This was the first activity the students participated in when first introduced to measurement. They were asked to use cubes to determine the length of their shoes. The big ideas for this task would be that shoes are different sizes and that you need to measure the length of a shoe to determine how big someone's foot/shoe are. This task elicited student thinking becausethe students met in their math circle before jumping right into this task. The students were asked to talk about what it meant to measure the length of a shoe. She engaged their thinking by asking, "Where should you start measuring on your shoe and where should you end?" This question opened a lot of different ideas for the students and it was evident when they were asked to work on their own to measure their own shoes. Because this was the first time the students learned about measurement, different students have different definitions of "shoe length". Some students flipped their shoes over and measured all the way from the heel to the toe of the shoe. Some other students went along the side of their shoes and stopped measuring once the shoe started to curve toward the toes.
This student specifically used his prior knowledge of going to a shoe store and how they measure your shoes. He created a personal frame of his shoe out of the cubes and figured out that he only needed to count the cubes along the side of his foot to determine how long his shoe was. Other students were confused about this, so my MT unattached the two strips of cubes attached to the long stick of cubes and attached them to the preexisting stick of cubes, to create one lone stick of cubes. She then asked the students if this student's shoe was 18 cubes long, and then took off the six extra cubes and asked the students if the student's shoe was 12 cubes long. The students were able to see that this student's handmade frame enabled him to see where the heel of his shoe started and where the toe of his shoe ended (finding the length of his shoe).
This student specifically used his prior knowledge of going to a shoe store and how they measure your shoes. He created a personal frame of his shoe out of the cubes and figured out that he only needed to count the cubes along the side of his foot to determine how long his shoe was. Other students were confused about this, so my MT unattached the two strips of cubes attached to the long stick of cubes and attached them to the preexisting stick of cubes, to create one lone stick of cubes. She then asked the students if this student's shoe was 18 cubes long, and then took off the six extra cubes and asked the students if the student's shoe was 12 cubes long. The students were able to see that this student's handmade frame enabled him to see where the heel of his shoe started and where the toe of his shoe ended (finding the length of his shoe).
This student understood that in order to measure the length of a shoe, you needed to measure all the way from the heel to the toe. He was able to create a frame of his foot to find the correct number of cubes it took to measure the length of his shoe. To advance his mathematical thinking, I would encourage this student to measure a different classmates shoe length and see if there are any differences in the lengths of the shoes. This student could also use a different measuring device besides the cubes to measure his shoe length, such as Popsicle sticks or even advance to a ruler. This would show the student that there are other measuring devices that you can use, that will give you a different answer for your length. For example, his shoe may be 12 cubes long but it may only be 2 Popsicle sticks long.
An excellent task, and your discussion of it here is very good. Make sure that in a task like this you think about not only what the big idea is, but what questions you would like to ask the students to make sure that they are thinking about the big idea, i.e., what representations / approaches / ideas do you want to compare...there are different ways to "measure" the shoe with the cubes...what does each different approaches reveal about the big idea (of measurement / area / length)? Those are explicit things to think about and write about in your lesson plan and analysis.
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