Teaching Students How to Study with One-Sheets

I would love for my students to learn how to prepare for a math test. This one-sheet idea is the closest I’ve come, as they (eventually) do it all on their own.

At the end of last year I had my students create a study guide for their final exam. I had them make one page (or notecard) of notes for each chapter we had studied. My students commented that although they liked the idea, this was difficult to do at the end of the year. They wish we had summarized each chapter while we were in the chapter so they could remember more things to put on their sheets.  My best ideas often come from students.

So this year at the end of every chapter I had my students summarize the most important topics on the front of one sheet of paper.  Since this was new for them, I gave them a list of topics, then had them brainstorm in groups on whiteboard. Afterwards I had them fold one sheet of paper into sections (one section per topic), and then write the information on their sheets.  I encouraged them to include homework problems they had difficulty on, and notes from the in-class review.

As you can see from the picture above, some students created really thorough one-sheets, while others barely wrote the basics. To help model great one-sheets, I shared the most detailed ones with the class.  But this was after the fact and didn’t help students who had not made thorough one-sheets.


In the end of year survey, most students mentioned how much they loved the one-sheets. But several students mentioned that while they liked having one-sheets, they did not enjoy making them (or make helpful ones).  And that they would love help making a great one sheet.  After reading their comments, I talked to them in class about how to help them create better one-sheets. Overall, more of my boys mentioned that they struggled with making helpful one-sheets.  They suggested that we make the actual one-sheets together in class, especially at the beginning of the year when they are just learning how to make them (and before they realize how valuable the one-sheets will be).

So next year this is how I plan on introducing one sheets.  The first time we do one-sheets, we will make the entire one-sheet together as a class.

  1. Give students a list of topics and let them brainstorm together on whiteboards.
  2. Instruct then how to fold the sheet into sections and label each section.
  3. Give them class time to fill in the sections, guiding them about what is important to include and modeling how to organize the material.
  4. Share great examples as I see them in class so other students can add that information to their sheets.
  5. Finish the one-sheet in class (instead of taking it home to finish).

As the year progresses and they get more practice making the one sheets, we will do less in class.  I want them to learn how to make the one-sheets on their own so they will have this skill for future classes.  However, I will make sure to give them class time at the end of every unit to start making their one-sheets.

About halfway through the year my students became upset with me when I didn’t have them make a one sheet for a chapter.  Some students did it on their own but they missed the class time to brainstorm and work on it together.  By the end of the year most students were creating incredibly detailed one-sheets.  Seriously, some of these one sheets were a work of ART.

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Here are some of the white-boards and one-sheets that my students created this year:



Survey Results in Word Clouds!

I made word clouds from the student responses on the end of the year survey I just gave.  I am going to share them with my students tomorrow.

I love and have always used Wordle, but I cannot get Java working on any computer I use.  I am sure I could if I had time, but I’m a teacher and it is MAY for goodness sakes.

Instead I discovered Word Cloud.  I loved using the  WordCloud website because you don’t need Java to use it!  And you can use different shapes and even upload an image.

One Word To Describe This Class:

One Word

One Word To Describe This Class




Advice to Next Year’s Students

Start 3





Most Difficult Topic To Learn

Favorite Topic

Favorite Topic of the Year

My Teacher Evaluation Survey

Thanks to so, so many of you who shared your amazing surveys with me!  I took questions from almost all of them and combined them. My students gave me some of the best information I’ve ever received from a survey so it was worth the time.

I made it anonymous so students would be honest. If you decide to make it anonymous, be aware that sometimes it may be tough to read.  Remember that it is probably not possible to please everyone.  Focus on the good comments and the majority of the comments.  Also, sometimes students are just in the wrong class. It’s not their fault, and it’s not your fault, but it still can make it a tough year for the student.  I need to read those comments, because I want to be able to help all students, especially the ones that may be struggling.

I’d like to survey students on a more regular basis next year so I can make sure that all of my students are in an ok place. (Again, I’m not trying to please everyone, but I would like to know if someone is really miserable when I still have a chance to help them.)  Instead of a formal survey on a regular basis, I’m planning on putting a quick question on every test, and doing a great idea that Megan gave me, which is asking post-it note questions.

I took some of the responses and made wordles with them that I plan on sharing with my students.  I’m still waiting on two classes to finish the survey, so I will publish the Word Clouds tomorrow!  Here is a quick preview of one word they would use to describe my class.

