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 2D 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. EL
14 Comments
Alicia Potvin
2/1/2016 01:12:41 pm
HI Erick! I love this problem!! I agree, creating WODB questions is much harder than it looks but very rewarding! You could also rule out the bottom right because it is the only one where the interior shapes do not include at least one quadrilateral (they are three irregular concave hexagons).
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8/2/2016 01:04:07 pm
Love this puzzle!
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marlow harris
9/6/2018 04:16:45 pm
there is no answer
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Glynnis Fleming
8/4/2016 06:23:22 pm
I've been noticing how children can "see" and notice shape which they cannot describe  like parabolas from the garden hose. But it's still mathematical to think and talk about these noticings, even if we can only use gesture to describe it. So I think that you accomplish mathematical amusement (fun with math) at the very least and the addressing of expectations at the most. I think that's the cool thing about wodb; you can be as precise as the grade level(s) / Van Hiele levels of the people with whom you are working!
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Jennifer Bruce
9/1/2016 11:11:37 pm
I stumbled upon your problem when searching for a warmup for my high school geometry students. Some great aspects of your triangle choices involve reflective and rotational symmetry, as well as congruence  all of which are topics in HS geometry. The top left doesn't belong because it is the only one with no rotational symmetry. The bottom right doesn't belong because it is the only with with no reflective symmetry. Throw in your observations about congruent shapes in the interior and we have a great warmup problem that reviews almost all of the vocabulary in my Congruence unit! Thanks!
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Hi Erick,
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Sunitha taduri
1/9/2019 01:36:27 am
Rules of symmetry apply for top left, top right, bottom left. The right bottom does not follow rules of symmetry
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JAnie
10/1/2019 11:24:50 am
Bottom left has right angles? If those 3 angles in the center are congruent 3(90) = 270 not 360 What do I not see?
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Lizzy
5/19/2020 01:52:01 pm
What is the answer???
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Erick
5/19/2020 02:00:38 pm
The answer is up to you. Any of the four shapes could be the answer as long as you come up with a justification for why. Which one looks like it doesn't belong to you? What makes it different from the other three?
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