I created the above WODB question for a group of elementary teachers. I spent quite a bit of time creating and revising it (you can see my drafts below). Making a good WODB problem takes a bit of practice I've found. I'm a bit embarrassed about how poorly designed (and sometimes goofy) some of my earlier attempts were.
Here are some suggestions why each image might not belong:
Top Left: It is the only shape with more than one interior shape (a triangle and two trapezoids). It is the only shape that is not composed of congruent shapes. The only shape without rotational symmetry.
Top Right: It is the only shape with 4 interior shapes. It is the only shape whose interior shapes are all similar to its exterior shape. It is the only shape with a single angle measure (60 degrees).
Bottom Left: It is the only shape with right angles in it. It is the only triangle that is point down (it tips over).
Bottom Right: It is the only shape which includes concave shapes. It is the only shape with interior reflex angles in it. The only shape without reflective symmetry.
Updated 9/2/2016 - Added some additional suggestions regarding symmetry from Jennifer Bruce.
I've been working with Van Hiele's levels of geometric thinking lately and how it relates to the geometry outcomes in the NS Mathematics curriculum. This got me thinking about how a student's level of geometric thinking relates to WODB problems. In designing the problem above, I was intentionally trying to create something aimed at students at Van Hiele's descriptive level vice the visual level. Given a student's level of geometric thinking, how might they respond to this problem? Are some WODB problems better suited for students at a visual or descriptive level or are WODB problems inherently differentiated and students at all levels can relate meaningfully to these style of problems.
Another question that I've been thinking about recently is how to use WODB questions. Should I use them to introduce new terminology or to review terminology that students have already been exposed to. For example, in the problem above, I made sure to include a concave shape. Would it be more effective to wait until students learn concave and convex polygons and then reinforce it with this problem or should I introduce the vocabulary here and then talk about its definition? These are questions that I'm still exploring.
Nova Scotia Mathematics Curriculum Outcomes
Grade 2 G03 - Students will be expected to recognize, name, describe, compare and build 2-D shapes, including triangles, squares, rectangles, and circles.
Grade 3 G02 - Students will be expected to name, describe, compare, create, and sort regular and irregular polygons, including triangles, quadrilaterals, pentagons, hexagons, and octagons according to the number of sides.
Grade 4 G02 - Students will be expected to demonstrate an understanding of congruency, concretely and pictorially.
Grade 5 G02 - Students will be expected to name, identify, and sort quadrilaterals, including rectangles, squares, trapezoids, parallelograms, and rhombi, according to their attributes
Grade 6 G01 - Students will be expected to construct and compare triangles, including scalene, isosceles, equilateral, right, obtuse, or acute in different orientations.
Grade 6 G02 - Students will be expected to describe and compare the sides and angles of regular and irregular polygons.
Grade 9 G02 - Students will be expected to demonstrate an understanding of similarity of polygons.