One word to describe

And here is the editable survey.

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Teenagers Used Their Phones 21 Hours Per Week

Wow.  My Algebra 2 with Trigonometry students are actively using their phones (screen is lit and active) an average of 21 hours per week.  Two students used their phones for about 35 hours in just one week.

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We started our data unit last week.  Wow, do I love our data unit!  We start with box plots, then move to histograms and land on standard deviations.  The calculations actually make so much sense, but they can be pretty dry.  I love data analysis, so I wanted to spice it up using an idea I saw from Illustrative Mathematics.  They compared the heights of women’s basketball and field hockey teams at the University of Maryland.  Since we are in NC, I looked up the data for UNC athletes for my classes to compare.  They really enjoyed it so I decided we should analyze their heights and sent them a Google Survey Form.  Wow.  High school kids love nothing more than data about their classmates!  We compared boys to girls, and even class periods against each other.  I had a blast!  The data had become real!  Instead of saying, “Outliers”, we could not say, “our outliers, Brian and Jairus” and the students had a visual point of reference.

This was so much fun I sent them another survey about shoe size, number of shoes, and number of hours they spent watching tv and playing video games in the last week.  We were all ready to dig into this data the next day when we were thrown a curve ball.  A student in my first class of the day showed us all how to find out how many HOURS we had all been on our iPhones in the past week, including listing all of the apps and how much they used each app for.  STOP THE PRESS.  Who the heck cares about shoe sizes when we could see not only how much our friends have been on their phone, but what their top app was!  We instantly started adding up and analyzing the data.  And it was incredible!

We found out that my students use their phone an average of 21 hours per week.  This is SCREEN time, when they are actively engaged in their screens, not apps running in the background.

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After seeing this data per class, I wondered if this much screen time was affecting their grades.  Because of some outliers in some classes, I decided to use median phone usage instead of the mean.  I compared it again the average grades for each class.  With even just a few data points, it appears to be negatively correlated.  Of course talking about the averages does not accurate reflect each student.  To get the actual regression I would need to correlate each students phone hours with their grade average.  Maybe this summer I will have time to look at it.  This quick chart does make me wonder.  As a high school teacher and a parents of teenagers it makes me very concerned.

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We had so much to analyze that we all leaned on Plotly for help.  What an amazing, easy to use, and FREE program.  And what an amazing data unit.

To see the screen time, students must have updated their phones, and they need to have an iPhone.  I am sure that other phones probably provide this as well, but we could not find it.  Go to Setting, Battery, Battery Percentage, Last 7 Days, then hit the little clock icon.  Prepare to be shocked.


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Infinitely Many Bounces

We recently finished up our series chapter.  One of the last questions we talked about was about a bouncing ball.  We just touched the surface of infinite geometric series, so I didn’t want to start out the question with infinitely many bounces.  I wanted to scaffold the question so it was easier for them, then hit them with the zinger!

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First of all, their illustrations were awesome (and varied).  Almost every student found the total distance after five bounces.  Once they had confidence, I threw down the challenge, “What if I asked you what the total distance would be in infinitely many bounces?”  Since they all summed 5 bounces painfully by hand, they looked at me like I was crazy.  There were even some moans (infinitely many bounces, ALL that math)?  But after I gave them “the look”, and they knew there had to be a better way.  I told them they could work on the problem by themselves or in groups.  Several kids wanted some help, or even a hint.  But since I had just decided to ask them about infinitely many bounces, I didn’t have the answer yet.  I truly had nothing to give them, and I purposefully tried NOT to think of the formula or answer so I couldn’t give it away.  I try not to help students too much, but helping is in my teaching nature so sometimes I just can’t help myself!

Many groups of students came up with the infinite sum, and developed explicit formulas that seemed to work (but didn’t recreate the sequence of bounces).  With five minutes left, one student actually started screaming in class, “I got it!  I think I got it!”  And she did.

I didn’t tell her she was correct until the next day (I didn’t want the answer to get out before I gave all classes a chance to solve it).  When she found out she was correct, she literally went screaming down the hall.  The history teacher walking down the hall at that moment thought something was actually wrong with her.

THAT is the joy of mathematics, and I wish every student could feel it just once.  But more than once, I wish they could feel it everyday.  I also wish I could do this everyday.

