Most of my classrooms’ math experiences are done as a group.
During this task the children had to cut out a white foot that was the length
of one foot (12inches). My MT wanted to make a rectangle that was 6ft x 4ft.
She then took the green feet of what the children cut out the week before. The green
feet were made by the individual children, measuring their own feet and then
cutting them out. My MT used the green feet to measure out 6ft x 4ft using the
green feet. The learning goal was for the children to recognize that it’s
important to have one standard unit of measurement. This task was designed to
elicit student thinking; after laying out the feet, my MT had the children
think about why it was important to have one standard unit of measurement. She
gave an example: “If I were to say to my
dad to help me measure a four foot window and he was using the green feet, then
the feet wouldn’t be the same. So it’s important to use the white feet (12 inch)
unit of standard unit of measurement so that the window will be the correct
size.”
One
strategy that could be used to represent this task could be to give the example
of making a window and how using one standard of unit is important. Another
approach could be to measure out a square or a rectangle as my MT did, to show
that the unit of measurement for the green feet is not the same for the
standard unit measurement of the white feet.
One way a student
might respond to this task could be they might think the green feet measure out
to the same length of the white feet. Another anticipated response is that they
might understand that we use the (12 inch unit), but they still might want to
use their foot to measure out things.
Both of these responses would be possible errors in the student thinking.
First the
teacher laid out the first rectangle of white paper (12 in) feet, then she laid
out the green feet of “6 ft. x 4ft.”
Then my MT asked the students questions about the importance of a
standard unit of measurement. The approaches to discuss the task revealed that
the children did understand the having one unit of measurement was is important
instead of using multiple different lengths of feet.
Two ways to
advance student’s mathematical thinking could be to use a different part of
their body such as their hand or an arm. This way they won’t be thinking of it
as a foot but as another unit of measurement. Another way to advance their
thinking could be to have them start using a ruler as a form of a standard unit
of measurement.
Wow, this is another genius measurement task being used in your classroom. Your classroom is full of high level tasks!
ReplyDeleteOf course, the key to making use of them is to anticipate student thinking and to think of thoughtful ways to connect student ideas (otherwise the students' exploration of this task is just haphazard).
You give a good analysis here, but also think about how you might connect different student representations from this task.
I would say that there is another important big idea here about measurement: that is, not only relating to a standard unit of measurement (which is definitely one of the big ideas), but also concepts related to area. What would be the units for the rectangle shown in your picture?(!)
ReplyDelete