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)


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?


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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


Visual Patterns Handout 1-12





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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.


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

So I stole an idea from Dan Meyer – *SHOCKER*

Dan Meyer provided our district’s math department with two days of PD in June.  I liked the homework he assigned to us, and I’m in the process of merging his idea with a problem-solving plan for a longer-term mini-project of sorts.

For their first homework assignment of the school year, my new crew of 7th and 8th graders were each asked to bring an image to class they believed would evoke lots of interesting questions.  I asked them to put on a “math lens” and look at the world as a place where math happens.  I showed an example photo that I had taken several weeks ago at our community pool’s picnic pavilion.

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Loving those triangles







I provided students with this template:

The Math Cam Day 1

On Day 2, we had a “gallery walk” where students walked about the room examining the images.  They were asked to write one question on each person’s paper in their row of desks, and return to their own seat to see what questions others had written.  Some students asked for an example of a question, but I politely refused to provide any. :-)

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Math Cam Gallery Walk

Just about every student was surprised by the questions written by their peers.  Virtually no one asked/wrote the question that the image-bearer expected to be asked.  Pretty neat.  Here are a few samples.  One of my favorites was the Target logo – you can’t get more familiar than a logo like that, and yet, how many students saw math when they looked at that logo prior to our class?  Who will see math when they view that logo from now on? ;-)

The shirt I was wearing

The shirt I was wearing

I could see students’ perspectives shifting before my eyes.  One student’s hand shot straight in the air after having some sort of math epiphany.  She said, “Mrs. Yenca, I’m starting to see math in your shirt!”

I encouraged students to use their iPhones and iPads to begin capturing and sharing images with the class and me, so that we can make connections throughout the school year.  Eventually, whether students use this initial image or find a new one, I’d like them to develop a question and see a problem through to a solution or resolution using a 4-step problem solving model.  To be continued…



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

#EanesPLC – Our Second Annual Professional Learning Conference (Buckle Up!)

Screen Shot 2014-08-16 at 8.43.18 AMThere’s a fine line between “overwhelmed” and “empowered”.

I straddled that line at our school district’s second annual “Professional Learning Conference” this week.  Eanes ISD does a FANTASTIC job of inviting world-renowned educators to work with our entire district faculty.  A detailed schedule of workshop choices, with session resources neatly packaged in an iTunes U course (not to mention food trucks parked outside serving local goods for lunch) really set the stage for the new school year.

This was not a touchy-feely event.  This event was packed with profound statements that raise big questions about why we do what we do.  I’ll attempt to share a few of my biggest a-ha take-aways, giving credit to the experts who provided the research behind these claims.  Yes, these folks taught our faculty, in-the-flesh.  I have gotten to learn FIRSTHAND from some truly respected legends in education. #grateful


1) Formative Assessment is the answer.

I don’t even think the question matters when it comes to teaching and learning… the answer is simply… formative assessment! (being a little tongue-in-cheek… sort of!) 
Dylan Wiliam 
emphasized the importance of teachers creating a culture of continuous improvement (saying that these two-day conferences don’t work, ha!).  Want to have an impact?  Work in Professional Learning Communities (we have PLCs every school day).  Focus on classroom formative assessment and teachers changing their assessment practices, yet customizing and choosing techniques that resonate with each of us and our own students.Screen Shot 2014-08-16 at 7.36.35 AM
Screen Shot 2014-08-16 at 7.36.08 AM

To take Wiliam’s work further… we have iPads with fantastic tools that can effectively and efficiently assess student thinking!  WE CAN DO THIS… and WE ARE DOING THIS!  I found Dylan Wiliam’s message to be an affirming pat-on-the-head AND push to be better.


2) It’s unwise to over-grade student work.

Carol Ann Tomlinson‘s words here can’t be taken out of context.  She stressed the importance of grading too!  Our grades should be based on specific learning targets, should be criterion-based (versus in competition… I sure hope no one grades on a curve…) and must be free of what Carol Ann calls “grade fog”.  That means… no extra credit, no grading homework, and grading student work LATER in the learning cycle rather than EARLIER.  (THINK – growth mindset)  This tweet quantifies Tomlinson’s claim to stop grading everything that kids do.  LIBERATING and AFFIRMING, again, in light of the fantastic tools we have on our iPads.

Wiliam reinforced this very idea when he shared the “hyper-correction effect” with us.  He explained if a student gets something wrong, then fixes it… the next time the student is asked about the topic he/she first got wrong, then corrected, he/she will get it right MORE OFTEN than a kid who got it right initially. Can we say, counterintuitive?  Making mistakes and correcting them are KEY PARTS of learning, and shouldn’t penalize our students through a “grade”.  Wiliam said, “Mistakes are evidence that the work I’ve given you was worth your time.”  (Looks like Jo Boaler has heard and is spreading this message as well, specifically with respect to learning mathematics.)


3)  Core learning goes up when the arts are integrated.

Dr. Frank Locker and Dr. Kevin Washburn reinforced each other in my mind.  Dr. Locker shared amazing 21st Century learning spaces, and resources to see how other schools are using project-based learning in these spaces.  We need to help our students with oral communication skills, working in groups, and using technology.  Locker suggested that we apply Gardner’s work to vary our instructional practices, and consider integrating the arts… yes, even in math class!  Later in the day, Dr. Washburn walked us through the Core Processes of Learning (experience, comprehension, elaboration, application).  Washburn shared that “application” is brain-friendly when Garder’s work allows students to reprocess presented information by writing a theme song, for example.  Students need to be engaged in explaining the connections.  It’s not the other creative FORM that we’re after here… it’s the thinking and the process to create that form that is going to construct new learning!  For me personally, Locker and Washburn affirmed WHY using the creative tools on iPad contribute so well to student learning, while potentially bringing the arts to core subjects along the way.

