This particular task helps illustrate Mathematical Practice Standard 3, Construct viable arguments and critique the reasoning of others. Possible secondary practice connections may be discussed but not in the same degree of detail. While it is possible that tasks may be connected to several practices, only one practice connection will be discussed in depth. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. Certain tasks lend themselves to the demonstration of specific practices by students. 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. If some students suggest that one half of this picture is shaded, the teacher may need to remind student that the shaded and unshaded regions must have equal area. Students struggling with this would benefit from having some tracing paper that would allow them to physically demonstrate that one can be rotated to exactly match up with the other.įor picture (iv), students need to compare areas of different shapes and decide whether the shaded area is more or less than one half. This is in part due to the fact that the pieces are less symmetrical, and the transformation needed to show they are the same size and same shape is harder to visualize for some students. It is less intuitive for students to think of the shaded region in picture (iii) as representing one half. From here, it is not a very big stretch for students to see that the circle in (ii) is composed of three pieces with equal area and that one of these is shaded and that this is less than one half. In third grade, students should be able to reason in general about the relative size of unit fractions based on the idea that they are created by partitioning a whole into a certain number of equal shares in second grade they begin to build this understanding by working with geometric figures that represent the unit fractions $\frac12, \frac13,$ and $\frac14$.įor picture (i), students will intuitively see that the circle is composed of two pieces with equal area and that one half of the circle is shaded. The purpose of this task is for students to see different ways of partitioning a figure into two or more equal shares, by which we mean decomposing the figure into "pieces" with equal area.
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