A Day Full of “One Good Things”

I love reading the One Good Thing blog.  It always encourages me to find the positive in my day, regardless of what kind of a day/week I’m having.

Yesterday was one of those days that was full of One Good Things.

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I started with the following Which One Doesn’t Belong in my first 6th grade class.  The conversation was SO good, and I loved hearing all the vocabulary my students remembered.  The conversation went equally well in my other two sections.

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Then we used this Desmos activity.  It was the first time this group of students used Desmos.  It was love at first Class Code.  The groans when I paused the activity were music to my ears -I even gave them a 5 second warning.

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In my 8th grade classes I used Vertical Non-Permanent Surfaces (#VNPS) for the first time this year.  Whenever I do this, I ask myself why I don’t do this more often.  I’m always amazed at how much more engaged students are and how much more they participate when we do this compared to seat work.

After grouping students randomly for this, I saw that two students who I struggle to get to do anything on a lot of days ended up partners.  I had my doubts about how their group would function, but the 20 minutes those students worked together was by far the best either of them had worked all year!

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When it came time for my 5th hour class, I logged in to Desmos to find that none of my custom activities or history showed up in my account.  What could have been a disaster (my 30+ minute lesson plan with 6th graders, gone), ended up going just fine.

For whatever reason, my students were crazy patient and quiet while I tried to log in to Desmos and figure out what was going in.  Then I finally realized what happened.  My school email changed over the summer, and I had been trying to change my Desmos account to my new address.  I had contacted Desmos earlier in the week to help with this and saw in an email that they were able to make the change for me just before 5th hour.  The change didn’t quite go as expected, and I needed to change my password and wasn’t able to do this.

We had just set up something else on my students’ Chromebooks, so I had them work in that while I emailed Desmos to try to figure out the issue.  I spent the next 10 minutes or so emailing Denis from Desmos -we may as well have been live chatting for as quick as Denis was to respond to my emails.  (Have I mentioned that Desmos is awesome!  After my initial split second of panic when everything in my account was gone, there was never a doubt in my mind that Desmos would be able to fix the issue.)

The hour ended, and I still wasn’t able to get my stuff back in my account.  However, I tried the same thing I had been trying during class one more time, and it worked!  I was ready to go for 6th and 7th hours.

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After school I was able to go and support a colleague whose family is going through a difficult time.  While the situation isn’t a good thing, I was glad I could be there for her during this difficult time.

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Exponent Unit

This was the first time I’ve taught exponents without explicitly telling students the “rules” at some point within the unit.  Many students still said things like, “Oh, so when you divide, you subtract the exponents.”  I have mixed feelings over this.  Yes, I want my students to notice patterns, but not at the expense of understanding the math they are doing.  This is one of the things I struggle ensuring as a teacher -that after my students have noticed patterns, they still understand what is actually happening.

I started the unit with a modified version of Andrew Stadel’s exponent mistakes worksheet.  (I know I found someone else’s version of this worksheet that I modified, but I can’t remember where I got it.)  This was something we came back to periodically throughout the unit.  On one of the last days of the unit, we went over the correct answers as a class for the first time.  After going over the sheet, I asked my students to think back to their reaction when I first gave them the worksheet.  Many sort of freaked out and several others were convinced that some of the problems were actually correct.  It was fun for me to see them realize they had learned something throughout the unit because they could now correctly do all of the problems.

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The rest of the first day we focused on identifying the base and writing things in expanded form.  The next several days I spent at least one full day on the product rule, power rule, and quotient rule.  The link for the worksheets I used is at the end of this post.  Again, I know I modified those worksheets from ones I found somewhere online at one point, but I can’t remember where I found them.

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I used this Which One Doesn’t Belong? as a warm-up one day.  I’ve really been loving using these as warm-ups this year.  I love how much vocab students use while doing these.

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About this point in the unit, I was not in my morning class a few days in a row due to state testing with my 6th graders.  I was looking for self-checking practice for students on exponent problems.  The challenge for me was we hadn’t talked about the zero power yet or negative exponents.  Most everything I was finding online included those types of problems.  Here’s what I came up with.

