Tagging Goldfish

This will be a quick post (23 days left of school, has this teacher in a craze to get everything in!).  Lots of people asked me about our Tagging Goldfish activity so I wanted to share fast.  As much as I love fancy lessons, cool activities, and technology nothing gets 7th graders more into learning than food.  This populations and sample activity was the perfect way to grab the kids attention after spring break and get them into statistics and probability mode.


Full credit goes to Harvey’s Homepage for the awesome SMART Board lesson that was the inspiration for the activity and to my amazing co-worker Jennifer Laytham for making the student work along which was the perfect addition.

Random Sampling (Smartboard Fishing)

The directions are pretty clear on the student worksheet but in order to facilitate this activity I give each student pair a brown paper bag filled with a random number of goldfish.  Using a small cup they go “fishing” to catch a random number of fish and tag them with food coloring (or sometimes we use magic markers to save on the mess).  Once tagged, the students dump their tagged fish back in the bag and shake them around to let the fish go swimming.  Next, they go fishing again to catch a number sample and record the number of tagged and total number of fish they caught before releasing them to swim again.  They repeat this process three times recording data as they go.  Once they have all of their data they add up the number of tagged fish caught and total fish caught before using proportional reasoning to estimate the total number of fish in their bag.  After I have checked their math and reasoning I let them dump the bag out to count the actual number of fish in their bag and as an extra review have them find the percent error of their estimate.  Of course the kids favorite part is eating the Goldfish after they are done!

My students really enjoyed the real life connection of tagging the goldfish like scientists tag animals in the wild to estimate populations as well.  I am sure there are TONS of variations and extensions out there but this was the perfect way for use to get back into learning mode before our last stretch of the school year!


Why I Taught the “Worst Lesson Ever Today” on Purpose

Here is a glimpse of what my students thought of my lesson today.  I can tell you that there were a lot more comments like the one on the left than the one on the right.Image


I estimate that more than 2/3 of the class declared it their “worst lesson ever” and I loved every minute of it!

The Worst Lesson Ever…an Idea is Born

I can’t lie, I am a little behind pacing wise and am working to get in the rest of the very important 7th grade probability unit before state testing and the end of the school year.  I don’t have tons of time to teach a lot of direct instruction type lessons on different aspects of probability and if you know me you know that isn’t my style anyway so I wrapped about 1/2 of the probability content into this one lesson.  Last week students were exposed to basic probability, probability on a number line and my favorite sample space and the fundamental counting principle through the amazing Mathalicious lesson “Pair-Alysis”.  They have no previous exposure to theoretical vs. experimental probability or the concept of a fair game and this is where today’s lesson comes into play.

It Started So Innocently

Our lesson started so innocently with a game of rock, paper, scissors.  Students played 20 rounds of the game in pairs and kept data on how many times each player won in addition to the number of ties the group had.











Once students completed their data collection they submitted it via their clicker so we had class data to examine.  Results were fairly evenly distributed and students quickly jumped to the conclusion that it must have been a “fair game” but when I asked them to prove why their arguments were week.  This led us to a rich discussion about how what we had just done was the “experimental probability ” but in order to prove the game fair we had to have the”theoretical probability”.  Students listed the sample space and determined that each player had a 1/3 chance of winning with the other 1/3 going to the “tie” category.

That’s Not Fair

So far this seems like a pretty boring lesson and rather unmemorable so I spiced it up in the next step by changing their groups to three people and having the groups identify a player A, B, and C.  This time scoring goes as follows:

Player A receives a point if all three players pick the same item

Player B receives a point if all three players pick a different item

Player C receives the point if two players pick the same item

After reviewing the rules most students thought this would also be a “fair game” assuming that player C assumed the “tie” probability from before and each person would have a 1/3 chance of winning.  As groups got finished I awarded the winning player (player C in every group every period) $500 in our team money.



Once all the groups were done we compiled all the data again and a riot  nearly broke out.  Students quickly figured out, if they hadn’t already, that this was anything but a fair game.  They worked in their group to identify the sample space and compare their theoretical and experimental probabilities of the game.

