Category Archives: one good thing

Open Data Collection with Party Favors

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Yesterday was my last day with AP Statistics.  Most had presented their final projects last Friday.  We had extended periods due to other courses taking finals.  Once everyone had finished their presentations, we had a lot of time left.

I opened the cabinet and got these items out…placed them on a desk.  I told students to get one (or more) and play.  After a few minutes of kid-like laughter, I instructed them their last daily assignment was to create a data collection lab.

Basically, they were instructed to come up with a question addressing their toy, determine what they could measure that would allow them to answer their question, outline a lab to collect data and suggest a statistical test that would allow them analyze their data.

It was quite humorous watching them combine toys to develop their questions.  It truly was a time of play, but at the same time – thinking was happening!

I believe this will be a task I use the next time I get to teach Statistics.  However, it will focus on the type of data we collect…categorical vs. quantitative and what questions could be answered based on the collected data.

Once again, I am amazed/not amazed at some of the ideas they come up with.  And remind me – why do I not do more tasks like this?  #lakerproud #awesomestudents

 

Cool Shoes #onegoodthing

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I struggle to find the balance between just the math and in a context.  That’s why I love modeling with math.  I have for years, tried to provide a context – a hook to grab students’ attention, and reference back to when working with “just the math.”

This week, we’ve looked at multiple ways of writing equations of lines – when given varied information:  Slope and y-intercept, slope and a point, given 2 points, given a point and parallel to a given line.  But its been very generic.  Just the math.  Some loved it. Some hated it.   But none saw a purpose or reason for it.

Anyway, today, we collected data.  Created scatter plots.  We drew a trend lines.  Chose a couple of points…to write the equation for our line of best fit.  Why did I choose to do “just the math” prior to using the lesson hook?  Not sure.  I’m still battling which should come first.  But today, I wish I had used the task first.  Provided a need for the math.

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It was in a class that we used Cool Shoes from Chris Shore’s big blue book Math Projects Journal (one of my favorites for years!)…that my day was made.  The task uses height to predict shoe size.  In our discussion, I mentioned how online shopping sometimes allows you to click a sizing chart.  A student all of a sudden exclaims – “Thank you!”

Me, “Okay.  for what?”

The student explains – “Finally, I see a purpose for all of this stuff!  A real, purposeful use.  Somewhere this can actually be used, be helpful.  How real people can use these math skills to do something.”  Smiling. Smiling. Smiling.

I went on to share – That’s what math really is…looking for patterns, modeling those patterns and using our models to predict, make connections, etc.  Why do they weigh us when we go to the doctor?  How do they know how much meds to prescribe when we are sick?  What happens when someone has a cancerous tumor?  How do they measure it?  How does the oncologist decide how to treat it?  How do insurance companies set rates?  How do businesses make projections for upcoming projects?

One small glimpse.  A student saw a purpose.  The student smiled in math class (finally).  I smiled.  It was a good day.

 

Students Making Sense of Quadratics

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I realize some folks will bash me for sharing this from an Algebra 2 class, but based on benchmarks, most of my students have major gaps in quadratics. 

I began with reviewing multiplying 2 binomials on our whiteboards.  I shared the box/area model and several smiles celebrated because they “saw it” and were doing it correctly!

Last week, I pulled out a box of Algebra Tiles.  We literally explored building squares.  I wish I had taken pictures because some of their squares were like a grandmother’s beautiful quilt blocks.  I began tying it back to our box/area models -I’d rather think of it as leading (not forcing) their thinking – but they were quickly picking up the patterns. 

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We then began looking at the algebraic equivalents, again, with a sketch along side allowing them to “see” the process.

Our next step was to find the missing value without tiles/picture models…and then I asked them to review their multuplying with 5 expressions alongside.

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“What? You think they’re the same thing?!?” I asked,  “Prove it to me. Well, by-golly-jee. You are on to something!”

The following day in class, I made a HUGE ordeal of different ways to write zero.

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I explained our next few minutes were a process. But we talked about it, step by step, completing the square, adding ‘that zero’ in our expression, the separating the trinomial and 2 constants.  Rewriting our trinomial as a binomial squared.

Ok. Why in the world would anyone want to do this?  I told them we were finding hidden information.

As they arrived at this form (x+4)^2 – 9, I paused, reminding them to think back on our function transformations before Christmas break.  How would this function y= (x+4)^2 – 9 move on our graph from this one y=x^2?  Quiet. “Move left 4 and down 9!” Someone exclaimed.  Really? Are you sure? We graphed the two and yes, it did just that.  So what does this tell me about my parabola?  They didn’t say vertex. Or minimum.  They said it shows us how the graph was transformed. 

I will take that.

I then asked them to move left 4 and down 9 from the origin.  What have you found? The lowest point.  The vertex. The minimum. All their responses, not my statements.

We set our expression equal to zero and solved the equation, using our inverse operations.  They made the connections with the x-value of the vertex being the “center line” of the parabola.  They realized the +- 5 were steps in either direction from the center line.

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I most appreciated the questions they asked on #3, 4 and 7.  Several chose #7 thinking it was shorter, thus less work. Snafoo. No middle term. What happens? 

I suggested they look at it from a transformations point of view.  Someone shared-It doesn’t slide left or right, only down.  Another student said-well, that’s the easiest equation to solve! (Yep.)

Why did #4 bother some? The middle term had an odd coefficient.  But once they shared their thinking, ok. Got that one too!

#3 was what we math folks recognize as perfect square trinomial.  But for the students, it was an a-ha.  Again, using the transformations context, we moved right 5, but not up or down.

L: But I thought all quadratics intersected x-axis twice?  I asked – did this one? No.

What about y=x^2 + 3?  It moves up 3. Ok. How many times did it intersect the x-axis? It doesn’t.   Hmmm.

A student who is rarely engaged then asked, if you can make a parabola that doesn’t intersect the x-axis, can you find one that doesn’t intersect either axis?  Me: Can we? What would it look like? S: Noooo. As its going up, increasing, it would be increasing outward, too!  More discussion, between them. Me not included. I was smiling.

And their questions were what drove our lesson today.   And I was so excited, telling them their questions make me think! And when they’re asking questions, their brains are processing the information – making it their own.

It was a good day.

One good thing… #MTBoS30 Post 19

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Our county fair is in full swing this week.  Our Jaycees arranged a free day for special needs children in our community and their families to enjoy.

Loved this post by a colleague who adores her family, is passionate about teaching English and capturing life-moments through photography.

“The Russell County Jaycees arranged for the carnival at the fair to be open and free to special needs children and their families today.  As the mother of an autistic child, I know I can never put into words how grateful I am for the people who made that happen and treated us with such kindness today.  Finley had a blast riding rides with his big brother (and his daddy), and we enjoyed a stress-free family outing, which rarely happens for us.”

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Thankful to live in a community of people who care…

Thanks Lindsay for letting me share this one good thing!