20 Minute Assessments

Last year, I decided to make all of my assessments 20 minutes or less, even in my AP Calculus classes.

My school created a post covid schedule, to reduce stress for students and teachers. In this schedule, students had three 70-minute periods a day. Since we had 6 total periods and a “drop day” each rotation, some weeks I saw my students three days, and some weeks I only was able to see them twice for class. The schedule was wonderful for everyone’s mental health, but it did significantly cut down class days. As an AP Calculus teacher, this was concerning. Because, excluding the month of April for review, I only had 58, 70-minute class periods to teach 126 days of AP content!

This meant that I needed to teach two lessons every single class period to teach all of the required AP material in. In order to not waste a single class day, I decided to make all of my assessments 20 minutes or less. I had been doing this in my non-honors classes for years, but I had been afraid to try it with AP Calculus. However, our schedule left me no choice.

I am so glad that I tried it, as 20 minute assessments changed my classroom. Shorter assessments took me less time to make and to grade, so my students got my feedback much more quickly after an assessment. Students who needed extra time could finish their entire assessment in less than one class period. This was so helpful for these students, who often have to schedule finishing multiple assessments during lunch and after school.

Giving shorter assessments meant that I never lost an entire day of instruction due to testing. Instead, I gained back time for my students to practice mathematics during class time! In addition to practice, we also had extra time to learn and even experience more mathematics together.

I spent less time on assessments, and more time teaching students effective study strategies for math. One of their favorites was working together to create One Sheets.

Additionally, with short assessments I had time to give immediate feedback during class time! After all students were finished, I had them put away their pencils and I gave them colored pens. I then went over all of the answers with them, while they took notes right on their test paper. Not only did they get immediate feedback in their own handwriting, but this saved me time grading, as I did not have to write as many comments and corrections on their papers. I did not do this for every assessment, but students really liked this, and often asked to do “colored pen corrections”.

I have always heard that long exams prepare students for the rigor of the AP test at the end of the year. So, I was a bit concerned that my AP students would not be prepared to take a four hour exam after having only 20 minute assessments all year. But my AP students pass rate actually increased by almost 15% from the previous year! In order to prepare them, after a year of 20 minute assessments, I gave them a timed, full length practice test a few weeks before the AP test. I broke this exam down into three days, so that students who were taking too much time on one day would be able to realize that and adjust for subsequent days. I had a couple of students who went over time on the first day, but were able to be aware of that and adjust on subsequent practice assessment days. I checked in with these students after the exam, and they told me they were all able to finish. I truly feel that they did better because we spend more time learning math and less time taking assessments.

Assessment Using Desmos

I use Desmos in class on an almost 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.


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”


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.

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.

Screen Shot 2016-05-20 at 6.29.42 PM

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



Student Survey Question on Assessment

Since I have been creating an evaluation survey for the end of the year, I decided to throw a quick survey question on the assessment I gave today.

Please tell me what you like and what you think could be improved about this data chapter.

I got all types of responses, from bullet points to entire paragraphs!  I did not expect such a thorough response.  My students wrote GREAT thoughts, and I really enjoyed reading them.  I replied to every one of them.  It took a bit longer than it usually takes me to grade papers, but I felt like I was talking to every single one of them, about their opinions.  I don’t get to do that often enough in math.  I think I may put this type of question on every major assessment next year.

FullSizeRender 16


Exam Time – Study Guide Assignment

It’s finals time!  I teach mostly freshmen, so I wanted to help them prepare for their Geometry final.  Many students have a tough time studying for a math test, and this one covers an entire semester plus of material.  Geometry is full of things to know as well, like properties of your favorite shapes, everything you never wanted to know about triangles and circles, and finding areas and volumes of anything and everything.

I created a Study Guide Assignment to help them.  I gave them an outline of the topics the exam would cover, and a rubric on how I would grade it.  I gave out the assignment a week before our two in-class review days, with the study guide being due at the beginning of class on the first review day.  I emphasized that they needed to create a study guide that would help THEM.  They did not have to do it any certain way.  They could take notes, use index cards, make a booklet, do it on their computer, any way they wanted!

IMG_3566Today students shared their study guides with the class.  They were very creative!  A few students went all out and created a brand new binder for their study guides.  They created page dividers for each chapter.  On the page dividers, they attached note cards where they had written the notes from the chapter.  In each section they included the most important notes (foldables), study guides, problem sets and assessments for that chapter.  One student even put every page in a page protector!

Here are some of the other things they created.  Below is a gallery of pictures I took today.

  • A binder with dividers, one for each chapter.  Notecards attached to the divider, then all quizzes, tests and problem sets from the chapter in the sections.
  • A section in their INB, so they would have their notes all together with their notes from the year.
  • Index cards, love the “again” card one student created so she would go through them “again”.
  • LARGE index cards (from half sheets of paper)
  • Booklets, like the ones we make in class to review
  • Quizlet
  • A word document (the student even learned to use equation editor – impressive)

The students did an amazing job and most students told me that it took them a couple of hours or more to do this assignment.   Yesterday many were mad at me (as they were finishing them up the assignment), but today they said, “Wow, this should really help me on the exam.”  Exams are still a week away, so hopefully getting this work “out of the way” should give them a huge head start on their studying.

