Just Playin’

We just wrapped up our first quarter of the year, and I’ve noticed something.

We like to play.

Every class period has it’s own culture… it’s own “thing”.  It’s usually not very math-related, but I’d venture to say this “thing” that unites us in each class helps us learn the math better.  Simply put, we choose fun.

Maybe I should have taken pictures all year and started my own #TodaysDate180 blog (ha!) but every day this year, I’ve created an expression whose solution is (wait for it…) today’s date.  Some days’ expressions are more challenging than others.  It’s a very simple way to continuously review order of operations, exponents, etc.  And in one class, every day, several students take it upon themselves to write a proof of sorts, demonstrating how they know what day it is.  Here’s a not-elaborate-at-all-on-my-part recent date, and a sampling of the daily date-proving ritual:

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Another example of how we play – students started noticing that every day is a holiday.  We start every class by talking about what holidays are listed on a goofy daily holiday website, and if it’s possible, we celebrate it.  High-five day was a recent favorite.  I don’t know how it started, but we do it.  Every day.

We hashtag.  A lot.  When I grade papers, students often hashtag comments to me, and I return the favor.

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When students use language like this to express themselves on a quiz, I take it as a high compliment.  This is how we interact.

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Play is important.  We start every lesson with a smile and make the kind of goofy memories that middle schoolers hold dear for a long time.

Don’t forget to play today.  #justsayin

Posted in Algebra 1, Pre-Algebra | Tagged , , | 2 Comments

Socrative and Slope-Intercept Form

IMG_8308With new TEKS in tow, my 7th graders taking 8th grade math have been studying proportional and non-proportional linear relationships (wow, right?).  The progression has been a refreshing, concept-based study of LOTS of scenarios featuring “constant rates of change” represented in tables and with graphs, making clear connections to the similar triangles we studied in our last unit (Thank you Desmos for this beautiful contribution!  Twitter can be SO POWERFUL in sharing resources, and I thank Desmos for entertaining my request by sharing this beauty!)  We didn’t even use the word “slope” until about day 3 of our learning when we introduced the traditional subscript-laden formula.  They didn’t flinch once they saw that the formula was simply showing what we’ve been doing all along, and the word “slope” became a lot less scary.

The next step was to add equations to the mix of representations.  Though the text introduces proportional linear first (think direct variation… or y = mx… or y = kx), I mixed things up and started with non-proportional linear (think y = mx + b).  That way, I could emphasize that “b” was just zero in the proportional flavor.

After some scenarios, we talked about how to find an equation if we weren’t given one.  Is it possible to write an equation of a line if all we know about the line is that it passes through two specific points?

Screen Shot 2014-10-11 at 8.13.52 AMI created this “chunking activity” to help students think through the steps.  If we want an equation in slope-intercept form, it would be helpful to have the slope (we can find that) and the y-intercept (we can find that too).  After writing each equation in slope-intercept form, we used Y = on our TI graphing calculators to enter the equation, view the table, and confirm that our line passed through the two points we started with.  After guiding students through the process, they had a few equations to muster up for homework.

Screen Shot 2014-10-11 at 8.56.32 AMThe next day, I used Socrative to review homework.  On the fly, I selected “Quick Question” then “Short Answer” and asked students to enter their first equation.  Using Socrative to type in equations reinforced the keystrokes needed to enter an equation in the TI using the Y = key. Anonymous equations appeared in a list at the front of the class, and conversations about discrepancies began.Screen Shot 2014-10-11 at 8.57.34 AM

 

 

Is the slope -7/5 the same as 7/-5?  How about -7/-5?  What do the folks who represented the slope as -5/7 instead need to know?  Sure, Socrative doesn’t have a “pretty” equation editor, but discussions about the meaning of (-7/5)x versus -7/5x versus -7/(5x) might not have happened without the wonky-looking representations.

Graphing lines

y = (-7/5)x

y = -7/5 and

y = -7/(5x)

simultaneously to test parentheses placements added a level of richness to this simple, initially skill-based task.  We entered each equation from the homework, one at a time, using the same process in Socrative, viewing the anonymous list and continuing the conversation.  By the third or fourth equation, we had a nearly unanimous list of slope-intercept form equations, as students had learned and made adjustments to their equations stemming from our discussions along the way.

I can’t overstate the impact that making student thinking visible using simple, free tech tools like Socrative can have on student discourse.

How are you using Socrative in the classroom?