I just discovered that we have motion sensors that will record bouncing data for us!  We could collect our own data.

I need to get better.

Candy Catapult for Quadratics, Plus Desmos

You should definitely shoot candy when you cover projectile motion in Algebra!  81dz6oj3kIL._SL1500_I got this fun idea from Sean, who even had his students build their own catapults!  He’s a rock star.  Luckily, our math department already had some catapults that I was able to use.  If you want to save time, the  catapults were only $7.89 from Amazon and worked great!  I used Starbursts instead of the included balls (candy for the win).  But students did have to create a tape basket for the shooter since the Starbursts were smaller and were falling through.  My students call this the Starburst Catapult activity and many said it was their favorite activity of the year.

This activity follows my projectile motion lesson, which will be very helpful for your students to do before Candy Catapult so they understand what the dilation should be and where it is coming from.  After reading Mimi’s comment on Sean’s post I amended Sean’s instructional worksheet (Candy Catapult Worksheet) to have the students do all of the quadratics work with just the time.  This makes it a projectile motion problem, and then they can use -4.9 meters/sec for the a.

Candy Catapult:

  1. In groups of 3 or 4, instruct students to carefully read their handout.
  2. Students shoot the catapult from the floor and time how long it takes for the candy to hit the ground and the distance their candy travels.  Students used their smartphones to time the flights.  I tell them to practice and make sure they are getting accurate results.  They do not get a target at this stage.
  3. They use this data to create a quadratic equation of the candy’s flight (in factored form). We used -490 cm/sec as the dilation since we measured in cm.
  4. They measure the height of a desk and use their equation and Desmos* to find out how long it will take their candy to hit the floor from the desk.
  5. After they find the time the candy will be in flight, they use proportional reasoning to calculate where to place the target.
  6. No one may shoot from the desk until all groups are finished, then we ALL gather around and watch each group shoot, one at a time.

*I made a Desmos Teacher Activity for students to record their data and then enter the equations that they created from their data.  This was a great visual check for them to make sure their equations matched their data before moving on.  The graphs also helped them find the numbers they needed when going from shooting from the floor to shooting from the desk.

I did this lesson with all four of my classes, and of course it got better as the day went on.  I always feel sorry for my 1st period class.  I started out having the groups do all of the work individually, even the final round.  But there was really ZERO excitement in that and it just kind of, ended.  By my last 2nd two classes of the day I had set up a true, “Final Challenge Round!!” where the entire class watched.  I even played Jock Jams to get them all “pumped up”.  Oh, the things I do to get high school students energized.

We did everything in an 85 minutes block class.  However, I wish I had spend one additional class day after the activity to reflect and even challenge them with variations of the catapult problem to whiteboard with.  I need to find giant catapult war related problems!  (Or I’m watching way too much Game of Thrones lately).  But really, wouldn’t that be the most fun!

Tips for Success:

  • MOST IMPORTANT!! Do the final round at the end, with everyone watching each other so they can root and especially heckle.
  • Play music during the finals. (I used a Spotify Jock Jams playlist.)
  • Print out a LARGE target!  I found a picture online and used 4 sheets of paper. Target.png
  • Emphasize consistency, consistency, consistency.
  • Use centimeters to measure, and -490 cm/sec for the dilation.
  • Remind them to sure the are consistently measuring in cm, not flipping the tape over and ALSO measuring in inches.  True story.
  • Bring prizes for winners
  • Spend an additional day reflecting, and even give additional problems to solve.

If you do this activity and create a reflection activity or additional problems I would love to see them! 🙂

Enjoy the action!



Candy Catapult Worksheet (amended from Sean)

Desmos Activity Builder

Assigning Desmos Homework

I read about #MTBoS30 on Twitter yesterday.  After blogging only about once a month (or even every other month) for the past year or so, I actually blogged three times in a row last week!  I doubt I can blog something every day.  We have AP exams this week so we are missing class days, and then we only have two weeks left until finals.  But, I am going to try!  I love and miss blogging and am happy to get back into the habit again. Plus, I absolutely adore Anne so I’m in for anything she starts!

I am writing this blog as a Public Service Announcement.  Or rather should I say, Prevent Stupidity Announcement.  If you want to assign Desmos for homework but DON’T want your inbox to look like this (imagine about 150 more emails), then use Desmos Activity Builder.