I modified Kate Nowak’s row game to work for where my students were at.

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I don’t know if “Two Truths and a Lie” is the correct name for the next worksheet I created, but I couldn’t think of another name and was running out of time, so I went with it.  Basically, students were to simplify 3 different problems.  Two of the problems would have the same answer (the two truths) and the other problem had a different answer (the lie).

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I also had a sheet of Yohaku puzzles ready which I LOVED, but I didn’t end up using it then.  I did, however, use it later in a few of my classes.  I love that there are so many different solutions to these puzzles.  I definitely want to look at the other puzzles on that site for future use.

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When I was finally back with all classes after state testing, we reviewed using this Desmos activity I created.

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absolutely LOVE this Desmos activity from Mathy Cathy for an introduction to zero and negative exponents.

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We ended the unit with some more practice combining all different types of problems.


Here is the link to download the worksheets from this unit.

Pythagorean Theorem and Rational/Irrational Numbers

It’s been one of those roller coaster weeks.

I finished my Master’s presentation last weekend (yay!), and a couple people have asked me if I feel like a “Master” now.  I have confidently responded, “Yes, I am definitely a much better teacher now than I was two years ago, and my Master’s program has played a huge role in that.”

I went into the week excited to be a teacher and not a teacher going to grad school for the first time in two years, but I got a dose of humble pie on Monday when the majority of my lessons were flops.  The week has been a series of ups and downs since then.  So it feels weird to write this post, which is a rough skeleton outline of a unit I taught several weeks ago that I felt went pretty well, after a week like this, which felt like a major flop teaching wise.


This was my first time truly teaching the Pythagorean Theorem rather than just reviewing it with students.  I’ve really been working this year to find ways to get my students to notice and discover things in math rather than me telling them stuff.  I’ve been surprised that often times a small change I make to a lesson makes a huge impact on the overall lesson.  (I’ve come a long way with my 8th graders.  6th grade is a whole other story.  That’s my project this summer.)

I started this unit off having students notice and wonder using the following image from this Desmos graph.

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I wasn’t quite sure where the lesson would go after this.  I had notes ready to go, but before I got to that I put an example where students needed to find the length of the hypotenuse up on the board.  I was excited to see students drawing the squares to find the hypotenuse.  Even though I was the one to show them the picture above,  I don’t know if I would have thought to do a problem problem using that visual until our discussion in class and we started doing the example together.  I decided to forgo the notes that day and continue with more examples using their own way of thinking about these problems before I formally introduced the Pythagorean Theorem.

By the end of that first day, students’ work looked something like this.

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I can’t remember if I gave them a problem where they had to find the length of a leg the first day or the second day, but I’m pretty sure it was before I formally introduced the Pythagorean Theorem.


By the end of the first day some students got it.  Others felt completely lost, but that was a great opportunity to have the conversation about how if students were confused that was a good thing.  I tell my students it means they’re paying attention and are engaged in what’s going on enough to be confused.  I tell them to stick with it and don’t give up.  I tell them to trust me.  I’ll get them where they need to be.  It was only the first day of the unit.

And guess what?  Later that week, those that were confused that first day, got it, and I reminded them of how confused they felt the first day and that conversation.  That I told them to trust me and stick with it and that they’d get it.  And they did.


One day when reviewing the Pythagorean Theorem in one of my classes, I asked a student why it worked.  I wish I would have recorded his response.  I thought it was pretty perfect!  “Well, if you find the area of the square on that leg and the area of the square on the other leg and add them together it equals the area of the square on the hypotenuse.  Then to find the length of the side you take the square root.”

I made this Desmos activity for some in class practice later that week.

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I also used this unit to talk about rational vs. irrational numbers.  It wasn’t quite where I planned to introduce it, but my units got switched around a bit because of state testing.

We spent a day or so on rational and irrational numbers.  I expected to find a Desmos card sort on this, but couldn’t so I came up with this one.  Shortly after I created that one, I also saw that Joel Bezaire also created one.  You can find his here.