 

 

Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , , , , | Leave a comment

Functions – Nearpod Learning Check

Looking ahead to our next unit, I was sifting through some ideas about introducing relations and functions to both my algebra students (8th graders) AND my pre-AP Math 8 students (7th graders experiencing new 8th grade TEKS and therefore, experiencing more algebra than in the past).  I created this function vocabulary ThingLink last summer as part of the “ThingLink Teacher Challenge” to help introduce the concept.  I plan to use Function Carnival after a bit more instruction about functions.  Between introductions and Desmos fun, I wanted to give students some sort of “learning check”.

I was exploring Open Middle for ideas (have you not heard of Open Middle?!?  GO!  NOW!) and was inspired by this simple prompt.

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Immediately, I thought of Nearpod’s “Draw” feature and giving students an opportunity to create a table that represents a function, AND a table that does NOT represent a function.  I’ve found that the constant contrasting between what IS and what IS NOT a function helps students understand the concept.  It’s brain-friendly to show contrast!

Why stop there?  Asking students to also create mappings and graphs that ARE and ARE NOT functions would further reveal misconceptions and hopefully solidify understanding in the end.

So, I created a Nearpod “Learning Check” (see below to grab it for your students).  Not every Nearpod needs to be a comprehensive lesson.  This one serves as a brief assessment after instruction has occurred, giving students the opportunity to show what they know by creating relations for themselves.  During the Nearpod session, student work samples can be anonymously shared with all students to further discussion.  There’s a quick 5-question quiz at the end too.

Feel free to use this NPP (Nearpod presentation) with your students.  Clicking on the image below will take you to the Nearpod login screen.  Once you log in, Nearpod will let you know I’ve shared a NPP with you.  Say you’d like to accept it and it’s yours to use.  Feedback welcome!

NOTE: If you’re using iPads, be sure you’re using an updated Nearpod app with iOS 8.  Otherwise, we’ve experienced some issues with the “Draw” slides and students not being able to draw on the far right side of their iPad screens.  A quick fix is for students to not lift their fingers, but draaaaag their fingers to the right side of the slide to continue drawing.  WEIRD! :-)

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Follow-up:  Thanks to Susan Oxnevad for mentioning my “What is a Function?” ThingLink on the ThingLink Blog.  Did you know that Tackk and ThingLink play nicely together?  Click below to check it out!

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Here’s a glimpse of some of my students using the Nearpod learning check.  I wish I could capture the emotion in the room.  They love seeing what their peers are thinking and talking about authentic work samples… even if they’re wrong.  Great discussions always ensue!

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Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , , , , | 4 Comments

Math Playdate (from Twitter to Tackk)

It started on Twitter.  My challenge was irresistible to fellow math buddy Kyle.

 Within what seemed like mere minutes, Kyle had a complete task, videos and all, with his own unique spin.  

Fast-forward a few weeks.  Just as Kyle couldn’t let go of the ice bucket, I couldn’t stop thinking about the Big Nickel he posted:

When Andrew Stadel posed this question, I couldn’t walk away.  It awakened within me the “perplexity” Dan Meyer talks about.  I just. needed. to. know.  And I felt responsible to report back.  

After all of my work, I thought using Tackk would be a great medium to share with Tweeps.  This task not only inspired me to explore my own fine-tuned question, but it also encouraged me to create a product to easily share my work with the circle of math friends involved in this conversation, and beyond!  Click the image below to see my Tackk.

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I have not asked students to use Tackk before, but how great could that be?   

There are limitless possibilities here – photos, text, and media can be displayed neatly in a Tackk… and once student Tackk links are shared with the teacher, they could easily be collected and shared in a ThingLink with an entire class, entire school, or the entire world.  Note that Tackk also has settings for conversations to continue within the Tackk itself (feel free to add to mine!  I know my estimate is an over-estimate!  How could we make this estimate more precise?)

Have your students created solutions to math tasks using Tackk or a similar medium?  If so, please share!  I’d love to have more student examples to show my own kiddos before asking them to create their own.

Thank you to all Tweeps involved in this Twitter conversation.  I cherish the amazing PD I receive through our interactions.  You challenge and inspire me!

Ready to take the Big Nickel challenge with your students?  Want to see classroom-ready visuals and resources?  Here’s Kyle’s take on the Big Nickel Twitter Playdate done in classic 3-Act style.

