Odd Thing Out

Problem

Brian, Margaret, Kim and Jo were looking at the shapes below.

Brian says, "Hey, the first one is the odd thing out."

Margaret says, "No, Brian, the second one’s the odd thing out!"

Kim says, "No, it’s the third one!"

Jo says, "Well you are ALL wrong! The last one is clearly the odd thing out."

Who is right and why?

Teaching sequence

1. Show the students the four objects of the problem. (The students might have made the objects in a previous lesson.) Hold up the sphere.
   Who knows what this is?
   What can you tell me about it?
   How do we use spheres?
2. Repeat step 1 for the other three objects.
3. Here’s what the four friends Brian, Margaret, Kim and Jo said about these objects. Tell the students the problem.
4. Get the students to tackle the problem in groups or on their own.
5. As the students think about the problem, go round the class and help them to write down some of their answers. Ask them if they can think of more than one way to tell the objects apart.
6. Students who are able to do this relatively quickly could go on to the Extension problem.
7. Get some of the students to report on what they have done. Suggest that a good way to gather all the information together is to write it in a table. Construct the table on a large piece of paper that can be put on the wall after the lesson ends. This table can be referred to later and even added to.
8. Discuss the Extension problem.
9. At this point or as a follow-up activity you might put one of the objects in a feely bag. Ask one of the students to put a hand in the bag and then tell the class what they feel. Warn the student that they are not to tell the class what the object is but rather what properties they can feel. The class should try to guess what the object is that the student is describing.

Extension

Ask the students to find other 3-dimensional objects in the classroom. Get them to say what makes them different from each other and from the four objects of the original problem.

Solution

In a way there is no solution to this problem because in a sense, each one of the students is correct. Brian is right because the sphere will roll no matter how you put it on the ground. Margaret is right because the cylinder is the only one that has a flat face and a curved face. Kim is right because the box is the only object that has six faces. Jo is right because the only pyramid has five faces.

You might ask the class to find as many reasons as they can to explain why each object is really the odd man out. This information could be displayed in a table like the one below.

This table could be added to both in the different properties of the objects and in the types of objects. Hence the Extension could be incorporated into the table.

You might extend this problem by looking at the objects and seeing what is the same about them. This might lead to another table.