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This should have been obvious to me, but I’m never my best at the end of a long week (especially this close to May).  Thankfully, the wonderful Dylan Kane is way ahead of me and made a “blank slate” template on Desmos Activity Builder!  This is such an ingenious way to utilize Desmos and cut down on a teachers workload.  Instead of searching through my Haiku inbox or 170 emails to see students work, I will now only have to look at ONE page on Desmos.

For those of you not familiar with Activity Builder, you can start with Dylan’s template, make an instruction page, and then have your students create all of their graphs in the same place.  As a bonus, you don’t have to wait until they are finished and emailing you before you see what they have done.  You can watch them working LIVE, and help them if needed.  Your screen will have ALL student names and graphs on one page (also, love the new “fake names” option)!  Screen Shot 2016-05-02 at 6.11.30 PM

THIS is what my homework should have been.  Feel free to check it out and even play along if you like!  🙂

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Exploring Convergent and Divergent Geometric Series with Desmos

I could not find a Desmos teacher activity exploration for series, so I made my own.  Everything is better with Desmos!

This activity works best if students are already familiar with geometric sequences and series.  They are really just exploring convergent and divergent.  I instruct them to look up the words convergent and divergent in the dictionary.  I thought knowing these definitions would help it make sense.  I also included a geometric sequence and series link from Math Is Fun at the end.

Desmos Convergent and Divergent Geometric Series Activity.

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Trigonometric Identity Activities

Trigonometric identities – I adore them.  They are like little challenging puzzles.  But high school students don’t always share my ardor.  I wanted them to understand what an identity actually was so I started the unit with Sam’s amazing Pythagorean Identities lesson.

The lesson was a little tough for my Algebra 2 class, so I helped them through the last two pages.  The next day, I had them white board some basic trig identity problems.  I usually just give them one side to simplify for starters.  This helps with the whole, “OMG – it’s adding fractions – but with trig!!” scare.  On the third day I put them in pairs to work on Shireen’s (Math Teacher Mambo)  Trig Identity Match Up activity.

This activity was fantastic because all of the identities were the steps in the simplifying process!  So even after they had matched them all up I had them put the cards in the correct order.  What a great activity!

I didn’t see this activity about having students create their own identities (from Sam as well), but I wish I would have!  I will definitely incorporate this next year!

From Fist Bumps to Formulas for Series

This is my first time teaching series.  Thank goodness I have the amazing Sam Shah to give me his great ideas!

The fist bump problem is essentially the same as the famous “handshake problem“, but way better because of FIST BUMPS!  You should read all about it on Sam’s blog because he not only describes it really well, he has a hilarious fist bump video short that my kids loved.  Sam finds the best YouTube videos.

So after having them talk about how many fist bumps we would have in our class, I asked them how they could all fist bump each other most efficiently, then I actually had them act it out.  Even in my last class of the day students were eager to get up and try out their fist bump efficiency strategy.  I don’t know if you teach high school students but this is a BIG win.  They never want to get up. like EVER.  And, the last class even told me, “I heard we move in class today.  Please don’t make us move.”  Yet, they jumped up.  I think it was because I had them come up with their own theories to test out instead of me telling them how to do it.

Sam timed his students fist bumps but I did not because I did this on a short day (55 minutes) instead of a block day.  Ok, I did decide to time my last block because hey, it WAS the last class of the day and I was dying to time it.  Plus, it was THE LAST CLASS OF THE DAY and even after begging me not to make them move when they first got to class, they happily jumped up to fist bump after working on the problem.

If you want your students to understand what is happening and even develop the partial sums for arithmetic question, you MUST give them time after the fist bumps to work.  I took their suggestions about how to sum up a ton of numbers and then introduced them this method.  I did not show them the video.

I tend to rush them, but it was Monday, so I let them work longer than usual.  Wow, was I impressed.  Almost all students were able to write a partial formula to describe what was happening.  Several students actually developed the entire formula.  I did not push them to use variables until their equation was very close, but many students jumped to variables right away.

I should have taken more pictures, but I was having way too much fun!  I did get one picture of a white board from the last block.  They figured out the formula and stayed after class to try to finish it.  What a great day!


I have been giving hi-fives a ton this year so some students actually hi-fived me instead of fist bumping me when I went through the line.  I love that.