**Textbook Pages 1-26: **

- Explain what it means to measure something. Does your explanation work equally well for length, area, weight, volume, and time?

-When you measure something, you are trying to see how long or tall something is. You are also possibly trying to solve how heavy something is.

-When I thought of measuring, I automatically thought of a ruler. It is the first thing that comes to my mind. Also, because I just moved this weekend, I mostly thought of measuring as trying to see how big, wide, tall, etc. things are. My explanation for measuring did not work well for area, volume, or time. My explanation did not relate to time or volume at all.

- Four reasons were offered for using nonstandard units instead of standard units in instructional activities. Which of these seem most important to you and why?

-I believe the most important reason to use nonstandard units when measuring would be because they provide younger students a good rationale for using standard units in the future. The whole goal is to improve student’s math and measuring skills. Nonstandard units can help prepare them for math in the future which is important.

**Annenberg Video Circumference and Diameter: **

- Describe Ms. Scrivner’s techniques for letting students explore the relationship between circumference and diameter. What other techniques could you use?

-Ms. Scrivner let students find circles around the classroom and measure and figure out the relationship of the circumference and diameter on their own. I thought giving them the hands own experience of finding their own circles around the classroom to measure was a great idea. Another way you could have students do this would be to actually give them a list of circles that are around the room. The students could focus on these things and that might possible knock out some of the incorrect information.

- In essence, students in this lesson were learning about the ratio of the circumference to the diameter. Compare how students in this class are learning with how you learned when you were in school.

-Students in this class learned the relationship of circumference and diameter by exploring own their own. I do remember something similar to this in my elementary school experience. However, we were given a list of certain circles around the classroom to measure and guided throughout the experiment. We also did not work in groups.

- How did Ms. Scrivner have students develop ownership in the mathematical task in this lesson?

-Students developed ownership of their mathematical tasks by finding their own circles and discovering the relationship between circumference and diameter own their own.

- How can student’s understanding be assessed with this task?

-Student’s understanding can be assessed by the charts that they completed throughout their activity. Also, by their explanations throughout the discussion after the activity was completed.

**Annenberg Circles and Pi Module: **

I had a hard time understanding problem A9…

Since Pi is an irrational number, can both the circumference and the diameter be rational numbers? Can one of them be rational? Explain using examples.

In my head, if we are multiplying by an irrational number, wouldn’t our answer be irrational? This question has me very confused.

I found problem B8 very interesting…

When you enlarge a circle so that the radius is twice as long (a scale factor of 2), what do you think happens to the circumference and the area? Do they double? Experiment by enlarging circles with different radii and analyzing the data.

When I first read this question I thought it was obvious that they both double. It was not until I actually worked through the problem that I realized the area was actually multiplied by 4 and the radii was doubled.

**Further consideration: **

Throughout this semester, we have explored many different ideas. One of the main ideas I will take with me to my classroom is having students collect data. I never realized all the different ways there are to collect data and how younger students can be involved in this as well. I also really enjoyed exploring different graphs. I think these are great and would like to help my students graphing skills as early as possible. I also learned through our children’s literature project that there are multiple book that relate to math standards that are available. I will definitely be using these with future students. I also really enjoyed learning about measurement in this last section. I would love to use different measurement techniques and relate different forms of measuring together like we have reviewed in the case studies and from the video in this module.

I agree that it is difficult to explain what it means to measure something that includes the different ways of measuring. I didn’t really even think of weight as a measurement, but it definitely is. I also thought that the most important reason for using nonstandard units when measuring was to avoid conflicting objectives in introductory lessons, but the article I read used nonstandard units in the way you mentioned. I believe this is important too, possibly more important than the previous one I mentioned.

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