Module 12

I apologize for the lateness I just kept running into different road blocks.
Case Studies:
 Barbara’s students in case 12 are under the impression of when referring to measurement you can use the terms, half, bigger, or smaller.  The students would use objects such as the wall to compare to saying it would be half the size of the wall.  Students did not necessarily know the units or distances of the measurements but they do know how to generalize size. The children in Barbara’s class still have to figure out how to take real measurements.  They also need to know correct terms instead of actually using half sized of objects.  

The students in Rosemarie’s case 13 struggled with the number of units in that they did not understand that the larger the unit they use the smaller the number was actually going to be, for example: if you use an inch instead of a centimeter then you would have less inches than centimeters. 

In Delores case 14, students actually were able to recognize the relationship between the sizes and the units.  Students were able to use a visual image to actually grasp the concepts. Everyone didn't measure in kids feet because they did not use kids feet but they used adult feet.  The other students are noticing that not all students feet are the same size because when looking around they made this observation. They are also noticing how most people measured as 60 and that  two students have really high numbers.

In Mabel's case 15, Students are able to recognize that you can in fact use a larger measuring device to measure smaller objects but you have to use the smaller lines that are on the larger measuring instrument.  In case 16 the issue of students choosing not a good tool for their measurements and not starting on the right place on the measuring tape was discussed among the class and solved.  Students worked through where to start when using a measuring tape.  The students understand how to use the measuring devices and realize how to start/where to start when using them. 

Ordering Rectangles Activity:

1. 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.

When placing my rectangles I came to the idea the rectangles that had the larger lengths and widths would have a greater perimeter and the ones with the smaller widths and lengths would have the smaller perimeters.  The order I chose to use was: E D G A C F B.

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.

Rectangle G and E with their similar lengths and widths I believe would have bigger areas than the rectangles with different lengths and width like C probably have the smaller areas.  The order I chose to put my rectangles in was: C B F D A E 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?

The perimeters smallest to largest are C D B E  F A G.  My first go around when estimating the order for the perimeters were pretty far off.  The strategy I used to compare orders was to use actual measurement lengths to get a number instead of just eye balling. 

 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?

I was way off on my order again on the area.  I came up with the order of E, D, A, B, G, C, F when I did the actual measurements for the area.  When drawing my color tiles and using the area formula I learned that the order I had chosen originally was not correct. 

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 in your small groups on the discussion

board.

These activities helped me to realize that estimating can give you an idea of measurements but you really need to take the time to do the actual measurements in order to determine the correct measurements.  I am still confused at how I was so off on my estimates though because when looking at the rectangles I thought I was really doing good.

For further Discussion:

As adults we use standard measurements almost without thought. Nonetheless, nonstandard measurements also play a role in speech and behavior. We ask for a “pinch” of salt or a small slice of dessert. We promise to be somewhere shortly or to serve a “dollop” of whipped cream. In some situations we might even prefer nonstandard measurements – for example, in cooking, building, or decorating. Do you or someone you know use nonstandard measurements on a

regular basis or even instead of a standard system? Give some examples and discuss why a nonstandard measurement might be preferred in some cases.

My family and I are all very guilty of using nonstandard measurements on a daily basis especially with direction and cooking instructions.  When asking where somewhere is we will say “right up yonder” or “just up the road.”  People all around where I live say things like that but people who were not around would not understand what we were trying to say.  When cooking my step-dad tells me recipes and he will say “a splash of milk, a pinch of this, a dab of this, and a dash of that”.  When you are trying to cook non standard measurements are hard to follow because you do not want to mess up a recipe.  With directions I do not have a hard time when someone gives me nonstandard measurements because I do not have a good idea of what a mile would be when walking or driving without actually measuring it.  Nonstandard measurements could be good but just depends on the situation.

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