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The last big concept in this unit was finding the distance between two points using the Pythagorean Theorem.  I started that day by reviewing the Pythagorean Theorem.  Then I posed this question to students.

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It was fun to see my students excited that they were able to figure this out on their own.  To me it seems like such a small difference from the types of problems we had been doing, but to my middle schoolers, this is an entirely different problem at first glance.  It’s fun to see many students who at the start of the year would shut down when any new type of problem was put in front of them now trying different things to attack a new problem.

Then I gave students two ordered pairs and asked them to find the distance between the two points.  As one group worked on this problem, one person started by graphing the points and another started by finding the difference between the y-values and the x-values like they had done earlier in the year to find slope.  Their conversation was another one I wish I had recorded.  As they compared their strategies I overheard, “No, it’s the same thing.  When you subtract the x‘s, it gives you the length of this leg, and when you subtract the y‘s, it gives you the length of this one.”


What I really liked about this unit was there was very little direct instruction -a little bit when I formally introduced the Pythagorean Theorem and a little bit when students took notes on rational and irrational numbers.  Other than that students were in groups working on problems the majority of the time.

Student Marbleslides

Last summer at Twitter Math Camp, someone mentioned that they have their students to to teacher.desmos.com to create activities.  Genius.  Pure genius I tell you.

This is what my students came up with.

Next year, I hope to be more intentional about how I use this with students because this year it just sort of happened without any sort of plan whatsoever.  What happened was awesome.  With a little more planning, maybe it could have been even better.  (Those were my thoughts when I started this post.  As I wrote it, I wondered if this ended up being so awesome because students didn’t feel restricted by the guidelines I gave them.  There were no rules.  They could do whatever they wanted.  If I had planned, would my planning have narrowed students’ thinking too much, stopping their creativity?)

The idea came out of desperation more than anything.  I had two 7th graders finish all their assignments super early.  My thoughts were something along the lines of, “What?!  You’re finished?  Already?  With how much time left of class?!?  And you finished the Marbleslides activity from yesterday?  Umm…I guess go to teacher.desmos.com.  Yeah.  Good idea.  Do that!”

I was amazed by what they came up with.  The first couple were basic -what I expected to see.  Then I overheard one ask the other, “How do you make the line stop like they did in the other one?”  The other girl responded, “Oh, I think they used those curly bracket things…” and in a couple of seconds they figured out how to restrict the domain -they didn’t know it was called that though as we had never talked about it.

In what seemed like no time at all, they came up with something like this.

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After the test that week, they asked if they could work on it more.  Their excitement over it got me thinking, “What if I had the entire class do this?”  “What if I gave those girls more time to work on this?  What would they come up with?”

I had to find out.  We ended up spending 2 days where most all of my students worked on creating Marbleslides.  Part of me felt guilty for “wasting” 2 days on this, but as I walked around, I was in awe of the conversations students were having and the questions they were asking each other.  I didn’t feel that this was really “wasting” 2 days and wished I had done this before the test instead of after.

The first day, I let students go with minimal direction other than to create their own Marbleslides.  If a student raised their hand, my response was typically, “I’ll listen to your question, but I can’t promise I’ll answer it yet.  I want you to work to figure it out.”  When students asked how to “cut off the lines”.  I directed them back to the Marbleslide activity they had done a few days prior to look at those graphs to try to figure it out, and they did.

When I wanted to push students’ creativity a bit, I pulled up an example from one of the girls who had been working on it for a few days.  They had figured out how to restrict the domain, so naturally all students wanted to know how to do that.  Students really took off after that!

The two girls who were the first to start, ended the day figuring out how to make the marbles go in two different directions!  I don’t know that I ever would have come up with that on my own.  I told them their homework assignment was to figure out how to make the marbles shoot back up.*

I was pretty much giddy going through what students had made after the first day, and it only got better after that!  I can’t count the number of times I’ve clicked “launch” on students’ work.

Some students created Marbleslides like they had done in the Desmos activity, where the person playing would need to change the graph to be successful.  However, as students’ graphs became more complex, more students just played around with creating the graphs and leaving them so they would see “Success!” when they clicked launch.  I loved seeing students come up with an idea and figure out how to make it happen.

