Mathematically, Which One Does Not Belong?


I know when you see the picture, the egg immediately jumps out.  It doesn’t belong because of the fact that it’s not a fruit, right?

But you can’t let the students answer that way.  You have to push their thinking. How does one of those items not belong MATHEMATICALLY? Can we talk about measurement, shape, symmetry, or patterns?

Whenever we want to have students use precision of language in mathematics, we need to give them the opportunity to have authentic conversations about real life things.  We can’t create a language rich classroom without connecting mathematical terms to something that they know. We need to listen for mathematics in their every day language, not just during math class.

No Answers Given for Deep Math Tasks

If you haven’t heard of Dr. Jo Boaler of Stanford University, you’ll need to make it your mission to learn about her this summer. She is an outstanding educator that is truly creating a revolution in the math world.

You can find out more at, where there are deep math tasks for many ages. I had the pleasure of working with a phenomenal fourth grade teacher who wanted to see these math tasks in action. Here is an example of one…


As teachers we were very hands off while they were solving, and decided to break them into small groups. We told them that we were going to come around and ask questions.  We told them they could use tools, use each other and that we would not be giving them the answers.

One particular group tried to just imagine it. That didn’t work. Then, a group mate began drawing. That still didn’t work.  So finally the group decided to build a model of the tic tac toe board.  Voila! The light bulbs turned on. They began to debate and talk and figure out which ones were repeats and which ones were unique combinations.


And guess what, we STILL did not give them the answer.  According to some of our most researched math educators/math gurus, it’s actually OK to not give an answer. Math isn’t about questions and answers, instead it is about THINKING.  It’s about estimating whether that thinking is reasonable. When you are shopping, and trying to figure out how many pizzas to buy for your giant family that is coming this weekend, there is no answer key. Right?

Don’t worry…I’m still adjusting to that way of thinking. This is VERY hard for me to not reveal any answers. More to come on these types of tasks!


Teachers, You Don’t Have the Summer Off

Summer is an anxious topic in my own mind. As an educator I go through so many emotions in the summer. First, it’s the disbelief that the school year is over! A little depression always follows, I miss the kids, I miss the staff and I miss the daily routine of getting up and having a purpose for working during my day.

Then, I have the guilt. The guilt of having this precious time off and feeling like I need to defend it to others. When I tell new people I meet that I am a teacher, the comments start rolling “Oh, how nice! You get the whole summer off?” and “Are you done working?” or “It must be nice to have all that time off!”.  Most of the comments are coming from kind, well meaning people. Others are jealous, others seem a bit judgy that I’m being “paid” for this time.  (Hello?! Can we finally dispel this myth that teachers are paid for their summers?)

But overall I feel a sense of calm. Yes, there are some work days that will follow but it’s a time for me to recharge and get my head around some of the things that were bothering me during the last school year.  I spend my time solving problems, thinking of creative ways to help kids learn more and just reflect. During the school year, I feel that there is SO little time for thoughtful reflection. It’s a constant rush and buzz and lots of stress with the things teachers are expected to fit in. In the summer my mind is finally quiet, and I can truly think.

So teachers, cheers to you. I know you’re not done working! I know that you are already thinking about the next school year, the next project, the next everything. And if you could also take a true break from that and check out mentally for a while, I won’t judge you.


Math Doesn’t Always Have to Be Numbers

Which one of these does not belong mathematically?



Visual mathematics will fire up your students, especially those that do not have an “answer”.  They also work as math warm ups and math shares at the end of your lesson. It’s SO easy to throw up 3 or 4 objects under your smartboard and voila! You’ve got instant math talk and math debate.  The only rule…there must be mathematical words when you describe and defend your thinking.

Your students will blow your mind!