Category Archives: real life graphs

January #MTBoSblog18 – Formative Assessment Strategies

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From Jennifer Fairbanks…

Happy Day – Our 1st one of 2018! Join us and blog today! Share anything you want! When you blog, tweet out the link.

Join us as we all blog on the same day – the 18th of each month!  Blog about anything.  Write at any time.  #Pushsend on the 18th.  Then, we will all have a plethora of good things to read.  We can use Twitter and the hashtag #MTBoSBlog18 to encourage and remind people to blog.  If you are interested, record your name and Twitter Handle, areas of interest/teaching/coaching, and a link to your blog’s website.  Don’t have a blog? 2018 is as good a time as any to start.  Take a risk and dive in! Or, read and add comments!

Hmmmm.  WElllll.  Okkkkkkk.  What do I blog about?  Here goes…

Our schoolwide focus this spring is on revisiting what we know about good formative assessment and putting it into practice.  Eventually, we will be encouraged to ensure we are utilizing the practice of PA on a daily basis – for those not already doing it.  After speaking with our SLC, we thought it would be a good use of time for our department virtual PLC – on our NTI (aka Snow Day) – to work on ensuring that each learning target in an upcoming unit has a quality FA in place.  And if not or if it really doesn’t measure what the target is intending, then plan a better one!

As we began building the document for Algebra I unit on Functions, I was reminded of so many great strategies  learned through the years and new strategies shared by others.  Most of these have been learned through trial and error, they didn’t “just happen.”  When trying new things, sometimes you need take NIKE’s advice and Just Do It!  See what happens, reflect and try it again!  So here is a list of a few things we ran across while working this morning:

  • Every Graph Has a Story

    When given a graph with no labels, numbers, etc. – can students devise a story that will related key features of the graph to the context of the story?

Here is @heather_kohn’s Ambiguous Sports Graph sports graph

  • Thumbs Up, Thumbs Down

Was reminded of this one by my colleague.  Basically, you can pose a question to the entire class, then ask for a Thumbs Up or Thumbs Down as to if it is true/false, example/noonexample, linear/nonlinear, function/not a function

  • Green Pens –

    I am super excited that my green pens arrived today!  I plan to use Amy’s idea for Bell Work, but integrate into independent practice time.  Students will have a brief practice page – when one finishes, I will check – if all good, they will receive a green pen and help me mark other papers.  After I have 3 or 4 Green Pen Helpers, I will have time to visit each table group for one-on-one help.

 

  • Give One, Get One –

    I believe the first time I ever used this was out of a Kagan book in Geometry.  In this unit, I plan to give students graphs of functions.  Before we begin, I will ask them to list 3 things they notice about the graph.  They will then have 4 or 5 True/False statements to respond to.  Here’s the GO-GO:  They will write one more True statement about the graph, then go visit someone else across the room, sharing / discussing their true statement, and receiving/discussing/recording their friend’s new statement.

 

  • White Boards & Summary Notes

    Individual to practice writing inverse function equations.  Nothing new here, I give them the function, they practice rewriting the inverse on the whiteboard, I walk around the room observing and noting…  Then I will address any common errors I see.  After reading this tweet:

debrief notes

and a discussion a few weeks ago with @druinok about student notes from the teacher – I was reminded…  we will discuss big ideas we noticed in our white boarding, then turn to our INBs and generate our own Summary Notes.  Since these are 9th graders, I will likely give them a few unworked Functions / Inverse examples to help them get started.  Once they have completed their Summary Notes, there will be some time later for independent practice.  Maybe even pull out those green pens again!

  •  Open Sort & Card Matching –

Years ago, I was taught about open sorts from a colleague who had attended John Antonetti training.  I plan to use this structure by giving students cards with several types of graphs, in the discussion with their noticing and sorting and support of reasoning – I am anticipating something coming up about dotted / point graphs and connected graphs.  In the debriefing of the sorting task, this will allow me to introduce / review the idea of discrete vs. continuous graphs.

The second part of this sort will be to place those cards inside the ziploc bag and get the other color cards out.  These cards will have various domains and ranges listed.  Again, in the discussion of their reasoning for their sorts and debriefing of the task,  I am anticipating someone sorting based on listed numbers vs. intervals, which will allow me to make the connection between the different notations for domain and range.

Finally, the matching task will be for students to match the correct domain and range to the correct function graph.  The best way for FA assessment to happen here – is to walk around, listen/observe and ask questions, never telling them, but helping them think on their own.

After some practice and discussion, I feel like this might be another great spot to have students create their own Summary Notes of the ideas shared / discussed.

  • 2-Minute Assessment Grid

Goodness, this may be one of my favorite student reflections.  You can read about it here.  You can copy the grid and have students fill it in.  However, I like creating a large grid on my board and giving students 4 sticky notes on which to respond.  Basically Students are asked to tell ! Something they want to remember.  ? A question they still have.  @ An A-ah – lightbulb moment and + One improvement they can still make / need ot study.

  • Class Closer Reflection

An easy, quick one sentence reflection – have students choose one of these sentence starters and complete it…  Something I’ve learned,…, Something I realized….  OR Something was reminded was of…

Follow-Up Action is what matters most.

