Math = Love: April 2017

Thursday, April 27, 2017

Using Probability to Find Contents of Mystery Bucket

When I dreamed up this activity, I envisioned myself using a box.  Therefore, I typed up the notes as "Mystery Box Probability." 

Then, my husband ended up borrowing the box I planned to use for an activity with his geometry classes.  I happened to notice a bucket on top of the shelf that I purchased a few summers ago at Dollar Tree.  And, that's the story of how my "Mystery Box Probability" activity became a "Mystery Bucket."  

I decided to use my ever-handy linking cubes (affiliate link) for my mystery items.

See the piece of paper sitting in the bottom of the bucket?  That's an attempt to fix the fact that the bottom of the bucket was quite see through...

That view, however, was NOT visible to my students.  I carefully guarded the bucket throughout the class period so that they could not see the contents.

I walked around the room and gave each student a turn drawing a block from the bucket.  After the class recorded the color on their tally sheet, the student returned the block to the bucket.  Once each student had a turn, I asked the class if we had enough data to make an informed decision.  Each class agreed that the more data we had, the better.

After the class decided we had sufficient data, we calculated the experimental probability of drawing each color.  Then, we multiplied the experimental probability of each color by the number of blocks in the bucket.

Having never done this activity before, I wasn't sure exactly how well it was going to work.  But, I figured even if our estimates were way off, it would still teach my students something about probability.

After our predictions were recorded, it was time for the big reveal.  Instead of just showing them the contents of the bucket, I removed the blocks one at a time.  I wanted to make the anticipation slightly painful for them.  I drew it out as long as I could.

One of my classes had all five of their predictions wrong.  That class unfortunately had a tendency to draw that black block from the bucket over and over and over despite it being the only block of its color in the bucket.  This really threw off their data!  My other two classes each got one or two colors spot-on.  The other predictions were close but not exact.  We discussed how we'd need to collect a large amount of data to arrive at a more accurate prediction.  

All in all, I really enjoyed using this activity with my students.  I will definitely use it again next year!

File for this activity is uploaded here.

Saturday, April 22, 2017

Blocko! Game for Practicing Experimental and Theoretical Probability

Algebra 1 is in the midst of our LAST unit of the year.  With the stress and craziness that comes with testing + end of year activities, I'm trying hard to make our probability unit as interactive and fun as possible.  Many of the other teachers in the school have resorted to Netflix for their lesson plans, so it's a struggle to get my kids to do anything.  

Oklahoma's new standards for Algebra 1 focus on experimental probability instead of theoretical probability. 

My husband recently reminded me of a probability activity I had used with 8th graders when I was a student teacher.  Natalie Turbiville calls the activity "Beano" on her Walking in Mathland blog.  As a student teacher, I decided that beans and middle school students were not a good combination.  So, I played the game with some counters and didn't exactly give it a name.  In fact, my first blog post about the activity was titled "The Probability Game Without a Name."

This year, I decided to rename the activity to "Blocko!"  This name was inspired by the fact that I gave students "blocks" as game pieces.  I used one of my favorite classroom manipulatives - linking cubes (affiliate link)!    

I created a quick game board for my students to use.  

Each student received 12 linking cubes (affiliate link).  Students were instructed to place their 12 blocks on the numbers of their choosing.  I told students that they could place all of their cubes on the same number or different numbers.  It was interesting to see just how creative they got with their arrangements.  At this point, I still had not explained the point of the game to my students.  

Here are a few of my students' starting arrangements: 

Some of my students were VERY stressed out that "1" had been left off of the game board.  I took this as the opportunity to explain what the numbers on the game board represented.

The premise of the game is quite simple.  I will roll two six-sided dice, and I will announce the sum of the two dice to the class.  If the student has a block on that number, he/she may remove exactly one block from that space on the game board.  If a student has multiple blocks on a certain number, he/she must wait until I have called that number multiple times to remove multiple blocks.  The first student to clear his/her board and shout "Blocko!" is the winner.

