Quadratic Fireworks! (Projectile Motion)

Today I taught my students about projectile motion.  Well, I say that, but I hate to actually TELL them anything.  I like for them to discover things!  They often make “much ado about nothing” when it comes to the projectile motion equation in Algebra 2, even though it should make sense to them.  They get all caught up in the particulars of the formula and stop thinking about what is actually happening.  So today, before I taught them about the equation, I gave them a picture of a quadratic graph.  screen-shot-2017-01-23-at-6-46-33-pmI had planned on making up my own scenario, until I saw this terrific post by Sara Vanderwerf that involved a creative fireworks graph.  I loved how Sara described clicking on one aspect at a time.  As soon as I saw this graph, I knew I had to use it!

I did not follow her fireworks task exactly.  Instead,  I just gave them this.  I told my students to create a story with their team from this graph, using as much information as they could from the picture (below). I told them they could write it, or draw a picture, or both.

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After they created their stories I had them share with the rest of the class.  As I walked around I heard one students say things like, “No, the rocket doesn’t start at the ground because you can’t start at negative time.”  I loved this part because of the conversations but especially because of the laughter.  Kids were coming up with some hilarious scenarios, and enjoying a math problem.  Here is what they came up with.

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Hidden Figures!


After they shared their stories, I clicked on each piece of the graph as Sara had.  And then I told them to write the equation that modeled the rockets path from the information I gave them.  This is what I left displayed on the board.  screen-shot-2017-01-23-at-6-54-12-pm

I also wrote two different forms of the quadratic equations on the board and told them they could use either form.   Some groups still forgot to include the a, so I had to walk around and remind them.  I loved seeing students pick different coordinates to plug in for x and y.

 

After everyone came up with a = -16, I gave them another problem.  This time I only gave them the roots and the the y-intercept, so they HAD to use factored form.  I am doing the Candy Catapult tomorrow, so they needed practice with this.

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After writing the equation, they solved for a and came up with a = -16 again.  As the groups came up with this, I asked each of them to think about what was going on.  Was this a coincidence?  What could be happening?  I had someone in every class realize it was gravity!  In Physics last year (our students take physics at 9th graders), they all used -9.8 m/sec².  I put that into a meter to feet converter so they would realize it was the same thing.

I also had the students convert the equations to standard form so they could see the y-intercept appear in the equation.

 

Exams / Testing Using Desmos

I use Desmos in class on a daily basis.  For our midterm, I decided to let my students use Desmos.  As new Algebra learners, many of my students often make small mathematical errors, especially on exams.  My hope was that using Desmos to verify their answers would help them see graphically when they had made an error, and be able to correct it.

How I created it:

I made a traditional exam on paper and then a Desmos Activity builder to go along with it.  I created a “Welcome to the exam” slide with instructions.  I created two slides for each question, one introduction slide and one working slide (usually a graph slide).  I also added “STOP” slides in-between each question to help the students.  Most of the questions were on paper,  then students verified their answers with Desmos.  However, I did have two slides where the graphs were on Desmos, and they had to write the equations of the graphs.  Here is a sample of the slides.

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How I implemented it:

If you have iPads, Desmos has a test mode app you can use.  We are 1-1 so my students did the Desmos part on their computers.  I did not want students having the exam on their computers, or accidentally sharing the exam, so I made sure that they were not signed in to Desmos.  Since we use Desmos frequently, I had to instruct my students to sign out of Desmos after they went student.desmos.com.  I sat behind the students, so I could see all of their screens at the same time to ensure they only were on this screen.  I had them close the window when they were finished.  When they put in the code without signing in, they have to hit, “Join without signing in.”

  1.  Go to student.desmos.com
  2. Sign out of Desmos  screen-shot-2016-12-23-at-7-33-59-pm
  3. Instruct your students to enter the code, and to click on “Continue without signing in.” I had them enter their first and last names. screen-shot-2016-12-23-at-7-38-32-pm
  4. I went around to each computer once they started to verify they were not signed in.  **To do this, at the top right hand side of the page, you should see their name, and then an option to sign in or create an account.  Then you know they aren’t signed in.screen-shot-2016-12-23-at-7-34-59-pm
  5. You can “pause” the activity at the end of the exam so students could not go back to individual screens after the exam. I did not do this, but will in the future. (Thanks John Rowe!)