THIS is why I want to use Book Creator more effectively.

THIS is why I want students to create more ThingLinks and videos.

THIS is why involving students in creating content matters so much.

There are my top three a-ha moments.  I am not doing them justice, but I hope at the very least that IF YOU ARE STILL READING… you will pick an idea here to further research and employ in your own practice.

THE Dylan Wiliam at #EanesPLC

THE Carol Ann Tomlinson at #EanesPLC

Discussing Learning Spaces with Dr. Frank Locker #EanesPLC


Posted in Algebra 1, Pre-Algebra | Tagged , , , | 1 Comment

Book Creator and Advocacy: A Summer eBook Project About Food Allergies

Screen Shot 2014-08-06 at 7.00.53 PMI’m going to prominently wear my “mom hat” for this post.

My son has severe food allergies.  In a day and age where this is more prevalent than ever (unfortunately) I’ve found the best way to protect those who have this very serious health condition is through education.  It’s tough to understand how having food allergies can make the simplest everyday events complex and potentially dangerous.  There’s a sinking fear every time my son leaves my care and is entrusted to other adults, or a meal is prepared for him by a friend, family member, or chef instead of me.  It’s an invisible force that’s ever-present.

Screen Shot 2014-08-06 at 7.01.23 PMRewind to last month, when fellow ADE Douglas Kiang gave a showcase presentation at the Institute in San Diego, and mentioned an app that allowed kids to express their feelings about having parents who were divorced. When I heard this idea, something clicked in my mind and heart.  I was literally brought to tears in my seat at the call to help my son create a resource to promote advocacy and understanding of food allergies.  I thought Book Creator for iPad would be the perfect tool so this resource could easily be shared with the whole world.

Screen Shot 2014-08-06 at 7.02.15 PMMy son has been working on this eBook for a few weeks.  Besides sharing the ePub file with you (which can be opened in iBooks as a neat-o multi-touch book), I was tickled to also have the ability to export the eBook as a video, thanks to that nifty Book Creator feature.  The video is 8 minutes long, and is available on YouTube.  Both the ePub file and video link are available below.

Our hope is that one boy’s story can educate thousands.  Please share this book with families, friends, school nurses, teachers, and anyone who may be entrusted with caring for our precious ones.

Thanks most sincerely!

Here’s the ePub file, which will give you a multi-touch eBook that opens in iBooks:Screen Shot 2014-08-06 at 7.24.31 PM




Here’s the exported video version of the book:

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Math, Music, and iMovie (No Turning Back Now)

When I first started teaching in the late 1990s, I offered an optional bonus-point-earning project to my students right before Christmas break.  The task: pick a friend or two, and rewrite a popular Christmas carol given a list of math vocabulary words as a help.  Students transformed and performed “math carols” in costume on the last day of class before the long-awaited vacation.  It was absolutely painful, but memorable and dare-I-say educational. ;-)  Did I mention performing the carol in front of the class earned twice the bonus points as just simply writing and submitting one…?

Fast-forward to 2014… students now have iPads, GarageBand, iMovie, and countless content creation tools at their fingertips.  That painful project has potential for revival and vast improvement in this 21st century.

Why wait until Christmas?  Well, I didn’t.  Here’s my sample project.  I’ll keep this one up my sleeve and show it to students at just the right time (if ever!)  Math music videos?  I’m thinking that could rock.  Don’t underestimate the amount of content one could pack into a 3 or 4 minute song.  Here are a few TEKs I think my math cover version of “Try” touches upon:

8.1(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate 

8.1(F) analyze mathematical relationships to connect and communicate mathematical ideas 

8.4(A) use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 – y1)/(x2 – x1), is the same for any two points (x1, y1) and (x2, y2) on the same line 

8.5(B)  represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0 

8.5(I) write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

Be kind. ;-)

(P.S. If you’re not familiar, here’s the original song with its own great message to young ladies!)

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

T-Shirts: Some Real-Life Math in Need of Act 3…?

IMG_7673This post is based on a true story… how it ends is where I need your help!  Think of it like a “choose-your-own-adventure” book… except you get a say-so in authoring it.

True story: I ordered a rockin’ Estimation 180 t-shirt from my math pal, Andrew Stadel.  I ordered a “medium” but it was a little snug for my taste.  I wondered… could we do something to be proactive and help other ladies order the correct size?  How do folks determine t-shirt sizes anyway?

So, I measured a few of my favorite size “medium” t-shirts and sent the data along to Andrew.  It appeared his size “medium” was a little smaller than other “mediums.”  After completing the exchange process, I’m happily wearing a size “large”… but is that it?  Is that the end to a story involving Estimation 180 t-shirts and measurement?!?

My wheels were turning, I had already gathered a bit of data, and this tweet shows up from Andrew:

Well aren’t those numbers purdy?  Except, my task isn’t so purdy… I’ve got to act!

Except… I’m missing Act 3!

Act 1:

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Act 2:

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image 2Sure, I have ideas of where to go with this, keeping 8th grade and Algebra 1 TEKs in mind… but it’s so much fun to ask you… where would you go next, based on the students and courses you’ll be teaching this fall?

And a bigger question… what if I *don’t* create a specific Act 3?  Is it okay to just leave this thing open and see what students will do with it?  What if I have several choose-your-own-adventure options up my sleeve, prepared to explore with students, but I don’t force upon them what *I* think Act 3 should be?  Discuss.

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