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.

Goldfish

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!

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Using Human Box Plots to Teach 7th Grade Variability

When I was a 6th grade teacher I LOVED teaching box plots.  It was easy to make them come alive for students using the Human Box Plot lesson that Julie Reulbach outlines here.  When I moved to 7th grade and adopted Common Core I was sad to leave my box plot lesson behind and overwhelmed with thoughts of trying to get students to make comparisons about variabilty using them.  After some trial and error I landed on a method to incorporate the Human Box Plot while teaching variabilty.

Start by selecting data to graph.  I have done about everything including student height, paper airplane flight data, and day of the month they were born.  Today we used the latter.  Then tape a number line to your floor (I love pretty tape but painters tape works great too and will make your custodial staff less hostile).  Label the number line with whatever interval works for the data you are using.  The use of the number line really helps the kids find their place in the data and keeps your variability comparison honest.

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Instruct students to find their place on the number line.  We usually have to have a discussion at this point about what to do if two students share the same data piece.  Their instinct is usually to stand beside each other so we have to work to make sure they know they are sharing the spot so they need to stand in front of or behind each other.

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Next I lead a discussion about the median and have the kids sit one from each end until we find it.  Mark the median with another piece of tape.  We repeat the process to find both the lower quartile and the upper quartile marking each with a piece of tape.  Finally mark each of the extremes with a piece of tape as well.  Construct the box around the quartiles with tape and mark the “whiskers” as well with the tape.

This is what it will look like when completed after the first class.

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Repeat with each class you teach.  I teach 4 sections of general and advaced pre-algebra which means I had four box plots by the end of the day which leads to some awesome variabilty comparisons.

After all four classes were completed:

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Once all four classes have made their box plot I leave them in place for the next class.  Students examine all four box plots and we have some really rich discussions about which class has the higher median, which would have a higher mean, why some quartiles seem smaller than others etc.  I let the kids lead the discussion and make natural observations and we build on that to discuss variability at a more in depth level.

I followed the lesson up with this task from Illustrative Math.  Students also selected at least two data sets that they wanted to make box plots with in order to compare variability.  They haven’t turned those in yet but I am interested to see what they selected and how they drew conclusions about the data.

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I leave post-it notes in all of the kids supply baskets in case they ever want to leave feedback about a lesson either positive or negative.  Here is what two of them had to say today.

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This lesson has really enriched our variability discussion and leads us in nicely to our mean absolute deviation lesson which is coming up right after we do the Mathalicious lesson “Wealth of Nations”.  How do you incorporate variabilty into your class?