## Monday, January 23, 2017

### Which One Does Not Belong

Which one doesn't belong is a great warm-up activity for math.  It allows students to think about similar characteristics while deciding what might make one different.

Any activity in this group you make should have at least two possible answers.  In addition to selecting the answer, students need to be able to articulate their reasoning.

For instance, in the example I made there are two possible answers.  You could say the triangle because it only has three sides while the other four are quadrilaterals. The other choice is the rounded edged quadrilateral because it does not have the angular vertices.

When you make your own "Which one doesn't belong." think about how students are going to interpret the choices.  I've had students justify their answers with "That one has no R's in it."  I ask them to see if there is a better reason.

Shapes are the easiest thing to use and you could put all four shapes in different colors so they have to look beyond the appearance.  I've used shapes but I've also used expressions such as x^2y^2, xy, x^2y, xy^2.  The possible answers might be xy because the exponent is one or x^2y^2 because its the only one with both variables squared.

I've even used things like beets, tomatoes, peppers, oranges just to make a change.  This one could be oranges because the others are red or beet because its the only real vegetable.  Of course this has lead to some really great discussions on the fact that beets, tomatoes,  and peppers come in several colors while oranges are pretty much orange.

If I wanted to have them think mathematically, I might show an apple, an egg, a lemon, and a lime and ask them which one does not belong mathematically.  In this case, I might say an apple because its a sphere and not an ellipse.

Sometimes I've listed terms, or lines, or graphs, in this activity but I've made sure that at least two could be chosen.  I love this as a way to develop mathematical conversation in class and to work on looking past the surface a bit deeper to create reasons with a real basis.

When introducing the activity, its fine to start with easy examples such as the one with fruits and vegetables.  After they get used to it, throw in the mathematical element which helps them expand their ability to think in deeper ways.

I love using these in class during my warm-ups.  Let me know what you think.