After explaining the game's basic rules, I gave students one last chance to make modifications to their game board.  I figured this was fitting since I had instructed them to place their blocks on the board before explaining the rules!

I used a lid to a paper box to keep my dice from escaping between rolls.

With an earlier class, I used my large foam dice (affiliate link), but I ended up getting quite the workout chasing them around the room!

Big Foam Playing Dice (12 Pack)(Discontinued by manufacturer)

After each roll of the dice, students removed a block, if possible, and made a tally in their notebook.  I created this sheet to help my students calculate the experimental probability of rolling each sum.

After each round of the game, I gave the winner a piece of candy.  Students, then used their tally chart to revise the placement of blocks on their game board for the next round.  Depending on the class, we played anywhere from probably four to six rounds of the game.  It was exciting for me to be able to watch their

As we progressed through the rounds, students' game boards slowly started to shift from the block on every single number stage to blocks in the middle of the game board stage.

After playing multiple rounds, my students counted up the number of dice rolls and calculated the experimental probability of rolling each sum.  The students recorded these probabilities on the table in their notes.

Then, I had students make a frequency chart.

After experiencing the experimental probability of this game for themselves, I had my students investigate the theoretical probability behind the game.  

First, we had to complete a chart to find all of the possible sums that result from rolling two six-sided dice.  Then, my students used this chart to help them calculate the theoretical probability of rolling each sum.  We compared the the theoretical probabilities we had calculated to the experimental probabilities we had found.  

It was super exciting to watch my students realize WHY the dice seemed to keep giving them the same sums over and over and over.  

We ended the activity by answering a few questions that I borrowed from the worksheet on the Walking in Mathland website.    

Here's a link to the game board and probability charts I created for students to glue in their interactive notebooks.  

Tuesday, April 18, 2017

Looking for Outliers in the OKC Thunder

Today's lesson is brought to you with special thanks to the OKC Thunder.  I chose to use data for the OKC Thunder because they are Oklahoma's only professional sports team.  Oklahoma is just a little bit obsessed with them!   

Here's the handout I gave my students to glue into their interactive notebooks: 

I got the salary data from Basketball Insiders.  When my students started looking at the data, they were shocked that I had been able to find that data on the internet! 

Up until this point in the course, the only way my students knew to identify outliers was to eyeball them.  This was really frustrating my students, and they kept begging for a more definitive way to see if a data value was an outlier.  I LOVE that my students were begging for a method for identifying outliers.  I need to find more ways to make my students BEG for solutions in math class!  

Before spilling the beans and telling them how we check for outliers, I asked the class to discuss who they thought must be an outlier.  100% of the class was absolutely sure that Russell Westbrook HAD to be an outlier.  Some reasoned that Enes Kanter must also be an outlier since there is such a big gap between Taj Gibson's salary and Enes Kanter's salary.  Others were not so sure.  

Then, the conversation got super interesting when someone suggested that we might also have outliers on the lower end of the data.  This was even more controversial than the conversation regarding Enes Kanter!  I had to stop the debate and get my students started on finding the five number summary.  

This was my students' first time ever finding the five number summary for a data set.  Finding the minimum, median, and maximum were a breeze.  Students were a bit confused by lower quartile and upper quartile, but that confusion was quickly cleared up.  

Next, we found the interquartile range.  I must have jumped too quickly referring to the interquartile range as IQR because when my students took their quiz, I got asked way too many times what "interquartile range" meant.  As soon as I said "IQR" they knew exactly what to do and got right back to work.  Oops...  Maybe I should only call it "interquartile range" in the future until students beg for an abbreviation!  

Defining outliers as being more than 1.5 IQRs outside of the upper quartile and lower quartile results in two outliers: Russell Westbrook and Enes Kanter.

My students ended up being engaged throughout this activity.  They seemed genuinely interested in finding out which players were outliers.  

One student begged me to look up data for other sports teams for their quizzes.  He said that if I used his favorite teams I would be his favorite teacher ever!  

Files for this lesson are uploaded here.  

Monday, April 17, 2017

Guessing Correlation Coefficient Game

State testing has thrown my teaching off so much lately.  I usually try to keep all of my Algebra 1 classes in the same place, but that just hasn't been possible these past few weeks.  