How I graded it:

I had them put all of their final answers on the test paper.  This way I could grade it like a traditional exam.  I went to Desmos if I had a question about their answers.  For a few students, I was able to give some points back if their Desmos was correct, but they messed up on their test paper. I loved being able to verify their test paper answers on Desmos.  It helped me see what they were thinking and award partial credit where appropriate.

I loved it!

During the exam I kept an eye on the teacher dashboard to see how kids were doing.  I loved seeing kids quietly go, “YES!” and celebrate at their desks when entered their answers in Desmos and it worked.  I also liked using the teacher dashboard to watch the kids work during the exam.  I saw one student enter the incorrect graph, and then see that it was wrong.  They went back to their paper to think and work more, and was able to enter the correct graph the second time.  It was amazing.  The tough part was when students didn’t know how to do the problem, and then their wrong answer was verified on Desmos.  For the future, I really want to try to incorporate Desmos into more assessments, not just midterm exams.

 

What they said:

Most of my students really loved being able to use Desmos.  It was a great reassurance for the majority of the kids.  The last question (if they had time) asked students how they felt about the exam and if they felt Desmos helped.  I loved reading their replies!  My favorite was, “DESMOS WAS A LIFE SAVER”

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Here is the Desmos code if you want to check out the sample Desmos midterm in more detail.

Updated – Great tips from commenters!

For future, just “pause” from the teacher dashboard and that prevents them from accessing it outside of class time. – John Rowe

John Rowe had an excellent suggestion that I had not thought of before!  At the end of the exam, you can hit the PAUSE button so kids will not be able to access the exam later.  Brilliant idea and I can’t believe this didn’t occur to me!

I made shortlinks and printed them on the assessment paper which had the actual questions so being logged in wasn’t as much of an issue.  – John Golden

John Golden had a great idea about using just a Desmos calculator link instead of an activity builder and then giving the students short links on their tests.  I love this idea, especially for shorter assessments.  It is what I was looking for to be able to incorporate Desmos into smaller assessments.

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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Enjoy!

My Favorite: Delta Math

Edited:  I finally updated my Delta Math post.  I love having a website that helps my students AND is so good that THEY ask me for it.  It’s the best!  Enjoy! 

We are now into Week 2 of the Blogging Initiative, “My Favorite”!  You should definitely check it out if you would like some blogging inspiration!  It is only four posts and it’s not to late to join in.

Screen Shot 2017-05-21 at 6.50.12 PMMy favorite for the week is Delta Math, a free online math practice program with problems ranging from middle school to pre-calculus. The amazing Mattie Baker presented Delta Math as one of his favorites at TMC15 last summer.  You can watch his presentation at the bottom of this post.

I rarely use Delta Math for daily homework assignments.  Instead, I use it to review those basic Algebra 1 skills that many students have either forgotten or did not master during their Algebra 1 year.  I give these basic practice sets well in advance of the corresponding Algebra 2 topic that I will be covering in order to get them prepared.  I assign one “Problem Set” of about 5 – 10 problems a week.  I also give a variety of problem types in the problem sets.  Students are able to rework each problem until they get it correct, meaning that they are able to receive full credit on their problem set each week with just effort.

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The students can see fully worked out examples of each problem and even watch videos for some problem sets.

Screen Shot 2017-05-21 at 6.46.14 PMI love the explanations on Delta Math, as they usually use methods that I teach in class, like the “box method” for multiplying polynomials.  They even color coded the diagonals!

Occasionally I will assign a Delta Math set for homework.  For instance, they have some fantastic practice sets for graphs, such as the one for finding domain and range visually.

Delta Math gives you amazing student data.  You can see which problems students missed and even their incorrect answers.  If I see many students struggling on a set, then I will usually reassign that set in the coming weeks.  You can even see how long students took on EACH problem!

