Surface Area & Volume Scavenger Hunts

How is it that even after several years of teaching 6th grade, I can still go to my old files looking for stuff to teach an upcoming unit and find pretty much nothing?  How?  How does this happen?  I know I taught it in the past, but what did I do?

This happened with a recent unit on surface area and volume, so I created two scavenger activities.  One on surface area and volume and another with word problems on the same stuff.

I’ve been using “loop” activities or “scavenger hunts” for a while.  I especially like them for the times when I need students to practice a specific type of problem.  It’s a great way to disguise a worksheet as an activity.  I love that they are self checking and get students up and moving around.

I have tried a few different ways of creating this type of activity up when making my own.  This is what I’ve found to be most efficient for me when I’m making the activity.  On the top of a sheet of paper I put the first problem.  Then I put the answer to that problem on the bottom of the next sheet.  It’s been a big help for students to make the font as big as possible so that students can see it from a ways away.  Then on the top of that sheet I put the next problem.  The final answer goes on the bottom of the first sheet.   At the end of the activity, I am able to check students’ work by checking the order of their answers.

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Students can start at any card.  They solve the problem and find that answer on another sheet.  This continues until they have done all the problems.  If they do everything correctly, they will end up back where they started.

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Because this is a self checking activity for students, I tend to be “less helpful” to students while they are working on activities like this.

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And an added bonus is that you can hang the problems just as well to the outside of the school as you can the walls of your classroom.  So when it’s beautiful outside and your class has been awesome all week, you take them outside.  🙂

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Here are the links to download the activities.

Update:  I also uploaded an area review worksheet I used to intro this unit.  I’m trying to incorporate more self-check assignments for my students so they know whether or not they are on the right track while working on them.

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I also thought I’d share the documents I used to create the images for these activities.  I recently discovered I can use Google Drawings to create prisms.  It works really well for triangular prisms and rectangular prisms.  It’s not quite as easy to create trapezoidal prisms, but it was the best I found.  Here is the link to the images I made for the surface area and volume scavenger hunt, and here is the link to the images for the word problem scavenger hunt.

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.


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.

“I got it, and I feel amazing!”

As a teacher, one of my favorite experiences is watching a student struggle with a problem, persist, finally get it, and say something like, “I got it, and I feel amazing!”

That’s what I overheard one of my most challenging students say a couple weeks ago in my classroom.  About a math problem.  I’ll be honest, at first I thought maybe she was being sarcastic, but a little bit later she was telling someone else, “I did it, and it feels great!”  She was truly proud of herself and wanted those around her to know what she did, and it. was. awesome.

Here was the task students were working on.

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The back side of the sheet had problems like this.

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As I think back on this day, something stands out to me.  If this student had been in my classroom last year, she probably wouldn’t have had that experience.  Why?  Because I probably wouldn’t have put that worksheet in front of her, or any other student in my class.

This was a worksheet I created my first year teaching.  I had found a worksheet with similar problems in our textbook resources, loved how it went, and wanted more problems like it.  I was excited to have students work on this task, but that excitement quickly turned to frustration when I found that students struggled with these problems much more than the ones on the worksheet from the textbook.  They were frustrated, and I was frustrated.  I was frustrated that things weren’t going as I had planned and that I didn’t know what to do.  I was disappointed what I thought was a great idea, didn’t turn out so great.  So we moved on, and the worksheet found its way to the back of my filing cabinet.

I let that one bad experience with this impact decisions on what activities I would and wouldn’t do in my classroom for several years.

Rather than try to learn from that day and try again, I opted for more familiar activities where I could pretty much predict how the lesson would go.  I avoided activities where I anticipated a similar outcome and chose to use activities that were comfortable for me because I didn’t know if I was prepared to pick up the pieces of a failed lesson.

And then like Princess Mia in Princess Diaries (1:15), I realized how many stupid times a day I use the word I.

What about my students?  How often do I rob students of their own “I got it, and I feel amazing!” experience because I choose not to use a task I knew was good for fear of how the lesson might go simply because it was less familiar and more uncomfortable for me?

Probably more often than I want to know.  So next time I’m planning a “safe” activity, I hope I will remember to stop and think twice about it and think about my students.  Sometimes safe is ok, but sometimes safe doesn’t lead to “I got it, and I feel awesome!” moments for students, and I want more of those moments in my classroom.

