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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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!

Inverse Functions and Logarithms

After the Zombie exponential problem, several students wanted to know WHAT was this mysterious LOG thing and especially why it worked?  Enter, inverse functions.

I made an Inverse Functions guided worksheet for my students.  It is self-directed and has them use two different colors for the graphs.  They can get through the entire sheet without much help, and make all sorts of great discoveries on their own.  I blew it in the first class I taught by trying to go over the sheet with them way too soon after handing it out.  I wanted to explain a couple of things before they got too far.  DON’T DO THAT.  Give them ample time to read it, graph things, make small mistakes, and discover.  It makes a huge difference not only in understanding, but in their engagement and attitude.  They really don’t want to hear me talk.  Instead, play music in the background, walk around and see their work, even answer a FEW of their questions.  It is so good for them to work on their own!

Algebra 2 Inverse Functions Worksheet.

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After we went over the worksheet together, we played with the awesome inverse graph created by Desmos that I modified with the equation y=2^x.  The kids can move the slider and it shows the point and its inverse on each graph!

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I created the graphs with an amazing program that Mrs.Davis found called GraphFree.

Algebra 2 Transformations Unit, Starring Desmos Teacher Activities

I teach out of the Discovering Algebra Book.  Last year I tried out the order in the book, and it was disastrous.  The book introduces a new parent graph with each transformation. That did not go well with my students.  It was confusion city.  This year, I went back to what I know.  I taught parent graphs first, then transformations.  Finally, they learned how to write equations given the graph with dilations.  Whew.

Glenn’s convinced me to use the “transformation form” (AKA h,k form) last year in Geometry.  That was a great start with my students in Algebra 2, as we were able to use it right away starting with linears.  I can’t tell you how many problems using the transformation form solves, and how relieved kids eventually are, not to be married to the y-interecept.  Many times, they aren’t given the y-intercept, so y=mx+b is used much more sparingly this year.  It takes my newbies a while, but they get it.  Why kill yourself trying to find where this stinking graph crosses the y-axis when you could put pick ANY point out on the line.

85dda-11850303_153438328335826_1353010797_nThanks to Glenn, I knew to use transformation form from the start.  Thanks to Meg, I had a ton of material to draw from.  And thanks to Desmos, the kids could actually discover transformations ON THEIR OWN.  Disclaimer.  Even with all of this wonderful discovery and conceptual learning, students NEED you to summarize what they have learned with them, and then keep them practicing their new discoveries to cement those discoveries into their brains.  With conceptual learning, many times they are pretty sure they understand what is going on, but they really love when you affirm that.  Also, some kids have a tough time getting there, so a thorough summary at the end helps everyone.

When I taught transformations years ago, I would teach parent graphs, then give them a list of transformation rules to learn and apply.  It was pretty dry and procedural.  Now, I have moved to Desmos, where the students play with graphs to learn what the transformations do without ever seeing any “rules”.  It is awesome, and it sticks.

Screen Shot 2015-10-28 at 8.31.28 PMI still teach parent graphs first and function notation first, along with domain, range and  interval notation.  I actually teach them with the material in the previous chapter so they can know the parent graphs cold before we even start looking at transformations.  After they learn the parent graphs, they study transformations and reflections and then move to dilations.  Oh, those dilations.  My students work with computers and each other for the entire unit.  I also give them handouts so they can take notes and graph as they go along.  I didn’t give them the “transformation rules” until one of the last days.

All of my transformation files are in this box folder.  And the Desmos Teacher Activities are linked below.  You can’t use my activities, but you can’t copy Desmos activities YET for editing.  I am sure that is coming soon.  You will see a vocabulary sheet referred to in the Desmo’s activities.  To start every chapter, I give my students a vocabulary sheet.  They takes notes on it and then most of their important terms are together in the same place.  The vocab sheet is also in the box.

Desmos Teacher Activities – Transformations

  1. Transformations – Shifts and Reflections
  2. Transformations – Dilations
  3. Dilations again (as a short review in-class lesson)
  4. Transformation – Extra practice

Desmos Teacher Activity Builder – Systems of Equations Review

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Desmos teacher activities are amazing!  You can find them all at teacher.desmos.com (not Desmos.com).  And now, you can even create your own!  I just made my first Desmos Activity last week on systems of equations.  It was incredibly easy to make!

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Overlay – See all student work at once.

I teach Algebra 2 students so many of them have already worked on solving systems of equations in Algebra 1.  However, since it was long ago, it is also far away in their brains.  I wanted to let them work through a review without having to directly teach the concept from scratch.  I also didn’t want to reteach parts of the concept they already knew. Desmos activities let you do this beautifully.

