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Getting started, I initially picked out of the puzzles I wanted to task first. For the first puzzle I didn't have a strategy going in. I basically picked up numbers and started adding and subtracting. This task required a high level of mental math.  If I were in grade school,  I would probably rely on the use of pencil and paper to check my work for accuracy.  As the puzzles expanded, one strategy that I found useful was to link one common number that could blend each angle.

6) Would you consider this task to be rigorous for students? Why or why not?  Yes, I  would consider this task to be rigorous because it challenges students to combined several math skills in one. I look at this task as an extension project for students who are capable of working independently.  For my students in particular, this task would only work if I modeled a puzzle several times before releasing them to work in pairs.

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When I first looked at the numbers, I tried to plug in the highest and lowest numbers on the same line. Then, I added them up to see what they equaled, tested the other lines to see if I could mentally add them up to equal the same thing, and went from there. I would take away one from a circle, and then add one to another circle from the same line.
#6. I definitely think this activity is rigorous enough for my fourth graders. It would make them use critical thinking and mental math, and would give me a good idea of where they are with their math skills. Instead of just reciting math facts, they are having to put them to use in a way that helps them problem-solve and use logical thinking. Hearing them talk about the different ways they could start the task would be very intriguing and would allow me as a teacher to understand their thinking patterns. For example, some of them may just start plugging in random numbers, while others take a second to think it through. Some may try to come up with a total without thinking about what the numbers could add up to.

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Ashton Williams                                                I started by using trial and error just to get a feel of the activity. I put random numbers in the circles. Once I played around with the numbers a little bit, I decided to use strategy. I thought of a sum and began plugging in numbers to create that sum for each line. I found that once I decided on a sum and found the numbers to create that sum it was became easier. 

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Ashton Williams                                                I started by using trial and error just to get a feel of the activity. I put random numbers in the circles. Once I played around with the numbers a little bit, I decided to use strategy. I thought of a sum and began plugging in numbers to create that sum for each line. I found that once I decided on a sum and found the numbers to create that sum it was became easier. 

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#6 I most definitely think that this task is too rigorous for my students. I teach students with disabilities in elementary school and the concept of each line be equal would be difficult for them to understand. I feel that this task would visually confuse my students. I could see my students having a difficult time coming up with a strategy to complete this task.

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How I got started: For this assignment I got started by just writing numbers in the bubbles and seeing what “sums” I made. While writing in numbers I made note whether or not the sums were prime or composite because when adding up the bubbles I had to take into account the numbers needed to make the lines equal. While working on this task I kept finding myself having to re-work because I would put larger numbers where they could not go or smaller numbers in the wrong bubbles as well. I did get stuck a few times but after going back to the sums I was trying to make I was able to continue working.

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How I got started: For this assignment I got started by just writing numbers in the bubbles and seeing what “sums” I made. While writing in numbers I made note whether or not the sums were prime or composite because when adding up the bubbles I had to take into account the numbers needed to make the lines equal. While working on this task I kept finding myself having to re-work because I would put larger numbers where they could not go or smaller numbers in the wrong bubbles as well. I did get stuck a few times but after going back to the sums I was trying to make I was able to continue working.

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Response to question six:

6) Would you consider this task to be rigorous for students? Why or why not?

I believe this task could be rigorous for students due to the strategies they are required to use. Students are to use mental math, manipulate numbers and reflect on their work as they go along. Part one would be easier than part two for students. Students are looking at what smaller numbers can make larger numbers and I believe that is where students are able to build number sense as well.

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Module 1, Task 1                        I got started on these math puzzles by first deciding on the number that I wanted the lines in the puzzle to equal. For part 1, the number was  between 15-20 because we could only use 1-10 as our number tiles. For part 2, the number was between 20-40 because we used all of the number tiles and the M shaped puzzle had a lot of spaces to fill in.  After deciding the number that I wanted the lines to equal, it was fairly easy to plug in different combinations without using a number tile more than once. 

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Module 1, Task 1                        I got started on these math puzzles by first deciding on the number that I wanted the lines in the puzzle to equal. For part 1, the number was  between 15-20 because we could only use 1-10 as our number tiles. For part 2, the number was between 20-40 because we used all of the number tiles and the M shaped puzzle had a lot of spaces to fill in.  After deciding the number that I wanted the lines to equal, it was fairly easy to plug in different combinations without using a number tile more than once. 

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#6 - I think part 1 would be rigorous for lower elementary students. They won't get overwhelmed with the amount of number tiles like they would in part 2 and and it probably aligns better with base numbers that they compose and decompose in class on a regular basis. I would consider part 2 more rigorous for 4th or 5th grade students because they have 20 different number tiles to choose from and the mental math will require them to carry over as they add and keep track of multiple addends while decomposing and composing a given number.

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For each of the puzzles, I started with the largest number and placed it in a line with the fewest circles connected to it.  From there, I typically moved to the next greatest number and would place it in a circle.  While doing this I thought of each line as its on algebraic expression that had to be equivalent to the other lines.  I would then fill in the remaining numbers to balance the expressions.
#6 This is definitely a rigorous task.  First, it requires students to utilize several Mathematical Practice Standards.  This task also allows students multiple access points, making it rigorous for all learners.  For students who struggle with math the teacher can plug in a number range at the top of the puzzles. For the higher achieving/AIG students, you can leave the  number range open and ask them to provide more than one solution.

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In the beginning, I just started putting numbers onto the spots that were given. After choosing a few numbers, I thought about how I could rearrange the numbers or add different numbers to make them equal. For me, it was more trial and error and some strategy. I did think about how the numbers would balance out by checking to see if there was a combination of larger numbers and smaller numbers.
#6 Yes, this task would be rigorous for my students. My 1st grade students would be very challenged in this task because they are still learning basic number concepts and addition and subtraction concepts. I think this task would give my students an opportunity to persevere through something that is difficult at first but then use learned and created strategies to help them solve these problems.

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When first starting the part 1 section, I thought about balancing each line with large and small numbers.  When I started moving numbers around, I had to mentally add and subtract to figure out what amounts would make them equal.  When figuring out part 2 and using more numbers, I used combinations of 10 to help me balance the lines.  Using a 6 on one line and a 16 on the other made me balance with 14 and 4 respectively.
#6 - I think this task would be rigorous for many elementary students and could also be modified. It involved thinking and solving problems, and if the students worked with others, they could help each other through their thinking and even show other solutions.

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I got started on these math tasks by essentially working backwards. I had to think about what number I wanted to create and think about different ways I could compose/decompose that number. I got stuck a few times and had to add/subtract, to figure out how much “space” I had left before I reached my sum and then I had to break down that amount. I actually really enjoyed this because it got the juices flowing and was quite challenging.

6) Would you consider this task to be rigorous for students? Why or why not?

Yes, because it uses many math concepts, adding, subtracting, adding multiple numbers, missing addends, decomposing and composing numbers.