Algebra 1 is currently working with scatter plots and regression.  My 6th hour class finished super-early compared to my other classes, so I pulled up a game on the SMARTBoard that asked them to guess the correlation coefficient of a scatter plot.  

Here's the link to the website I used.  The website loads four different scatter plots. 

The four scatterplots each have the same four choices, so it is essentially a matching activity.  I really like that the site tells you the historical chance of error below each problem.  

I had students volunteer to come up to the front of the classroom and play along.  Each student would click their answers on the SMARTBoard and click "Check answers." 

If the student got all four answers correct, he/she got to pick a piece of candy out of my prize bag.

My kids got really into this activity.  Even the kids who weren't playing at the SMARTBoard were following along.  There were numerous times when a kid in the audience gave the person at the board a really big hint.

I definitely want to include this as part of my main curriculum next year instead of a random filler activity!

Sunday, April 16, 2017

Dry Erase Workmat for Finding Five Number Summary, IQR, and Outliers

My Algebra 1 students are in the midst of our next-to-last unit of the year: data analysis.  This is my first year of teaching Algebra 1 where my students do not have to take an end-of-instruction exam in Algebra 1.  This means that I don't have to rush through concepts in order to have enough time to review for a test in April even though school doesn't get out until May.  Usually, our unit on data analysis is super-short as a result.  

This year, I have plenty of time to really develop my students' skill at reading data displays and creating their own data displays.  Today, I want to share an activity I created to give my students practice with finding the five number summary and IQR of a set of data.  Students then used this information to check for and identify outliers.  

I started by creating a workmat template in Publisher.  I use Publisher to create almost all of the resources I post on my blog.  

I titled it "Identifying Outliers Practice," but it also gave my students practice with finding the five number summary and IQR.  Not sure what I could title it to include those as well...

I printed this workmat on 11 x 17 cardstock (affiliate link) that I slid into one of my 11 x 17 dry erase pockets (affiliate link).  I have a set of smaller, 8.5 x 11 dry erase pockets (affiliate link), too.  But, I prefer the 11 x 17 size (affiliate link) for partner work.      

I also created a set of data value cards (1-36) that fit exactly into the data set boxes on the work mat. 

Each set was cut apart and placed in a tiny bucket from Dollar Tree. 

These stacked up very nicely between classes!

Like many activities I create, I ended up modifying the activity throughout the day to improve it and make it more effective.  Originally, I had planned for each pair of students to roll a 12-sided die (from this set of polyhedra dice from EAI Education - affiliate link) to determine how many data values they should draw from their bucket before starting.   

My thought behind having them roll a die was that I wanted them to get used to how to deal with quartiles when there are an even number of values and an odd number of values.  

But, then my students were ending up with data sets of 3, and the data practice just wasn't rigorous enough. 

For my afternoon classes, I did away with the dice and had each pair of students draw 12 data values from their buckets.  This ended up working soooo much better!  

As students worked, I circulated the room and checked for errors.  In the picture above, the IQR should actually be 18.5.

As pairs finished, they would raise their hands to have their calculations spot-checked.

One of the issues I didn't foresee with this activity was that the majority of students did not find any outliers in their data.

It ended up being okay because after I check each pair's work, I would challenge them to create their own data set that had outliers.

This ended up being the perfect extension activity!

I love how much collaboration I can see with my students in these pictures!

There are a few changes I would like to make in the future to this activity.

After students draw their data values and before they begin doing any calculations, I would like to have my students make a prediction re: outliers.

Then, after they finish all of their calculations, I would like them to write a sentence explaining why or why not the data contains outliers.  My students really struggled with writing a sentence to justify their outliers on their quizzes.  Need to start practicing that earlier!  

Additionally, I would like to create a set of "challenge cards" for students to work through.  For example, each card would tell them how many cards to choose from the bucket.  Students might randomly pick cards, or they might pick specific cards to try and achieve a specific thing.

The file for this activity has been uploaded here.