Posted in Algebra 1 | Tagged , , , , | 2 Comments

iPhones #WCYDWT

With all the (understandable) iPhone hype lately, I couldn’t help but fall for this math-potential-packed image:

#WCYDWT ? (What can you do with this?)

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Attached below is a PDF I made that displays each of these iPhone models to their accurate sizes.  I made the image more transparent to save us all some ink.  Would love to hear back if you use these images with students.  Happy hypotenuse!

iPhones Accurately Sized

 

Posted in Algebra 1, Pre-Algebra | Tagged , , | 3 Comments

Story Time (Algebraically Speaking)

Algebra students have been solving multi-step equations.  Quite a great, semi-sneaky way to review all sorts of topics students should already be “fluent” in – operations with rational numbers, the concept of “isolating the variable”, properties of equality, and so on.

I presented students with this simple equation:

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Rather than rush to strategies to solve for a, I asked students to tell me the story behind this equation.  “Once upon a time…”

Students’ first inkling was to describe half of something:

EX) “I have half of an apple… no… half of an… armadillo!”

They had “half of” all sorts of appropriate and inappropriate things.  I asked, “Do you have half of just one of those things…?  How many halves do you have?”  Hmmm…

Next, students seemed to notice the other decimal values and opted to talk about money:

EX) “So, something costs five cents each…”  Whoops.  Why does that ALWAYS happen?

We got our place value straightened out pretty quickly:

EX) “No wait, that’s FIFTY cents each…”

I heard a story about Hawaii:

EX) “So I’m going to Hawaii by bike and it costs eight dollars and seventy-five cents…”  Wait… waaah?  Gotta love 8th graders!

I heard a story about underpaid restaurant staff:

EX)  “A waitress makes fifty cents an hour and gets $8.75 in tips.  If she gets $13.25 at the end of the day, how many hours did she work in this awful restaurant?”

I heard a story about gum:

EX) “I buy some packs of gum for fifty cents each, and a container for $8.75.  If I pay $13.25, how many packs of gum did I buy?”

I heard a story about lemonade:

EX) “Some little kids have a lemonade stand.  They charge fifty cents for a glass of lemonade.  A lady feels bad and gives them $8.75 for no lemonade.  How many glasses of lemonade did the kids actually sell if they made $13.25?”

What I can’t capture in a blog post is the energy in the room.  Even for goofy problems, or problems with wrong thinking, students OWNED these stories.  Turning a strategy on its head and ASKING FOR the word problem rather than GIVING the word problem and asking kids to write and solve an equation was a simple, novel, and apparently unexpected strategy.  When we solved the equation (using several different, valid methods), the solution had meanings that students had assigned to it, whether it be gum, lemonade, or hours.

I’d recommend the 5-minute (story) time investment. :-)

Posted in Algebra 1 | Tagged , , | 2 Comments

ThingLink: Anchoring, Pre-Teaching and Gap-Filling

I anticipate my students will finish their first unit test at varying rates tomorrow.  I always take my own tests as if I were the student.  I show all the work.  I time myself.  I multiply my time by 3 and then by 4, establishing what I believe is a fair range of minutes to expect students to be able to complete the assessment. I learned this rule-of-thumb from I’m-not-exactly-sure where, but it has worked quite accurately through the years.  I finished tomorrow’s test in less than 7 minutes, so I fear it may be too brief!

All that to say, my students will need something meaningful to do when they finish the test that meets the following criteria:

A) They must try the meaningful thing individually and silently (others will still be testing… think anchor activity)

and

B) For those who don’t have time left to do this meaningful thing, they can’t be penalized, if you will, if they need the entire period to complete priority #1 – the test.

ThingLink has been my go-to tool for moments like this.  I noticed some problems in the upcoming unit make assumptions about students’ prior knowledge, and a ThingLink that addresses this would help.  Some of the similar figure problems assume students can recognize vertical angles, and that students know that vertical angles are congruent.  We haven’t addressed any types of angles at all, so ThingLink will do a little bit of pre-teaching for me.  Maybe I went overboard by including other angle relationships, but I’m hoping it helps when we eventually study a geometry unit later.

The ThingLink topic of angle relationships reminded me of a website I had to design a few years back as an assignment for a grad class.  I forgot about this little project!  Time to put it to use by linking several “nubbins” to it.  Remember when xtranormal was such amazing technology? ;-)


For ideas on how to use ThingLink for “Pre-Teaching” check this out.

How are you using ThingLink?  