The Worst Lessons are the Most Memorable

To say they were upset with me over their classmates winning $500 e-bucks in an “unfair” game was an understatement.  I think they really thought at the end of the day that I would give them all $500 e-bucks but that would have defeated the purpose of the unfairness.  In the end we had fun and although they may have declared this as the worst lesson ever I would bet it will also be the one they remember most. I don’t foresee them forgetting the concept of fair games anytime soon.

Who or What Broke My Kids?

I am Desperate

I am on a desperate search to find out who or what broke my students.  In fact I am so desperate that I stopped class today to ask them who broke them.  Was it their parents, a former teacher, society, our education system or me that took away their inquisitive nature and made math only about getting a right answer?  I have known this was a problem for a while but today was the last straw.  

A Probability Lesson Gone Wrong

It started out innocently enough working on the seventh grade Common Core standard 7.SP.C.5 about understanding that all probabilities occur between zero and one and differentiating between likely and unlikely events which I thought would be simple enough. After the introduction and class discussion we began partner work on this activity from the Georgia Common Core Resource Document (see page 9).  The basic premise of the activity is that students must sort cards including probability statements, terms such as unlikely and probable, pictorial representations, and fraction, decimal, and percent probabilities and place them on a number line based on their theoretical probability.  I thought it would be an interactive way to gauge student understanding.  Instead it turned into a ten minute nightmare where I was asked no less than 52 times if their answers were “right”.  I took it well until I was asked for the 53rd time and then I lost it.  We stopped class right there and proceeded to have a ten minute discussion on who broke them.


If You Can Type the Problem into Wolfram Alpha and Get an Answer You Aren’t Doing Math

When did we brainwash kids into thinking that math was about getting an answer?  My students truly believe for some reason that math is about combining whatever numbers you can in whatever method that seems about right to get one “answer” and then call it a day.  They rarely think about what they are doing as long as at the end of the day their answer is “correct”.  Today they were given a task with no real correct answer and they lost it.  It did however lead us to have a very productive discussion about that fact that they are lucky, after all they live in the 21 century where they can solve any computation problem with technology with no issue.  The problem I told them lies in the fact that they have no idea how to interpret that answer.  We talked about the need for them to stop worrying about if I think their answer is right and to start worrying about whether or not they thought their answer was right.  I told them I was sorry someone (maybe me) broke their desire to think about math and instead taught them that math was a means to an end where there was always one right and one wrong answer and then I told them to try their assignment again.

Probability Revisited

Things went so much better the second time around with not one student asking me if their answer was “right” (perhaps out of fear of another Powers meltdown).  For the first time I heard some really rich discussions that were sometimes correct and sometimes were not but the important thing was the kids were talking about the math.  There was a great discussion about the circle that was shaded in vs. the circle that was not shaded in.  The obvious answer was that the shaded in circle represented one and the unshaded represented zero but another group of students thought maybe the non-shaded circle was actually shaded in with white and would therefore represent one as well.  Fabulous.  Another group focused on the statement “it will rain tomorrow”.  One student had seen the weather and knew there was a 90% chance of rain the other had not seen the weather and though the probability was 50% since it would either rain or not.  They compromised and picked the middle but that’s not the part I cared about, I cared that they had a reasonable discussion about their thoughts.

Why Constructing a Viable Argument and Making Sense of the Reasoning of Others is Crucial

This may seriously be the most vital mathematical practice.  If students can’t share their ideas and understand the ideas of others is there any real point in them “doing the math”.  After our lesson redo I paired each group with another group to share their number line.  Their goal was to look for similarities and differences and explain their rationale about why they placed controversial cards where they did.  I heard some of most logical and articulate arguments we have had all year.  I think I heard, “I like what you did there, but…” repeatedly along with “I hear what you are saying”.  We brought it back together as a whole class to follow it up and each group shared the most interesting conversation that they had.


In the end our meltdown and redo took more time than anticipated by me but it was time well worth it.  If we are to truly make progress in getting our students to understand the concepts presented in the Common Core to the depth intended we must help them learn to stop looking for a right answer and start looking for a right reason.  I still don’t know who broke my kids but I know it is up to me to fix them one argument at a time.