Tag Archives: error

Parabola Review Worksheet

I created the following worksheet to help students review what they learned about identifying the different characteristics of a parabola.

After printing it out I decided that I wanted to make it an error analysis exercise instead, so I filled it out myself and made one or two mistakes for each parabola.   I had students put check marks by the correct answers, circle and fix the wrong answers.  Here’s that worksheet:

The Goods:

ParabolasCharacteristics

ParabolaCharacteristicsError

Get it Wrong

Yesterday I was teaching solving two-step equations in algebra, and I gave them a worksheet with 5 problems on it.  We did two problems in my teach/pair/share format.   Then I asked them to trade papers with their partner, and do problem #5 on their partners paper.  The only catch was – they had to do it wrong.  They needed to make a mistake.  Problem #5 looked like this: 2x + 8 = 16.

I told them not to get it obviously wrong, no dividing both sides randomly by 113. But to try to do a common mistake that either they have made in the past, or something that might happen.

It was pretty funny for the class as I walked around and looked at each persons paper and said something like “That’s definitely not right.  Great Job!”.  After 5 minutes I had students trade papers again and correct the mistake their partner made.

Students will not know why you are having them do this, so hit them with something like this–> Important Speech:  The reason we are doing this is because when you are trying to get something wrong, you inevitably have to think about how to get it right, because you have to know what is right in order to avoid it.   So getting a problem wrong is another way to think about how to get a problem right.  The added benefit is that by doing a problem incorrectly, you also get to expose yourself to the most mistakes that are made, so then you won’t make them in the future.  And lastly, you even get to correct someone elses mistake, which even further improves your understanding of a problem.

After I said something similar to above, most the class had an “oh yeah, that makes sense” look in their eyes.

I would be careful to use this technique on the first day I introduce a topic.  I am a bit concerned how effective it would be if half the class has no idea how to do it the right way.  I have only used it during the 2nd or 3rd day (55 minute classes) we look at a topic.

Math Hospital

The Description:

Math Hospital is an activity I try to do every other chapter.  I was given to me by my old district instructional coach.  He had given me a two page handout, but I have since lost it, and I don’t have a digital copy.   Here’s how it goes:

– The day before I give the students a problem to do on an exit ticket.  Then I look through those tickets for a common mistake, and scan that students work into my slides (student names redacted).

– The Initial slide for Math Hospital is always a reminder of the theme of Math Hospital – failure is helpful and not shameful.  I took that theme from a Dan Meyer post you can find here.  This is where I remind students that getting things wrong is a great opportunity to learn.

– Each student gets one exit ticket to do their work on.

– The 1st part of Math Hospital is called “Reading” and is simply where I ask a couple students to read the problem out loud.  It’s good that the class hears how other people interpret math language.

– The 2nd part is where we talk about things we like about the problem.  Common answers are asthetic things  – equal signs lined up, etc.  I tell the students here that “you have been in math for 10 years, you should develop a taste about what you think is good or not good.  Imagine if you were painting for 10 years, you would have an opinion about what makes good art”.  I have them all write down one thing that they like.

– The 3rd part is where we talk about things that are correct.  This is where I always say “remember, in every wrong answer, there is always something right about it”.  I have them all write down one thing that was correct about the problem.

– The 4th part is where we discuss what went wrong, and what corrections need to be made.  I have them all write down one thing that was wrong about the problem.

– The last part is where we discuss key points.  “What can we take from this problem, that is going to help us when we take the test?”.  I have them all write down one key point.

– After the Math Hospital is finished, I have the students work a similar problem to what they just analyzed.  I have them do it on the back of the exit ticket.

–   Lastly I tell them that if they are still confused then they might want to consult another physician.  In this case the other physician is Salman Khan,  and I show a slide that highlights the exact videos on Khan Academy that cover the topic we were discussing.

Here is the handout that I give each student the first time we do the Math Hospital.  It is basically the same as what my instructional coach had given me, but since I did not have it digital, I recreated it.

– I recommend repeating the purpose of Math Hospital everytime you do it.  I always go back to the theme “failure is helpful and not shameful” and I always during the second round I say “you’ve all done this problem, what about this work could you say ‘yeah I appreciate that’, or ‘I would not have thought of that'”.

– This is really meant to be a 15 minute activity.  Quick error analysis.

The Goods:

Here’s the .pdf –  Math Hospital

Update 1:

I remixed this a little bit, that post can be see here.  I now give each student a copy of the patient so they can circle and point to things that are right or wrong, that they like or dislike.  If I do this at the end of the class, I can now say “make sure this patient is healthy by tomorrow” and use it as a homework problem.

Macro-Differentiation

These are a listing of hastags that I use to catagorize my lessons plans.  Each catagory represents a different style lesson plan.  My instructional goal is typically to make sure that I use each hashtag at least once a month.  The goal of this blog is to share all the lesson plans that I use under each hashtag.

My detailed lesson plans are my Keynote slides.  But along with those, I make a quick, calendar-style overview to me a general idea of what I am doing.  It’s on this calender where I place the hashtags at the bottom of each day.  This allows me  to quickly look back at what I have been doing, and know whether of not I am differentiating.  For example, here is two weeks worth of my lesson plans in geometry.  Notice that I can quickly see whether or not I have differentiated my instruction, without having to analyze each specific lesson plan.  The hashtags allow me to get a quick sense of what I have been doing, and what I have not been doing.

*Notes –

-The term “perplexity” is being used as described by Dan Meyer here