Eva, Tamati, Noah and Jo are looking at the objects.

Eva says, Hey, the square is the odd one out.

Tamati says, No, Eva, the circle is the odd one out!

Noah says, No, it is the box!

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

Who is right and why?

This problem explores some basic properties of shapes. It is important for students to get a good 'feel for' shapes, to name common shapes correctly and to begin to identify their properties.

There is no correct answer to this problem. It is likely that the students will come up with several answers that are not listed in the solution. Accept correct answers and ask for students to explain their thinking.

Copymaster of the problem (English)

Pictures of a square, circle, and (irregular) pentagon, and a cube for the class to use.

A cube

### Problem

Eva, Tamati, Noah and Jo are looking at the objects.

Eva says, Hey, the square is the odd one out.

Tamati says, No, Eva, the circle is the odd one out!

Noah says, No, it is the box!

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

Who is right and why?

### Teaching sequence

- Show the students the four objects of the problem. Point to the square.
*Who knows what this is? What can you tell me about it?* - Repeat step 1 for the other three objects.
- Read what each of the four friends say about the objects, and read the problem question.
- Have the students to work on the problem in groups or on their own. Have them record their ideas in their own way.
- As the students think about the problem, go round the class and write down some of their answers. Ask them if they can think of more than one way to separate the objects.
- Have some student report back. Collate their ideas in a large table for display and future reference.
- Discuss the Extension problem.

### Extension

Ask the students to find other objects in the classroom. Get them to say what makes them different from/ siliar to each other and 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. Eva is right because the square is red and the other objects are blue. Tamati is right because the circle is the only on that will roll. Noah is right because the box is the only 3-dimensional object. Jo is right because the other objects have symmetry (that is they can be rotated through quarter and half turns on to themselves) but the pentagon doesn't.

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.

square | circle | cube | pentagon |

it's red | it will roll | it's 3-dimensional | it has no symmetry |

it has four sides | it has only one side | it has 8 corners | it has five sides |

it has four angles | it has no angles | it has 6 faces | it has five angles |

it could be used to tile a floor | ? | it has 12 edges | it has exactly 2 right angles |

? | it could be used as a dice | ? |

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