What other strategies do you use for awkward moments like providing meaningful tasks for students to do after completing a test?

 

Posted in Pre-Algebra | Tagged , | Leave a comment

What to do with only one iPad…?

Screen Shot 2014-09-13 at 3.01.35 PMMy mathy friend Eric Milou recently asked me to help a middle school math teacher he knew because she only has access to one iPad in her classroom and isn’t sure how to best use it.  Additionally, she has access to Apple TV.  Since I went from zero experience with iPads to a one-to-one environment, it was challenging to think about what one might do with only one iPad.  Here are some ideas I offered… do you have more?  Please comment! :-)

Always great to hear from you, Eric!

Melissa, I have some ideas for you!  I use the iPad a lot for assessment, and many of the tools I frequent would require every student to have an iPad… BUT… I think with one iPad, you can do some amazing content creation for your students.
UnknownFirst of all, since you have an iPad AND an Apple TV, did you know you have a mobile document camera? :-)  If you mirror your iPad on a screen at the front of the class, and use your Camera app, you can walk around the classroom and feature/project live student work for all to see!  You could also take photos of student work (perhaps anonymously) and project various samples to use as discussion points.  Having both correct work and incorrect work would be great for error analysis.  Maybe project the work and say to the class, “Tell me something you like about this work… then tell me something you don’t like.”
Unknown-1Consider making a screencast using the Explain Everything app.  Maybe adding a video element of something you’ve created would be a nice “state change” during your instruction.  For me, every time I’ve gone to YouTube or Khan Academy to find a video to supplement one of my lessons, I wasn’t quite happy with the way they explained the mathematics, or the examples they used.  Making my own videos has always been worth it because I can explain the content MY WAY.  And once you have that video, you can use it again and again!
Unknown-2Keynote and iMovie would also be great for content creation, just to add a digital element to a lesson that could use a lift.  Today with my 8th graders, I used a slide I created in Keynote to present examples for my students.  I exported the Keynote slide as Unknown-3a PDF.  I mirrored my iPad to the big screen up front and used Doc AS, a PDF annotation app, to present the slide.  Then I pinched and zoomed in and out of each example, working the problems digitally in Doc AS using a stylus.  For me, I gave every student access Unknown-4to the PDF so they could “annotate” it too.  However, if the examples are simple enough for students to copy, your presentation will be spiffy and they will still have access to the examples and math they need by writing it in their notebooks.

A slide I created in Keynote, saved as a PDF, and “annotated” with students in Doc AS using pinch-and-zoom for LOTS of workspace!

I hope this is a start for you.  Please let me know if you have specific lesson ideas in mind and I’ll do my best to help.
Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , , | 5 Comments

New TEKS = Visual Patterns for All

Screen Shot 2014-09-07 at 11.11.26 AMIf you’re not up to date on Texas math standards, we have new TEKS this year for grades K through 8.  (How many standards are new or have moved from one grade level to another?  Check this out!)  Our district purchased new curriculum materials to help us adjust.  While Texas is clear about *NOT* being “Common Core” we are definitely following the trend to teach higher-level math sooner and (in theory) in more depth than we used to.  Next year, high school math courses will have new TEKS as well, so this year is an unusual year for me.  I generally have one foot in “middle school math” and the other foot in “high school math” because I teach Algebra at the middle school level as well as 8th grade math.  All this to say, I will be doing much more algebra in my 8th grade math courses than ever before.  SWEET!  Um… I think! ;-)

A change for me this year is that I am not teaching 8th grade math to 8th graders, but primarily to 7th graders with a sprinkling of 6th graders in the mix.  If you’re curious about what it means to teach and learn 8th grade math in Texas with the the new TEKS, click here.  For our current Algebra TEKS (which will be changing for the 2015-16 school year) click here.

With such an emphasis on functions in both of the courses I teach, I think this is the year to introduce Fawn Nguyen’s Visual Patterns.  I keep reading hither and yon about effective uses of these patterns, and I’m intentionally adding them to my practice this year.  I have no idea why I haven’t thus far, except to make the typical reason/excuse that I’m concerned about “time” (which is generally a lame reason NOT to do something that will benefit kids and give them a deeper understanding of mathematics versus “covering the curriculum” in an allotted timeframe… but I digress…)  So there, I’m doing it.  Not sure when, but I’m doing it.  My plan is to use Visual Patterns with “4-corners”.