As with any FA – its not about the strategies – they only provide a vehicle for the information you get from student learning.  What happens next is very dependent on what information you receive.  In class strategies, you must be present, listening, allow yourself a few seconds to think through their responses / questions before responding to them with a question.  With reflections, exit tickets, target quizzes, we have the opportunity to filter through all of their responses, looking for commonalities and misconceptions – that will help us plan our next actions.  Do we need to address with the entire class?  Are there a handful we need to pull to the side while others are completing bellwork the next day?  Is everyone on the right track and ready to move forward?

Real Life Water Line

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After some good old Dan Meyer Graphing Stories last week, we began our next phase of functions by predicting what our graphs (#s coops & water height) would look like for these containers:

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And then we actually scooped water to see how close we were…

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Walking around, listening to conversations…
“NO. It can’t go back down, you’re still adding water, so the height of water keeps increasing.”

“It might slow down or speed up, but it won’t decrease until we empty the vase.”

“So we need to reverse the steepness…where it’s steep, we need to flatten it out and where it’s flT, we need to make the graph steeper.”

I required them to complete a group graph to predict before I gave them their scoops to start data collection.

Several had to go back and finish details like labels and scales on graphs…a good reminding activity.

One student asked – do you do activities like this often?  It makes it (math class) fun.  

It was a good day.

Painting a Bridge

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In my Algebra I, we are looking at parent functions. Students said this week was quite easy, they felt they were doing 3rd grade work.  But I assured them
recognizing the parent equation and making connections to the parent graphs may seem easy, but it’s a lead-in to more intense math!

We’ve done several data collections throughout the semester, mostly linear, a few quadratic and exponential.   But today we took a look at rational with Painting the Bridge, which is embedded in a MARS lesson. 

Students are asked to sketch the relationship x:# workers and y: # hours each works to complete the given job.

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Those are a good overview of what we saw.  I allowed students to ask questions about things they wondered about others’ graphs.  At first glance, a couple of the graphs may look odd, but given the chance to share thwir thimking, student reasoning made perfect sense in the real world.

Though I didn’t have an actual student create this graph, I included it on the board.

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I followed the suggested questioning in the MARS lesson, which led most students to some A-ha moments.  What does point Q mean? Points S? Does it make more sense for the graph be solid or dotted? Why?

As a data collection to follow up this discussion, we picked up erasers. One student held a cup in their dominant hand and picked up one eraser at a time and placed it in the cup, we timed.  Then another student helped.  Continued adding workers and it eventually became too crowded, they were dropping erasers and slowed them down.

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We compared the shape of our scatter plot and decided maybe exponential or quadrant 1 of a rational (inverse) function.

The calculator power regression resulted in
y =76x^-1.  Which gave us a chance to discuss that -1 exponent.  How it meant the inverse of multiplying by x, which was to divide by x.  So we graphed y=76/x. Nice. They were seeing the connection to our Painting the bridge discussion. 

Oh wait, how many erasers were we picking up? 78. Not bad, huh?

My goal is to give them a concrete data collection for which they can access and connect back to the math.

To end the day, they asked if they could draw a graph on the board and everyone guess the parent function name.  Sure.   They were on task and engaged so I was fine with it.
They began graphing the endpoints of their graphs,  so their classmates were finishing the graph and naming the function. It was humorous. But again, they were engaged.

I love these kids.  They were my favorites today.  It’s been a tough semester at times, but I want to end these last weeks strong. I want them to leave our classroom having grown in confidence and changed their attitude toward math.  That’s my goal. 

INBs – Graphing Stories LHP Assignment

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Following @duinok’s lead, in her Favorite First Day of School post – I checked out Dan Meyer’s Graphing Stories to use as an intro to my first unit.  We viewed 8 of his videos – I asked students to sketch what they thought was the correct graph, then in a different color / style of line – I gave them time to sketch the “correct” graph.  We folded our Graphing Stories sheet and entered attached it to our INB on a RHP.  Within the discussions, we addressed choosing good intervals – a reminder of things our graphs should include from axes labels to titles.  It was a great review of good graphing techniques without actually “reviewing” – students were actually doing.

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On the LHP, students were asked to write a brief reflection of their graphing experiences.  The second part to the assignment was one I held my breath on…  would they actually do it.

Create your own video / story.  Include a graph to model it.

The next day, I shared a scoring guide with them.  We talked about reasonable deadlines – I passed around a sheet and they chose their due dates.  With only a handful – who came to meet when they were not going to be able to meet their deadline, they were anxious to turn them in.

Several chose to write a story – but many of them made videos – I had a student running up the side of a house – sitting for a moment before jumping back to the ground (yes, it was interesting), another student running at different rates, someone tossing a ball back and forth in a store, a student doing a standing back tuck, a student swimming laps in a pool.  These are only a handful of videos I saw – but this was exactly what I wanted – students taking something of interest to them and connecting it to math.

My plan is to attach their graphs to the LHP.  I have smiled & laughed a lot while watching their videos.