 

 

How I Use Delta Math:

  1. I assign about 10 review problems per week, due every Tuesday at 8:00 AM.*
  2. I usually require 1-2 of each kind of problem, with a “1 off” designation.  This means that they can miss one problem without penalty, but if they miss more than one in a row, they go back to zero.
  3. I assign Algebra 1 problems well in advance of the corresponding Algebra 2 topic.
  4. I assign problems on a spiraling basis where problems increase in difficulty each week.  I am staring rational functions in about a month, so next week I will start assigning them basic fraction problems.  Next, I will assign them fraction problems with x in them,…
  5. I hold help sessions the day before their problem sets are due for my students that struggle recalling their Algebra 1 skills.

*This biggest drawback is that students forget to do their Delta Math since it is an online program and only assigned and checked once a week.  Moving the due date from Monday to Tuesday helped tremendously with this.  I also love the Tuesday due date as opposed to Friday as some students wait until the last day to complete it and they are usually pretty wiped out by Thursday night.  I use Remind to remind them and mention it in class.

Optional Summer Assignment:

Another way I use Delta Math is that I give all rising Algebra 2 students at our school an optional summer assignment on Algebra 1 topics in order to help them refresh their basic skills.  I assign just one question per topic, but students can do as many questions as they like.

Zach Korzyk (@MrDeltaMath), the creator of Delta Math, is a great person to follow on Twitter because he loves to help teachers!  Follow him and say “Hi!”.

Mattie (@stoodle) – Thank you for introducing me to Delta Math!  (Delta Math portion begins at about 3:00)

Click here for video.

My students really love Delta Math!  Here is some of what they said in my last course survey. 

  • Having Delta Math for homework helped me a lot because it showed me how to do the problems so that when I did a problem similar to the previous, I would know how to do it with a lot more confidence.
  • Start doing more Delta Math.
  • Do More Delta Maths.
  • Do Delta Math – It helps a lot!
  • Do the Delta Math (this will definitely help)!!
  • Delta Math was very helpful.
  • Please give more Delta Math assignments.
  • I think continuing to assign Delta Math would be wise.
  • Delta Math really helped when it gave examples.
  • Please start doing Delta Math more. 
  • Delta Math assignments, they helped me a lot!
  • DO THE DELTA MATH ASSIGNMENT BEFORE SCHOOL STARTS

TinyScan – PDF Scanner App for Smartphones and iPad

IMG_6195I have been using an amazing app that I really don’t know how I lived without called TinyScan.  Holy mac, this app is a teachers dream!  There is a free version which I tried first.  But, I quickly upgraded to the premium version for $4.99.

With TinyScan you take a picture of something with your phone (for me, it is usually the worked out solutions to homework), take a picture of the page, then TinyScan beautifully turns it into a crisp and clear pdf file.  You can edit, crop, and rotate the file.  You can make it black and white or color and darken or lighten the ink.  You can take pictures of several pages in one file (you may have to have the premium version for batch scanning documents into one file).  Once you have edited your pdf, you can email, AirPrint or fax the pdf’s with one click.  The very best part is that you can instantly upload the pdf to your Google Drive from within the app!  You can also set the app to instantly upload to Google Drive (or other services).  To do this, go to settings and choose Auto Upload, and you can choose from Google Drive, Dropbox, Evernote, Box or OneDrive.  It’s so easy!

The best way that I use it is by uploading the files to my Google Drive.  I created a shared student folder on Google Drive, so as soon as I finish the key I can take a picture of it and upload it to the student file so that my students have immediate access.  I also take a quick picture of all of my test keys and keep them in the same folder as the original in case I lose the key.  I love this app.

Glenn showed me a couple of different scanning apps at TMC15.  His apps were able to rotate a picture automatically if you took it crooked.  However, he could not automatically upload to Google Drive.  So if you look at a different scan app, make sure you can seamlessly upload to Google Drive if that is important to you.

Fill Out This Form to Connect With Other Math Teachers On Kahoot!

There are thousands of public Kahoots! made by teachers to chose from.  Kahoot! has a search feature that allows you to search by title, subject, tag, or username.  You can also share a Kahoot! that you have made with another teacher if you know their username.

