as 10 1 or 17 as 10 7. Also, when you are talking about base ten manipulatives it is important that we call them by their place value not rods or flats. We need to be aware of our language we use.
2. Grouping helps students have a better understanding of place value as well. When using manipulatives, using individual materials like beans or chips that students are able to group into groups of 10 will help students see that there is a group of ten and it has 10 things within it. That is why using base ten manipulatives are sometimes confusing for students because you cannot break them apart.
3. A lot of times teachers teach place value as an isolated skill when actually it helps us see connections and relationships between other numbers and math skills, For example you can use place value to help with addition and subtraction or regrouping. It also helps with skip counting and seeing the different patterns there are in math as well.
2 Wonderings
1. How do you teach students the correct name of a number but still use the base ten language to help with their understanding? Or what do you say when they ask why we can't use the base ten language and why we have to use the standard language?
2. What is the best way to teach students how to write the number the correct way instead of 207 as 27? Or what would you tell them if they ask why they can just write it that way?
1 AHA moment
Place value goes a lot deeper than just knowing the position of the place value. The students need to actually understand the value of the number and what it means. Having students make their own sense and understanding of place value will help them make different connections with different numbers and see all the patterns that appear in math.

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3 Takeaways
1. Division and Multiplication is a progression overtime. You start in second grade and everything you learn since then is building up you're understanding. All the concepts and strategies go hand in hand. You start with models, and it leads you to representations, drawings, numbers, then groupings and next thing you know you are understanding the standard algorithm. Everything you did before that got you to where you are today with multiplication and division.
2. There are so many different types of strategies and types of problems for multiplication and division. I have always thought of multiplication and division as one-way problems, but I was proven wrong. There is different context of each. It is important as a teacher to introduce all these to your students, so they develop operation sense.
3. Students need to do a lot of their own exploring in math to help them grasp a better understanding. Let students find what strategies work best for and what makes sense in their mind.
2 Wonderings
1. How do you catch students up if they are not where they need to be in math? Specifically based off of the common core state standards.
2. How do you find time to teach all the different strategies?
1 Aha Strategies
1. The more strategies the students experience, the better they can make a decision as to which ones best suits the situation at hand. All students think differently therefore they need as many opportunities as possible to find what works for them. Therefore, they need the exposure to the different strategies.

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3 Takeaways
1. There are all different types of measurement. When I was in school learning about measurement, I just associated it with length or distance of something. After reading this chapter it showed me that money, time, angles, and weight are all a different form of measurement.
2. In chapter 18 it states that measurement "is a number that indicates a comparison between the attribute of the object (or situation, or event) being measured and the same attribute of a given unit of measure." This is a way I have never looked at measurement before. You are always comparing when you are measuring. You are comparing the unit you are measuring and the attribute you are measuring. This is a different approach than what I learned but I think this is a great way to learn about measurement.
3. Understanding length is the gate way to understanding permitter, area and volume. This showed me that measurements can connect and help you build knowledge off of past/current knowledge. I always split measurement into sections but if you connect things together students will be very invested, and it will make more sense to them/

2 wonderings
1. Why did the US decide not to adopt the metric system, and do you think they ever will? Also do you think it would be easier for students to understand.
2. What is the best way to teach measurement while using nonstandard materials? How do you transition from using nonstandard materials to actual measurement units?

Aha Moment
1. I never got the point of estimation of measurement in class. I now had an aha moment as to understanding the importance of estimation. I now realize that it is used to help students focus on the unit and the attribute and really think deeper about each. It provides intrinsic motivation for students because they are so determined to find the right answer. Lastly it creates skills you may use in the real world like building something, painting something etc.

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He just needs to look at some models and understand the conceptual meaning behind fractions and then fractions will come easier to him. haha 

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3 Takeaways
1. Students need to understand the concept behind fractions. Algorithms do you not teach students the meaning behind fractions, it just teaches them how to solve the fractions. Having a variety of contexts and contexts that are interesting to students will help students develop the understanding of fractions and purpose of the fractions as well.
2. Having models for students like linear models (Cuisenaire rods or fraction strips) or area models will help students make connections to fractions and see the fractions visually. Having models help students form mental images and imagine what they need to do to solve a fraction problem. Models are also very useful for creating the connection between decimals and fractions, they are able to physically see how a decimal and fraction may be the same. Some models for connecting fractions and decimals could be a number wheel, hundred blocks, 10 x 10 grid, and a meter stick.
3. Estimation is a big part when it comes to fractions. This is something I never realized. Estimation helps build understanding and procedural fluency with fraction operations. Estimation of fractions requires no computation. You are able to just look fraction addition problem and see what you notice about the two to make your estimation. Doing this you are able to develop that deeper understanding of fractions.

2 Wonderings
1. Why did I learn so many algorithims in math and only one way to do math when I was a student? Because now I know none of them taught me to think conceptually about math.
2. Why do we not teach fractions and decimals within the same unit?

AHA moment
If the meaning behind a math concept is never taught or never understood, it is never going to be put into use outside the math classroom. For example, I was never taught the importance of multiplying fractions, therefore I never use that skill now. When really, I could use it all the time.