**Box and Whiskers Plot: **

- Make a box and whisker plot for the data in your class and draw it under the German class’s plot using the same scale.

- Suggest three good questions that you could ask your class in making comparisons between the two plots. Answer each of your questions.
- Based on the box and whiskers plots, what are the minimum and maximum values of each class? What does this tell us?

-In the German class, the min. value is around 30 and the max. value is around 90. In our class, the min. value is 32 and the max. value is 114. This shows us that the range of our class is higher than the German class.

- What are the main differences you can tell between the box and whiskers plots?

-The box on the German class starts around 41 or 42 and ends around 88-89 and the median appears to be around 53-54. In our class, the box starts at 57 and ends at 90 with a median of 83.

- Why does our class have a higher range than the German class when they have 42 students and we only have 18?

-I am personally not sure why our class has a larger range when the German class has considerably more students. The only reason I could think of is maybe the German class emptied the same trash (like the kitchen trash) each night and since everyone was measuring the same room the results were similar. Maybe our class used different room’s trash to measure? Hope, do you have any ideas on this?

Also, Hope I was wondering if you knew what the second line through the box (after the median) on the German box and whiskers represents? I wasn’t sure of this.

**Common Core Standards: **

Respond to the following questions/ statements…

- Write down two “first impressions” you have about the standards.

-One of the first impressions I had about the standards was that they were really detailed. However, when looking further, I could see that they were very broad. Each standard was an end goal and it is our job as teachers to build objectives off of these standards.

Also, I became a little overwhelmed when first looking at just how many standards are in each grade. I started looking at third grade standards since this is the grade I am working with for my field experience. I couldn’t believe all the standard and wondered how we were supposed to fit them all into a year.

- How do the concepts progress through the grades?

– I believe that the concepts pretty much stay the same through the grades, they just become more detailed and difficult. I provided an example of this in the question below. (I believe I answered this question correctly. I thought it was very similar to the next. Hope am I missing the meaning to this question? I feel like I should have had a better answer.)

- How do the concepts change and increase in rigor and complexity for the students?

– One of the things I noticed from looking at different grades was that a lot of the standards were similar; however, they just became a little more detailed and more difficult. For example, Common Core Standard 2.OA.1 (2^{nd} grade) is to use addition and subtraction within 100 to solve one-and two-step word problems. Common Core Standard 3.OA.3 (3rd grade) is to use multiplication and division within 100 to solve word problems.

- Does the Common Core Standards align with what NCTM states students should be able to know and do within the different grade level bands? (Note that NCTM is structured in grade level bands versus individual grade levels.)

-The common core standards do align fairly well with what NCTM states students should be able to know and do. The main difference is that the common core standards really focus on what they feel each individual grade should be able to complete.

- Give examples of which standards align as well as examples of what is missing from the Common Core but is emphasized in the NCTM standards and vice versa.

-I really focused on looking at the K-2 section. The Common Core did a good job of splitting each grade up; however, it cut a lot out of the Kindergarten grade that the NCTM standards say they should be able to complete. For example, Common Core Measurement and Data K.MD 3. States that students should classify objects into given categories; count the number of the objects in each category and sort the categories by count (limit category counts to be less than 10). However, the NCTM standards say that this same grade should be able to pose questions and gather data about themselves and their surrounding; sort and classify objects according to their attributes and organize data about the objects; and represent data using concrete objects, pictures, and graphs.

**Curriculum Resources: **

** **

I read and answered the questions on the 1^{st} grade, “Would You Rather,” article.

- When using this activity, what mathematical ideas would you want your students to work through?

-I would want my students to be coming up with different ways to collect and represent their data. The assignment is to ask each student in the class whether they would rather be an eagle or a whale. The students need to think of the best way to collect their data from the class, then think of the best way to represent the data they collected.

- How would you work to bring that mathematics out?

-I would work to bring this out by having a class discussion before having students collect data. I believe this will help their ideas start flowing and help them discover new ways of collecting data they might not have known before.

- How would you modify the lesson to make it more accessible or more challenging for your students?

-I believe this is a very simple lesson that I could easily make easier or harder. I could make it easier by already having pictures of eagles and whales cut out and having student use these to make a pictograph with their results. I could make this lesson more challenging by having students graph their data without using pictures.

- What questions might you ask the students as you watch them work?

-I would like to have students paired for this activity (they would each complete their own information, but have someone to discuss information with and to ask questions). I would ask them to look at their partner’s data and graph. Do they look the same as yours? Why or why not? Did you both represent your data the same way? If you both chose different ways, which works best?

- What might you learn about their understanding by listening to them or by observing them?

-I believe with this activity you could tell whether they are collecting data correctly by observing their work. It is pretty self-explanatory. They are all collecting the same data, so their representations should be similar. If one is way off then they are obviously missing some concept.

- How do the concepts taught in this lesson align to the Common Core Standards?

-This lesson aligns with the Common Core Standard 1.MD Represent and Interpret data. 4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

I’m not sure why the range of our class (the smaller class) has a greater range. That’s a good question that you brought up. I was thinking that they were measuring all the trash that their house discards each day, maybe our class has larger families, or maybe we really do throw away that much more trash than them? I wonder how our landfills compare to those in Germany. I was trying to think if the lower number of participants would affect that, but I can’t see how it would.

It’s funny that you mention the second line through the box on the German box, I wondered the same thing. I think it may be representing the middle of the box or 55 on the number line. It helps me see where the median falls in relation to the number line and gives me a better idea of what the median are, either 53 or 54 (I think). Other than that, I’m not sure what it’s for.

I noticed that you and I have a lot of the same ideas regarding the CC standards (among other things). I agree that the questions were very similar. I think you did a good job of answering it. After I read the third question I realized that part of my answer for the second question (where I elaborated more) belonged under the third answer. You did a really good job of including an example with yours though. I guess the questions were similar for us because the third question fell into line with our answer to the previous one. Maybe for others this wasn’t the case.

P.S. I love the pic of the kittens :). Too sweet!

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I think you brought up some great ideas about why the weight of the trash differs. I believe this would be a great lesson to incorporate in with social studies. Have students brainstorm why they believe we have a larger range than the class in Germany. After this, have them do some research on the landfills in Germany and other topics. Do they recycle more in Germany? Could this affect the results? I believe it has the probability to become a very interesting unit.

I also did the same thing when answering question two. I realized that half of my answer should go with the next question. And thank you, I am glad you thought the examples helped. Having examples always helps me understand more.

-I’m glad you enjoyed the picture of the kittens! I thought it would be cute and lighten up all the work! 🙂

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