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Since my Kahoot! post, I have found that many math teachers that I know also use Kahoot! and are using it in ways that I have not even thought of.  For instance, Laura Wheeler uses Kahoot! a few times a week as a warm up for a fun way to do spiraling reviews.  I would love to easily find and see her reviews, since we both teach high school math.

Then, as is often the case, an amazing idea was born on Twitter.  Wouldn’t it be GREAT if we knew our math teacher friends Kahoot! user names?  Then, we could search and share with teachers that we know.  Additionally, if teachers would tag the Kahoots! they use with MTBoS, we could also search that way.

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Sharing your Kahoot!

So, please fill out this form if you are interested in easily sharing the Kahoots! that you create and use with other math teachers.  I asked for the subjects you teach so that other teachers can more easily find teachers that have similar needs.  And don’t worry if you don’t make your own Kahoots!  I rarely make Kahoots! from scratch.  But, I do go through each Kahoot! I use carefully, and often edit them, so other teachers would probably benefit from the Kahoots! that I use.  If you are not already using Kahoot!, you need to sign up for a free Kahoot! account here to get your username.

Here are the results: Google Form of MTBoS Kahoot! user names.

Once you finish the form, you will be directed to a Google Form of MTBoS Kahoot! user names.

How to Search and Add Tags in Kahoot!

Also, to search by tag, you can’t just enter mtbos.  You have to type in doc.tags:mtbos.

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Don’t forget to tag your Kahoot! with MTBoS after you finish making it.

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Fill out this form to connect with other math teachers on Kahoot!

Fill out this form to connect with other math teachers on Kahoot!

Plickers aka “Can We Do This All Period?”

If you want 100% of your students engaged and asking you to do an activity, you need to try Plickers.

photoThe amazing Pam Wilson introduced us to them at Twitter Math Camp.  We were ALL amazed and impressed!

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A Plicker is a “paper clicker” with a bar code that the students hold up and then you scan with any smartphone or iPad.  Only one device needed, no batteries required!  The students can pick A, B, C, D or True/False.  The data immediately shows up on your phone AND on their website as a bar graph.  I assigned my students a number, so I can even see who missed the question as I am scanning the room.

From your computer, you can project their responses onto your overhead.  It only shows the correct responses in the “Live View”.

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It also stores the data on their website so you have a record of correct and incorrect answers.  I know you think that I must be lying, but I am not.  These things are AMAZING.

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I decided to affix my students Plickers to the back of their INB with clear contact paper.  That way, they should always have them handy during class, and hopefully they won’t get destroyed!  I oriented them all differently (either A, B, C, or D facing up) on their notebooks so they couldn’t see how other students were holding up their notebooks to get a hint.  It’s so much fun for the students and for me!

I have been using it as a warm-up, to asses prior knowledge or expose them to a new topic that we will begin that day.  I think it would also be a great “Pre-Assessment” or “Exit Ticket” tool.

You can see below how other teachers are using them in class as well.  If you have an idea about how Plickers could be used, please put it in the comments.  Also, if you have blogged about Plickers, please post your link in the comments so that we can all get great new ideas!

Global Math Webinar – March 4: Student Creativity in Math with Technology

Don’t miss Global Math this Tuesday night, March 4th, Student Creativity in Math with Technology. Rafranz Davis (@rafranzdavis) will be presenting.

Rafranz is an instructional technology specialist for a Dallas/Fort Worth area school district. As an advocate for passion-based learning, Rafranz uses her experience as a secondary math educator to help teachers integrate technology using innovative teaching strategies aimed at empowering students to be autonomous learners.

 

Visit the Global Math Page to reserve your spot!

Our Code.Org Coding Success – A Summary

Screen Shot 2013-12-17 at 12.43.19 PMLast week my students participated in the Hour of Code.  It was an overwhelming success!  They enjoyed it so much that they continue to code, and they continue to ask me everyday if we are going to code in class.  As soon as they have any extra work time in my class, they are coding!  With these amazing results, I am looking to the future.  I would love to plan lessons and projects with coding involved.  I only hope I have the time to prepare this for my students.  They deserve it.