Screen Shot 2015-09-11 at 4.32.02 PMSince you can see their work on your computer in real time, you can see if the whole class needs some review on a topic or if you just need to go and visit a few students.  I project the overlays, and students love to see all of their work together.  Another neat feature when you add a “Question Page” is that students can see previous student answers AFTER they type their answer in.

I also want to thank Sam and his new Better Questions Blog because that is where I got the first question of the Desmos activity I created.  It was a wonderful way to have students think about systems of equations!

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Geometry Transformation Foldable – Translate, Reflect, Dilate

I only had about a week to cover transformations so I focused on translations and reflections, and then briefly covered dilations.  I used coordinate changes, where (x,y) transformed to (x +2, y-1) or (-x,y) as I feel that will benefit them in later Algebra classes as well.  Michael Pershan’s created an excellent Tool for Exploring Transformation Rules using  Desmos that I love.  I gave my students the link and let them play with it.  Screen Shot 2015-02-16 at 2.11.57 PM

Then I had them take out the +5, and +8 so they only had (x,y).   Screen Shot 2015-02-16 at 2.05.39 PM

I challenged them to make the house FATTER.  It took them a while to figure out they had to multiply a number instead of add.  After they were all able to make very fat houses asked them to make it skinner, taller, and shorter.  After that, I asked if they thought they could turn it upside down.  The students enjoyed making the house different sizes and moving it around.  But the best benefit came days later when I only had to mention the house to remind them how to differentiate between the translations and dilations in future work.

Here is the link to the Transformations foldable I created, using Kuta software for some of the graphs.

Maximizing Box Volume with Popcorn

IMG_2916Thanks to Fawn, my students actually cared about making the maximum sized box out of their 8.5″x10″ piece of graph paper.  If you don’t do this, you should!  It was very easy and great fun!  You will need to go and read Fawn’s popcorn post because she has all of the great lesson details.

I went minimalist and only showed them a box I had made, and the squares I had cut out to make my box.  I gave them a ruler, scissors, tape and ONE piece of graph paper.  I told them they only got ONE piece of paper.  They worked well and carefully.  Most students chose to fold  the sides in instead of cutting just in case they messed up.  Love them.

Screen Shot 2015-02-15 at 9.56.16 PMI recently bought an Orville Redenbacher air popper so I brought that in to make the popcorn.  Seriously, this is the best $22.49 I’ve spent in a long time even before I used it for a math lesson!  I even brought in butter.  One of the students took a picture of the air popper so she could buy one.  It was pretty cool with all of the popping going on right in the back of the room.  It smelled heavenly!

Once they made their box they measured it and entered the measurements and resulting volume on a Google Form.  Then I filled up their box with popcorn!  We ate while looking at the Google Form results and then I challenged them to find a general equation for an size cut.  Several students came up with it pretty quickly and then I had them graph it in Desmos to show them how their maximum volume was also on the graph.


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Function Transformation Discoveries using Desmos

Calling all teachers to help me make these better!

Screen Shot 2014-10-04 at 11.40.52 AMThis summer at Twitter Math Camp, Glenn (@gwaddellnvhs) and Jonathan (@rawrdimus) showed us how they lead students through all of the functions in Algebra 2.  Basically, they put all of the equations into (h,k) form.  Fortunately, the book I am using this year, “Discovering Advanced Algebra” does basically the same thing.  Since it is a “discovery” book, they have some good ideas that I have been able to modify and made into INB (Interactive Notebook) form.  Never fear, this just means it’s a worksheet that you fold in half.

Screen Shot 2014-10-04 at 11.58.29 AMThe first discovery was also my students first introduction to graphing with Desmos on their own.  Of course they have seen me use Desmos multiple times by now since Desmos has all of those great example graphs in their side bar!

Here is how I progressed through discovery for linears, quadratics, square root, and absolute value.  The Box files with the word docs are at the end.

  • Horizontal and Vertical Shifts
    • Linear Equations (first time with Desmos)
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    • Quadratic Equations
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  • Reflections with the square root function
  • Dilations with the absolute value function – these last two are combined into one.  I would love any suggestions on this – before Monday.  I know, I’m asking for too much here! 🙂
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Also included is a “Transformations Parent Graph” foldable that I made to sum it up.  I kind of hate this one, and would love suggestions here for sure!  Should I add dilations?  Why is it so ugly?  What else do I need to add?  I need help here for sure.

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Algebra 2 Function Transformation Discoveries

Please note:  I did not make all of these discoveries from “scratch”.  I created some of them.  But some were inspired by the textbook I am using this year, “Discovering Advanced Algebra” and some were created by my amazing co-teacher.  I then adapted all of them for INB (Interactive Notebook) form.