Here is the link to download both the pdf and Word versions of the worksheet.

A “One Problem Lesson Plan” that didn’t Go as Planned

I’ve been trying to incorporate more “one problem lesson plans” into my classroom this year.  My first few attempts were pretty successful.  My most recent one didn’t go quite as I had hoped.

I gave students this problem from 1 to 9 Puzzle.


I was disappointed at how many students had forgotten how to multiply fractions already, but at the same time I was happy to see them use their resources to figure it out before asking me how to.

I really didn’t expect this to be as much of a struggle as it was for students.  I don’t know if it was the fractions or what, but was like we were back to the first time I had given students a problem like this.  They didn’t know where to start, so many just sat there.  Ugh!

Shortly after students got in groups, I could tell this was going differently than the other times we did problems like this.  There were times throughout the class period that I thought about giving up, having students stop, and move on to the next lesson, but I decided to use this as an opportunity for myself to learn how to move students forward in situations like this.  I don’t know that this was the best approach to this, but here’s what I did.

  1.  About five minutes into student work time on this problem when many students were “stuck on the escalator”, we talked about how students could get off the escalator.  They gave me a couple ideas of how to do this in the context of this problem.  (Scroll through this post from Sara Van Der Werf to read about the escalator and beagle video she shows her students.  I highly recommend using them in your classroom!)
  2. A little while later when I noticed students getting “stuck on the escalator” again, I brought the class together and asked students to share anything they had figured out so far.  A few students shared fractions they had put in cells a and b.
  3. A while later, I gave students one number in the puzzle – I think it was 7.  I told them I wasn’t sure if this was the only solution to the puzzle, there may be more, but for one of the solutions, this is where the 7 goes.  For whatever reason, this really got students going and excited to work again.
  4. With about 5-10 minutes left in class and as the students energy started to work on the problem started to decrease again, I let students vote on what number they wanted me to give them next.  I think they voted for me to tell them where the 1 went.

By the end of class I think 2 groups out of about 10 had figured out the solution.

The homework for students that night was to spend 10 minutes working on the problem.

When we came back the next day, the majority of my students told me they spent 10 minutes on the problem, and in that time I think one or two students came up with a solution.  We did go over the answer the next day.  My students worked on the problem for an entire class period and most spent additional time on it at home, and around 5 students had a solution, yet I gave the entire class the solution.  Was this there right thing to do?  Probably not.  Should I have had students work on it again that night?  I don’t know.  When a problem like this is more of a struggle for students than I anticipated, I don’t know the right balance between giving them enough time to wrestle with the problem and burning them out/frustrating them too much with one task.

BUT I do know that because I, as the teacher, persisted through the lesson rather than giving up and moving on, I gave myself experience in this situation that I can use in future lessons that don’t go as planned and because of that, I don’t consider the lesson a complete fail.

And in case you’re interested, here is a solution to the problem.

Arithmetic and Geometric Sequences

Arithmetic and geometric sequences was another unit where this was my first time teaching this when I was the one introducing this to students.  There were parts of this unit that I really liked, but there are definitely things I want to improve for next year.  Looking back on the unit, I’m surprised at how many students struggled with arithmetic sequences after having just spent so much time on linear functions.

I started day 1 with this warm-up:


After that we did Notice/Wonder using the following image.  Next time, do I keep the sequences color coded but have them random on the page rather than sorted with the line down the middle?


We then took notes on arithmetic sequences, common differences, geometric sequences, and common ratios.  I used some of Sarah Hagan’s notes found here and made others similar to hers after reading this post.  I also used her half sheet as practice.  The link to my notes is at the bottom of this post.

The warm-up for day 2 was this Which one Doesn’t Belong?


On day 2, we talked about writing the rule for the arithmetic sequences.  We made the connection to common difference and the slope of a line as well as the zero term and the y-intercept.


Sara Van Der Werf’s “Sarified” standards have become my Bible for my state standards.  I LOVE how she has combined the vocab allowed along with the examples given for each benchmark.  However, I’ll admit I was a little bit perplexed by the standards and examples for arithmetic sequences, so if you’re a MN teacher reading this and can clarify for me, please do!

Here’s how the standards define an arithmetic sequence:

f(x) = mx b, where x = 0, 1, 2, 3, …

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But then in this example, unless I’m completely off track here -which could absolutely be the case, -1 would have to be the 1st term based on the answers given.