After our Hour of Code, I surveyed my students to see if they liked coding (on a scale from 1 – 5), and if they would like to continue coding in class.  The results are below.  I have included some excerpts and  you can also read their responses in detail here.  They were emailing me their creations, so I created a “Coding Creations” wiki page where they could add things they have created (or continue to create).

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Quotes from students:

It was really fun to just type in all the stuff and have no clue how it was going to turn out. It was also really fun when I got home and had to figure out what was wrong in all the billion lines of code I had typed in class. After hours of work all I had needed to do was take out the commas in the character’s speech. Thanks to the Hour of Code I am ready to go back and add in more complicated things to my campaign. Computer programming is really fun, and I can’t wait to do some more.

It was interesting and pushed my mind further and gave a sense of power in my mind and keyboard

I love coding so much! I think it is so fun to watch the videos and learn how to code! I woke up at 4:30 two mornings ago to code, and at 5 the day before. I am obsessed.

I thought it was really cool how you type in numbers and words, and it is linked to a little picture. I loved how you could make the holiday cards on khan academy! It was so fun! I also loved how it seemed really hard at first, but after you got the hang of it, and memorized the basic codes, you could create complex pictures.

I think it is really fun to look at all the things we use computer programing for and how important it really is in modern society and then be able to learn to do it! Its AMAZING!

I loved computer programming because you got a head start for the future. This has made me want to do more computer programming in the future!

I did 5 because coding is fun and interactive. It may seem scary but there is a world of computer science out there and coding is one major part.

I LOVE TO CODE!!!! DO MORE!!

I also asked them, “What did you like best about coding?”.

I liked best about coding that I could just type some letters and numbers and make what I imagined come to life! It truly is amazing.

It was very cool how you really got to control your computer and that you could build anything you wanted to.

I liked that it really made you think.

What was so cool was that after you got the hang of it you were basically doing it by yourself, at your own speed, and what every you wanted to draw.

It let your creativity flow, you could make anything you wanted with no strict deadlines.

I like coding because it lets you express your self in a more complex way.

The multitudes of possibilities and how simple it really is.

The fact that i could create those things on a computer just by typing in stuff!

The challenge and the good feeling when your character does exactly what you planed for it to do.

Hour of Code = Amazing Success

I cannot say enough good things about the “Hour of Code” that my students participated in today.  When I showed them the intro film yesterday they were so excited about coding they begged for the website link.  I gave them code.org/learn.  Another teacher told me that they started working on it immediately in work time yesterday.  Multiple students told me they went home and worked on it last night, some for a couple of hours.

Today, they ran into my room before class even began and asked if they could start.  I was overwhelmed with their excitement and curiosity in coding.  They started with the code.org/learn tutorials but many of my students quickly moved on.  Some of them ended up on Tynker or Code Academy, but the majority landed on Khan Academy and learned to write Javascript on their own.  It was easy for me as all of the websites have video tutorials.  Students were working together and asking each other for help if they had questions or when they got stuck.  At one point, I had half of the classroom around one students computer until he told them to “go and sit down so he could think!”  I took some pictures and videos to share (see below).  If you watch the video clips, be sure to listen to all of the students brainstorming about their programming in the background.  I just noticed that when I watched the video again.  There definitely was a “electric math/computer” buzz from all of my students in the background!  Videos on YouTube!

I signed up on the code.org website but did not receive an email with instructions or a teacher code.  I later saw that I could have the students enter my email address on their code.org page, but by that time they were very involved and I didn’t want to interrupt them to have them put my email in.  Even though I would love to get a summary of what they accomplished it was not worth stopping them.  The whole point of the day was to get all of my students coding.  The mission was accomplished, as I’ve had several students email me the progress they have made tonight with the projects they are still working on!

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I’m not sure how long these tutorials will be available, but I do intend to find a way to give students class time to learn coding in the future.  We have been inspired and I want to give them the opportunity to develop this skill and keep this excitement alive!

Videos on YouTube!