## IM Commentary

This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps. If students do not recall this fact readily, one way to review it is to have them draw a strip of ten stamps on graph paper (so they don't have to draw all the individual stamps) and then draw ten strips that are side-by-side to represent a sheet and ask how many stamps there are in one sheet.

Given how closely pictures in this problem correspond to base-ten blocks, having experience with those and/or having them on hand would be helpful.

The second part of the problem highlights the fact that while reordering is allowed in addition (because of commutativity), we cannot reorder the digits of a number, since these digits are attached to different place values. Its solution engages Standard for Mathematical Practice 6, Attend to precision.

The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of mind that students need to develop in order to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While it is possible that tasks may be connected to several practices, only one practice connection will be discussed in depth. Possible secondary practice connections may be discussed but not in the same degree of detail.

This particular task helps illustrate Mathematical Practice Standard 6, Attend to precision. In this particular case, Mike wasn’t making the connection that digits are attached to different place values. Due to this misunderstanding, he wasn’t paying attention to the different arrangements of the stamps (single, strip, and sheet) and how each arrangement related to place value. Thus, he interpreted the total number of the stamps incorrectly. Students will need many experiences with place value and digit placement to be able to interpret quantities precisely and accurately.

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