I also love what Sean does here.  What are other ways you use Marbleslides with students?

Here is the link again to their creations.  I’m just so darn proud of them!

Below I’ve commented on a few of the Marbleslides my students came up with.


This is one from a student who isn’t always confident in what he is doing.  Partway through the second day he goes, “I’m the master at this!”  He had a star WAY down the line on the bottom right and was timing to see how long it would take to see “Success!”  He gave me thoughts for other ways to use Marbleslides.

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This student also intentionally put a star way off to the right so the marbles barely make it.  Again, she’s not always the most confident.  It was fun watching her teach other students how to do things.

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This student had fun getting the orange line just right so the marbles would bounce off the end.

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*Those two girls did their homework.

One of the other math teachers I teach with is the dad of one of the girls.  He showed her how to make a parabola, and the things she came up with after that still amaze me.

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Her dad helped with the orange parabola, and she came up with the rest.

The next day she showed the other girl how to make parabolas.  The other girl was working on this one.  You can’t really see the line on the graph, but it’s the 3rd equation.  She figured out that she needed that little line there because without it, the marbles wouldn’t go to the right when they fell through the two parabolas there.

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Estimation 180 + Desmos

Last year I used Estimation 180 almost weekly in my middle school classes.  Students had access to this file on their iPads and filled it in each week.  This worked ok, but I wanted to find another way of doing this that students publicly committed to an answer.  I think I’ve seen other teachers who have their students use Post-it notes and put their answers on the board, but this just wasn’t something I could envision working in my classroom on a regular basis.  For one, I covet my Post-it notes way too much to have students use them regularly for this.  😉

I missed doing these activities with students and knew my students could use practice with their estimation skills.  After becoming more familiar with Desmos activity builder this summer, I thought that seemed like a much more realistic option for my classroom than something like Post-its.

I’m sure I’m not the first person to combine Estimation 180 and Desmos.  When I was looking for what else was out there, I struggled to find something to steal from someone else.  I saw this tweet from Andrew Stadel, which is awesome.  However, I was looking for something quick I could use as a warm-up activity.  My goal was to combine Desmos with Estimation 180 into an activity that could be done in 5-10 minutes with students.  I wanted to be able to put the class code up for students as they walked in the room and let them go so that I could take care of attendance, passing back papers, etc.

This is what I came up with and used on 3 consecutive days in one of my classes this week.

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Overall, I liked how this went compared to how I did this last year, and I realized how much my students really need practice with this!  I think I will continue to use this structure, but I know this could be made better.  What would you do to improve this?

 

Update:  Since the original post, I’ve done a few more of these with students.  I’ll add the links to all the activities I’ve done below.

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Desmos Multiplying Integers Investigation

While looking for a way to introduce multiplying and dividing integers to my students, I found this Desmos activity.  I really liked the progression of the activity.  I liked how the activity asks students to notice things, emphasizes patterns, and has students work to figure out these patterns and rules on their own, rather than telling them these things.  These are all things I am trying to do more of this year.  However, I wanted something for multiplication rather than addition and subtraction.

I created this activity by modifying the above activity.  Overall I was happy with how things went.  I would love to hear any feedback on how to improve it or advice/tips on how facilitate these types of activities.  This was one of the first times I’ve used the Activity Builder in Desmos, and I found that I’ve got some learning to do on how to best implement things like this in my classroom.  How often do you pause and have large group discussions?  I like that students can work at their own pace and struggle to know if/when to stop for discussion as students are at different places within the activity.

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(Note that I’ve since changed the numbers in the above slide to be consistent with the numbers in later screens to try to emphasize the pattern better.)

I was happy to see many groups of students applying the patterns they were noticing throughout the activity and to see them figure out the “rules” on their own.

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Not all groups had answers like these.  There were some groups that missed the mark on parts of the activity.   I think if I had been better at setting things up for students and reminding them of certain things along the way, those groups would have done better.  However, I also wanted to see what these students would do on their own with this. This group of students looks to me for answers quite often, and they start to get uncomfortable when I don’t rescue the class by answering my own questions.