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.

Introduction to Transformations Marbleslides!

I just made my first Marbleslides in Desmos!  It was incredibly easy, and the students said it was a really fun way to learn.

This Marbleslides activity introduces students to transformation form and lets them practice moving graphs around with Marbleslides (SUCCESS!!) using the new parent graphs they just learned.  My students know transformation form with linears, y = a(x – h) + k, but have not moved any other graphs around yet.  (For this activity I used the absolute value, quadratic, square root, and cube root functions.)

I have two goals with Desmos this year.

  1. Shorten my Desmos Activity Builders, so that I have time in class to practice with the students outside of Desmos.
  2. Make worksheets to accompany my Desmos Activity Builders, so the students can have notes to look back on.

I felt this activity accomplished both, and my students really seemed to enjoy it.  I have provided the activity and the worksheet for you to try.  I would love feedback!

Desmos Introduction to Transformations Marbleslides

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QR Code Stations – Function Notation

We have been working on “building” equations to solve for x , literal equations and an introduction to functions.  After flooding my students with function notation, I decided we needed a day to practice.  One of my favorite ways to let students practice is stations.  I love station work because they allow students to move around the room AND work with different people all period.  I let them pick their partners to start, and I put 2 sets of partners at each station.  They can work with all of the people at their table.  However, I strongly encourage them to work at their own pace.  If they finish and want to move on, or want to stay longer it’s all ok.  Students that work at about the same pace usually end up with each other. No students are bored waiting on others to finish, and I can spend time working with students who have question.  I rove from station to station answer questions so I feel like I get to connect with individuals as I help them.  It is a great day all around!

I still use the clear picture frames to display the problems, but now I put the answers online, so all students can easily see them and have them for later.  This also allows students who may not finish (or who are absent) to access all of the questions and solutions later.  Students can access the answers by scanning a QR code at each station.  Many of my kids have a scan app, but I found out yesterday (from the students of course) that Snapchat has a QR reader.  Here are my function stations.  The QR codes will be active until the end of the 16-17 school year.


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Monthly Algebra 2 Blog Posts! #Alg2Chat

Thanks to all of the Algebra 2 Teachers who submitted a blog post this month!  Don’t forget about our Algebra 2 Twitter Chat, this Thursday at 9PM EST (#Alg2Chat).

We would love to have you blog with us!  Here are the topics that we will be discussing at the #Alg2Chat’s on Twitter this month.  It would be great for you to blog so you can share your blog link during the discussions.

9/8/16 – Student Engagement

9/15/16 – Rich Problems for Algebra 2

9/22/16 – Making Groups Work

9/29/16 – How You Use Technology

Fill out this form to submit your blog post.

Algebra 2 Twitter Chat! Thursday, 9/8/16 at 9PM EST #Alg2Chat

The first Algebra 2 chat will be on this Thursday, 9/8/16 at 9:00 PM, EST.  The topic this week will be Student Engagement.  What can we do to get students excited about mathematics (even if they don’l love Algebra 2)?

The chats will happen once a week on Thursdays at 9PM on Twitter at the hashtag #Alg2Chat.

If you have never participated in a Twitter Chat before, you can read this post for tips!

Topics for this month:

9/8/16 – Student Engagement

9/15/16 – Rich Problems for Algebra 2

9/22/16 – Making Groups Work

9/29/16 – How You Use Technology

 

Algebra 2 Monthly Blog Spot

I can’t wait to read about everything other Algebra 2 teachers are planning and doing in their classrooms! I thought it would be fun if we all blogged and then I could post a compilation of our blogs about once a month.

I would love for us to blog about how your curriculum is organized (sequence of topics).  I think it would be great to see as it seems we are all usually teaching the same topics at about the same time.
Other great ideas for blog posts could be:

  • First day / first week activities
  • Goals for this year
  • Great icebreakers
  • Math class set-up

You don’t have to choose!  If you go crazy and want to blog about all of them, please do!  Submit every post to the form below and I will post them all!  And don’t forget to tweet out your post with the #Alg2Chat hashtag.  Also, if you are in a blogging frenzy, check out #MTBoSblaugust, and include that hashtag to your post as well!  You don’t have to wait, you can get started now!  🙂

Join us on Twitter and even with blogging!

Please join us on Twitter at #Alg2Chat.  If you aren’t on Twitter yet, now is a GREAT time to start.  You will be amazed at the resources that will come right to you!  Also, if you have always wanted to start a blog, do it!  We have a great website, Exploring The MTBoS, that can help you with both!

Algebra 2 Math Chats (#Alg2Chat) Coming in September!  Thursday nights at 9PM EST

Check out #Alg2Chat Thursday nights at 9PM EST, beginning in September.  If you are interested in helping moderate, or have some great topics you would like to discuss, please tweet me at @jreulbach.

Click here to enter your blog post, or fill in the form below. 🙂

 

Algebra 2 Teacher Blogs!

Check out these blogs from teachers who teach Algebra 2! If you teach Algebra 2, Pre-Calculus, Math 2, or Math 3, then please scroll down to add your blog to the list!

These are the blogs of the teachers who signed up to connect already.  You can fill out the form at the bottom.  I will add you to the list when I update this page (about twice a month).

Check out the #Alg2Chat hashtag on Twitter starting in September.  We will be meeting Thursday nights, 9PM EST.

Amy McNabb
Jonathan Schoolcraft
Beth
Henri Picciotto
Jonathan klupp
Dylan Kane
Wendy Menard
Shaun Carter
Lisa Winer
Mark Kreie
Andrew Stadel
Trever Reeh
Shai McGowan
Sean Sweeney
Bonnie Davis
Lisa Henry
Brandy Cajudoy
Melissa Allman
Ali Grace Eiland
Tara Daas
Lane Walker
Mary Williams
Matt Baker
Julie Reulbach
Brian Palacios
Lauren Goldfish
Marsha Foshee
Heather Rosson
Nolan Doyle
Jennifer abel
Laurie Hailer
Christie Bradshaw
Robin Mathews
Sara VanDerWerf
Andrew BC
aanthonya
Steve Dull
Suzanne von Oy
Madelyne Bettis
Nate Goza
Jennifer Kelly
Tara Daas
Elissa
Jill Weitgenant
Jennifer White
Nathaniel Highstein
Anna Vance
Jennifer Fairbanks
Sara B. Vaughn
Taylor Horn
Scott Keltner
Kat Glass
Amy Gruen
Meg Craig
Lois Burke
Rachel Fruin

If you teach Algebra 2, Pre-Calculus, Math 2, or Math 3, please add your blog to the list!

Once added, you can see the other Algebra 2 teachers in this spreadsheet.

Calling All Algebra 2 Teachers! #MTBoS #Alg2Chat

TMC16 this year intensely motivated me, to the point where I cannot stop thinking about math ed, even on vacation!  I came up with this idea this morning, and have to get it down before I go to the beach so I will stop thinking about it, and relax!

If you are going to be teaching Algebra 2, please add yourself to the list below!  I did this when I taught middle school, and it was great!  I even was able to develop a monthly newsletter of resources for those who signed up.  No promises, I have much ambition before school starts and then run out of time. But for the first time in two years, I am feeling my old momentum come swinging back!  Hurrah! And thank you all for inspiring me!

I created a shared Google Folder for us to drop our favorite goodies in.  How great will it be to have a place with ALL THE THINGS when we are looking for resources?!  As a community, I know we can do this!

Julie, @jreulbach

PLEASE add the #Alg2Chat to any Algebra 2 post you tweet about.  🙂  Let’s bring this back!