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So after debating and overthinking, I decided to give students some examples where the first number given was the zero term and others where the first number given was the first term.  I also told them in the directions which term the first number given was.  Was this the best solution?  I don’t know, but it’s what I did.  If you have thoughts on what I could do next time, please share!


Next up was writing rules for geometric sequences.  I didn’t want to just give the formula to students and have them use it, but I couldn’t think of anything I felt was great.  Last minute, I came up with the following and again had students notice and wonder things about it.  Was it the best thing ever?  No, but my students were able to come up with the formula for geometric sequences on their own after looking at this image.


Again, we took notes on geometric sequences and did a couple examples together as a class.


When students graphed the sequences, we also looked at the graph on Desmos and talked about how because we see a small portion of the graph, it may look linear, but when we look at more of the graph we see that it isn’t linear.


When students were working with arithmetic and geometric sequences separately, they did fine, but the wheels started falling off for some students when the sequences were mixed up.  Students mixed up where the zero term went and where the common difference/common ratio went.  I was frustrated that my students were frustrated because, to me, this wasn’t really that much new stuff.  Arithmetic sequences were like linear functions which we had just spent weeks working with.  After school that day I put on my “non-math teacher brain” and tried to look at the formulas from my students’ perspective.

Arithmetic:  f(x) = mx + b  (m = common difference;  b = zero term)

Geometric:  f(x) = ab^x (= zero term;  b = common ratio)

When I wrote the two formulas out like that, I understood why students were frustrated. Although there’s a “b” in both formulas, it doesn’t represent the same thing in both.  In arithmetic sequences it’s the zero term, but in geometric sequences it’s the common ratio.  I could see and understand why they felt the “rules” were changing on them.  Once I understood the confusion, I was able to address this better when working with students.  When students were confused, I pointed out that in both formulas the common ratio/common difference is the number “with the x“.  I don’t know that’s the best way to go about helping students who struggle with that though.

If anyone else has students who struggle with this and have found ways to introduce this so that students don’t get mixed up with this or have ways of explaining this so students understand, please share!

Here is the link to the notes I used in this unit as well as a few worksheets.

Much of the format in the notes is stuff I’ve borrowed or modified from Sarah Hagen.  I don’t do true interactive notebooks (INB).  I upload the notes as a pdf to Google Drive for my students at the start of a unit, and they use an app called Good Reader on their iPads so they can write or type in the notes.  Here is Sarah’s page of INB resources.

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.


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.


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.

Movement: Incorporating Math Concepts into Movement Activities

(I’ve written several other posts on movement:  Post 1 • Post 2 • Post 3)

Movement has been a huge part of my classroom since attending Sara Van Der Werf’s session at a conference my first year teaching.  When I first started being more intentional about incorporating movement into my classroom, I would often have students do 10 jumping jacks, 5 push ups, or skip around the room, etc.  Every once in a while I have an epiphany about a way to incorporate the concepts I’m teaching students into these movement activities and think to myself, “Why did it take me so long to come up with this?!”

Here’s the list of what I’ve found to work best so far, more for my future reference than anything.

  • Perimeter/Area – I have students skip around the perimeter of the room or hop through the area of the room.  (I will also often add clockwise or counterclockwise to the directions.  I’m always shocked at the number of students who don’t know these words!)
  • Exponents – When doing something like jumping jacks, I started giving students an exponent to evaluate, rather than just a number.  This way I can sneak in exponents all year long.  “Do 3 to the second power jumping jacks.”
  • Prime/Composite – I’m all about finding ways to expose students to vocab words all year long.  I sneak these vocab words in by having students “Do a prime number of push-ups.” or “a composite number of sit-ups.”
  • To get back to their desks when we’re doing with a movement activity, I will sometimes have students count the number of “hops” to get to their desk and then do something with that number such as find the prime factorization of the number or we’ll talk about who hopped a prime number of times or whose number is divisible by 3, etc.
  • Ratios – I pick 2 activities and have students do them at a specific ratio.  For example, “Do jumping Jacks and sit-ups at a ratio of 3:2.”  (This was my “Why haven’t you thought of this before now?” moment of this year.  6th grade is ALL about ratios.  Seriously, why did this one take me so long to do?!)

I would love to hear how you incorporate the skills you’re teaching into movement activities in your classroom!