From reviewing the case studies, I have learned a few very valuable concepts about teaching children measurement. I learned that children come to the classroom with preconceptions about measurement and ideas about comparing things. In the Kindergarten case study, students were measuring using comparison to other objects. Right away it can be realized that students have pre-knowledge about non-standard measurement. This really helped me tie together ideas from our power points and assignments this week. The power point breaks down the measurement thoughts that we have each day. Students are likely to have the same thoughts and will need to use measurement as well.
- Take the seven rectangles and lay them out in front of you. Look at their perimeters. Do not do any measuring; just look. What are your first hunches? Which rectangle do you think has the smallest perimeter? The largest perimeter? Move the rectangles around until you have ordered them from the one with the smallest perimeter to the one with the largest perimeter. Record your order.
My first hunch was that rectangle C appeared to be an inch wide and resembled a ruler like shape. I would say that it would have a fairly large perimeter but not the largest. Rectangle F appears to be double the size of C.
Smallest to largest = A, C, B, E, D, F, G
2.Now look at the rectangles and consider their areas. What are your first hunches? Which rectangle has the smallest area? The largest area? Again, without doing any measuring, order the rectangles from the one with the smallest area to the one with the largest area. Record your order.
Area is a bit more of a challenge for this activity. However, I first notice that these rectangles are going to be a close call when comparing areas. I believe that some of the rectangles will have the same areas such as C and D and F and G
Smallest to largest: A, C &D, B, F&G
3.Now, by comparing directly or using any available materials (color tiles are always useful), order the rectangles by perimeter. How did your estimated order compare with the actual order? What strategy did you use to compare perimeters?
Smallest to Largest: D&E, A&B&G, C&F
My estimated was a bit off than what it was when finding actual amounts. The actual orders had some perimeters that were the same, whereas I had paired them to have similar areas. I used small square tiles to compare.
4.By comparing directly or using any available materials (again…color tiles), order the rectangles by area. How did your estimated order compare with the actual order? What strategy did you use to compare areas?
Smallest to Largest: E,C,D,B,F,A,G
My estimate and actual orders were quite different. I realize that my logic was actually around perimeter rather than area making a mix up of things. I used square tiles that were in inch all around as a tool to compare.
5.What ideas about perimeter, about area, or about measuring did these activities help you to see? What questions arose as you did this work? What have you figured out? What are you still wondering about? Share your responses to all the questions in 1-5 on your blog. Spend some time discussing your answers with your blog partner.
These activities helped me see the developmental process of measuring . This also taught me to use other things as a mean of measuring such as simply comparing rectangles. My main question was how I could compare these with no tools at all. I found that I was imagining cutting several rectangles in half and seeing if they would fit in another. Although, I did not cut them I tried to work that out in my mind.
** Which of these steps best helped you compare the rectangles?
** Do you think this would be an appropriate assignment to give elementary school children?
TCM Measure up:
Much like this modules case studies, the article introduced us to children’s conversations about measurement. A student stated that the larger the unit the “lesser” times we will need to use it. With that thought in mind, I think it is safe to say this concept will be brought into my classroom as early as possible. This is significant for students to realize because then they will be able to see why Cm measures so much more than Ft. It was also interesting to read about the ideas students had when comparing fractions. One student stated that ¾ is always greater than 2/3. Tying concepts together such as this teacher did with fractions causes for optimal opportunities for student learning.
Non standard measurement can be an extremely valuable tool for plenty of field work. I personally use nonstandard measurement with out even thinking. As a wife, most nights I am the one to make dinner for my family. With that being said, I am the cook and I am a cook who refuses to measure anything (unless backing desserts). I often find myself following a recipe but do not use the measuring tools. I often just measure by hand what might be “about a cup” or what a teaspoon/tablespoon might look like in my hand. This helps me move through the cooking faster but still ensures me that the recipes are tasty. I am sure there are other careers out there that provide the need for nonstandard measurement, such as estimators of any sort. If there is anyone like me out there sometimes you must get the job done quick, which is why nonstandard measuring can be significantly helpful.
*** How do you use nonstandard measurement on a regular day?