IMG_3574I feel that their study guides are already effective and helping them.  Today, after they shared their study guides, I let them work with other students if they were missing sections on their study guides.  Afterwards, I gave them an exam review packet of problems and was happy to see many students flipping through their own study guides to get help on the problems instead of asking me immediately.  Seriously, I should do this before every test.  Success!

Grading Side Note – I didn’t want to have to grade ANOTHER project before exams, so I had them self score the rubric.  Then, I scored their rubric as they presented.  It counted as a small quiz grade so I graded it pretty easy.  The main point was that they were organizing and re-writing many of their notes.  And most of my students could use a small good grade this time of year.

Differentiation in Math Class – MS Sunday Funday

#msSunFunClick here to submit your MS Sunday Funday post!
This is not the first time that we have blogged about differentiation.  However, it is such a crucial topic that I’m excited to feature it again – especially since we are joining up with
Tina’s blog!  I am adding our previous posts to this list as well.
Next week our topic is “Supplies – What’s in Your Cabinet?” Please blog a quick list of your favorite math supplies (and why if you have time)!  This could be books, manipulatives, or even things like giant whiteboards!

SOS – Math Review

Screen Shot 2013-03-23 at 7.53.50 PM

This tweet was favorited, retweeted, and/or responded to at least 20 times after I posted it last night.  Teachers everywhere feel this.  I couldn’t decide if all of the attention made me feel slightly better, or worse.

So, the math review topic could not have come at a better time for me.  For some crazy reason, I decided to grade tests on a Friday night.  It was a “round up” type of test covering important topics from pre-algebra this year; evaluating algebraic expression (involving order of operations), exponents, exponent rules, combining like terms, and multi-step equation solving.  The good news is my students have finally learned to use parenthesis when substituting values for variables and can solve equations LIKE MAD.  The bad news?  They are apparently mystified by the order of operations, especially within the vicinity of any sort of exponent rule problem.  I felt so defeated after grading those tests.  I failed.  After my dog used me as a trampoline in the middle of the night, I could not go back to sleep thinking about it.  I do so much to help them learn math, but what am I helping them do to remember it?  I have failed.

The most common math mistake that I encountered was:


Students had order of operations issues and just wanted to distribute things.  Michael, here come.

What happened?  First, I HATE PEMDAS.  This starts early, and students are already brainwashed by 6th grade when I get them.  I teach my students GEMS instead of PEMDAS but all of the GEMS in the world can’t seem to fix this.  I hate PEMDAS because students see parenthesis and go into “I must do that first” mode, even when there is only ONE number inside the parenthesis.  Just because it is in parenthesis, one number, for example (2), does NOT a group make.  I must frequently emphasize this, because very few students made this error when there was just one number in the parenthesis.  But, this knowledge did not transfer when they had two numbers.  The distributive property trumped all.  They do love to distribute.  They also distributed the exponent to both numbers inside the parenthesis.  I have no idea why they would do this, because I don’t even teach them the power to a power exponent rule.  I have them expand any set of parenthesis with an exponent.  They do love the distributive property, but we-e have never, ever, ever, distributed an exponent.  Sigh.  I failed.

This year things are worse than before because our classes are shorter than last  year.  I have replaced my daily warm-up review with “Make a new page in your notebook and update your TOC”.  It’s been awesome for our INB, but obviously tragic for the Order of Operations.  So, starting Monday, I am going to have one problem of the day for both classes posted on the board.  It will look like a variation of this.  Evaluate  -3x^2 – 2x + 5 when x = -2.  I’ll throw in fractions, decimals, and any other basic, easily forgettable concept.  This should help them quickly practice evaluating algebraic expressions, exponents, and the order of operations, EVERYDAY.  And we will go over it, together, everyday.

I will NOT go down, without a fight.

What are YOU doing to review past math topics?  What are YOU doing to help them remember what they have learned?

I’m Presenting “Choice Homework Assignments” on Global Math! LIVE – Tuesday, 02/05/13 at 9PM EST

Listen to the recorded presentation at Global Math (recording will be up 2/6/13).

The first Tuesday night of each month, math teachers present their favorite ideas and lessons at the Global Math presentations.  It is called “My Favorites” and has become my favorite presentations to watch on Global Math!  Usually 5 or 6 teachers share something that they LOVE (lesson, idea, activity).  I always come away learning so much from this one hour talk.

This Tuesday night is “My Favorites”, and I am presenting one of my new favorite things I have started doing in class, Homework Choice Assignments.  My student LOVE my new choice homework assignments.  They are working harder on homework and learning more as well.  Plus, Homework Choice Assignments automatically differentiate their homework assignments without me having to do it.  I can’t wait to share it with you tomorrow on Global Math!

To attend the meeting, all you have to do is click on the link below.  You can sign in with Twitter or Facebook, but you don’t have to sign in to watch the conference.  And, you don’t have to talk or even participate.  You can just watch/listen and come and go as you please.   You can also “reserve” your spot if you click on it now instead of waiting until tomorrow night.  To reserve your spot now or watch tomorrow, click on this link.   Global Math, “My Favorites” Tuesday, 02/05/13 at 9PM EST

This week the presenters are:

1. Jonathan Newman (@newmjh3)
2. Alisan Royster (@G8rAli)
3. Julie Reulbach (@jreulbach)
4. Matt Vaudrey (@MrVaudrey)