I’m not sure if I do 4-corners “correctly” or if this has been #Yencafied but here’s how I play.  I create 4 different problem sets that are similar in content and difficulty level, and identify each set with a number or clip art or something.  Anything to distinguish each of the 4 sets.  I mix them up (well, I make the photocopier mix them up – see the end of this post) and hand them randomly to students as they enter my classroom.  Students try each problem set right away, individually, and silently at their desks.  The first time I do 4-corners with a class, no student realizes that there are 4 different sets of problems, so it’s kind of fun to say, after they’ve been working for a few minutes, “You may have noticed that there’s a card suit (or whatever) at the top of your paper next to your name.  Did you know that there are 4 different problem sets floating around?”  Maybe it’s just *my* middle school students, but I liken this moment to me performing a magic trick.  “Ah!  Oh!  I didn’t even see that!” and so on.

At what I deem to be the appropriate time, I send all spades to one corner of the room, clubs to another… you get the idea.  Truthfully, not every corner of my room is conducive for student groups to meet, so I *should* call this “4 groups” instead.  I usually end up sending a group or 2 to the hallway to meet, just so kids can be spaced apart from the other groups.  They compare their papers, discussing and possibly correcting discrepancies.  I ask each group to provide me with one paper they believe serves as an “answer key”.  After I have a “key” from every group, we look at them using the document camera.  Sometimes students explain and present the key, sometimes I do, but that’s the way I do 4-corners as a warm-up of sorts.

Here are Fawn’s resources remixed for 4-corners.  I did the first 12 patterns this morning as a start, so I can have these ready to go.  A photocopying tip for #Yencafied 4-corners: make a one-sided copy of the page with patterns 1 and 2, and do the same for the page with patterns 3 and 4.  At this point you’ll have 2 copies of each page.  If you put the original two pages face up and right-side-up in the photocopier tray (the patterns 1 and 2 page and the patterns 3 and 4 page), then the newly copied two pages face up and upside-down in the photocopier tray, the copier will do the daunting task of mixing up all 4 versions quite nicely so you don’t have to.  Sure, some will be right-side-up and others will be upside-down, but that doesn’t matter at all if you’re just handing them to kids as they enter class.  You’ll still have to pay the paper cutter a visit to chop the pages in half vertically, but they’ll be nicely mixed up already.  I hope all of that made sense.

Thanks to Fawn!  I hope you don’t mind my mini remix of your stuff. ;-)

Word Doc:

Visual Patterns Handout 1-12

PDF:

Visual Patterns Handout 1-12

 

 

 

 

Posted in Algebra 1, Pre-Algebra | Tagged , , , , | Leave a comment

Different.

IMG_7855I can’t put my finger on it, but I’m going through some kind of teaching rite-of-passage.

For the first year ever, I had no butterflies in my stomach the first day of school.  No nerves, at all.

I’ve worked with my students for only 9 days, and somehow, I feel like I’ve been working with them much longer than that (meant in a positive way, *NOT* in a “has-it-only-been-9-days-with-these-kids?” way).

I’ve never been a shy teacher, or one who holds back enthusiasm or energy, but this year just feels different… and I like it.

Perhaps it’s because I knew my first teaching job in Pennsylvania in the late 1990s would come to an abrupt end when my husband and I started a family.  We knew the plan was for me to stay home awhile.  Did I ever really settle in?

Maybe it’s because when I transitioned from at-home-mom to my “math coaching” days in PA, I knew my position was grant-funded, so that feeling of being “temporary” and “optional” was ever-present.

Photo from my first year of teaching – gotta love that orange carpet at Shawnee Middle School!

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Literacy Fair “Poster Session” at Northeast Middle School, Bethlehem PA, when I was a “coach”

I think I am finally claiming a home.

I may sound all “rose-colored-glasses” here, but I can’t say enough how thankful I am to be doing what I’m doing.

In 9 days, my students and I have already begun to build relationships that will carry us successfully through the year.  Two “back to school nights” brought the most positive and supportive parents to my classroom to visit.  I’m hosting a (sweet!) student-teacher again this year, and one of our lessons this week moved her nearly to tears when a student expressed his enthusiasm openly for what he was learning.

So, I’m not showcasing a digital tool, math lesson strategy, or student work samples today.  Instead, I’m simply pausing to smile, humbled by this thing I have the privilege of doing.  May every teacher experience this exhausting and fulfilling bliss.

 

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Posted in Algebra 1, Pre-Algebra | Tagged | 4 Comments