Students learn about ultrasound and how it can be used to determine the shapes and contours of unseen objects. Using a one-dimensional ultrasound imaging device (either prepared by the teacher or put together by the students) that incorporates a LEGO(TM) MINDSTORMS(TM) NXT intelligent brick and ultrasonic sensor, they measure and plot the shape of an unknown object covered by a box. Looking at the plotted data, they make inferences about the shape of the object and guess what it is. Students also learn how engineers use high-frequency waves in the design of medical imaging devices, the analysis of materials and oceanographic exploration. Pre/post quizzes, a worksheet and a LEGO rbt program are provided.

This task asks students to classify shapes based on their properties. The task itself is straightforward, but there are a number of opportunities to present this task in class and push the level of discussion and reasoning. For example, the rule for the bottom circle is that all shapes must have all sides with the same length. Some students will likely conjecture that the rule is either that all shapes must be regular polygons or that all shapes must be equiangular. Either of these would be true except for the rhombus.

Though this would likely extend beyond the scope of 5th grade understanding, it might be interesting to look at the pentagon with the right angle. In the eyes of a 5th grader, it looks as if it might have sides of equal length. They have not yet derived any rules about the sum of interior angles in polygons, but they should be pushed to see that mathematicians cannot make assumptions based on the appearance of shapes. We only know that each of the shapes in the bottom circle is equilateral because the tick marks indicate that the sides are the same length. In that same line of reasoning, we must be careful to specify in part b that the rectangle does not have equal sides. A deep discussion would allow students to construct viable arguments and critique the reasoning of others (MP 3) and attend to precision (MP 6).

This website provides a collection of submitted puzzles for math students and their teachers. For each puzzle, students work to determine how each of the numbers, shapes, or graphs & equations are unlike the other three in the puzzle. There are many different, correct ways of choosing which one doesn't belong, and no answer keys are provided.