Good Things: Volume 9

Volume 1 | Volume 2 | Volume 3 | Volume 4| Volume 5 | Volume 6 | Volume 7|Volume 8

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There have been many more opportunities for my students to “play” with math this year in my classroom.  This has sort of happened by accident as I don’t feel that I have been super intentional about this, but this is definitely an area that I want to be more intentional about -creating more opportunities for all of my students to play with math.  These times when students are playing with math have been some of my absolute favorite times in my classroom this year, and I want to find ways to incorporate this more regularly in my classroom and incorporate it into my curriculum compared to something that is done in spare moments.


My play table continues to be one of my favorite things in my room.  I went to Target numerous times to find the Christmas building blocks and had them out the two weeks prior to Christmas break.

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In the afternoon on the last day before break, we have different activities for students set up in different classrooms (decorating Christmas cookies with our cooks, a Christmas craft, a bean bag tournament, dodgeball, karaoke, a Christmas movie, etc.), and they get to hang out and go to the different activities.  I had  group of students ask if I would open up my room so they could continue working on building with the blocks.  It was fun to see them all work together to create something.

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Here’s their final creation.

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After Christmas I had these hexagon blocks from Target out on the play table.  They are several years old, and I keep waiting for Target to get them in again.  One student came in after lunch the first day they were out, “Oh my gosh!  Where did you get those? I need to add them to my birthday list!”  When I told her they were old, she still wanted to take a picture of them to add to her birthday list.

I also had a student tell me that he got Kanoodle for Christmas after he played it in class.  I love love love that my students are enjoying these mathy toys enough to want them at home!

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Another thing my students have been loving are making flextangles.  I’ve shared the video before, but I’ll share it again.

They’ve continued to ask to make these when they have some spare time.  We just finished up fraction stations, and I had many students ask to make these when they finished.

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I even had one student cut out the little tiny Pattern Guide in the corner of the template and glue that together to make one!

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Balance.  In the past year and a half, I’ve had MUCH better balance in my life.  As much as that should be a good thing, I honestly struggled with it for quite a while.  I’ve been meaning to write a post about this, but here it is in short.  I felt like I wasn’t doing enough as a teacher since I rarely work on the weekends now or take things home with me.  Because my weekends were finally a time for me to recharge personally rather than try to stay afloat as a teacher, I would spend Sunday nights dreading having to go back to work and felt guilty for not looking forward to going back to school.  A couple weeks ago, I had a realization about this, and since then I’ve been able to truly enjoy my time at school AND my time at home.  Again, that’s a post for another day, but it’s been SUCH a good thing for me to have had that realization.

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I had a group of students that were ahead in one of my classes, so last minute I decided I wanted to see if I could try some coding with them.  I’ve seen Ashley, one of the creators of the site CS and Math, post a lot about this on Twitter.  I reached out to her, and she responded so quickly and was super helpful!  I had pretty much no previous experience with Scratch, and it had been years since I’d taken computer science in my undergrad.  In an hour or so, I was able to familiarize myself with Scratch thanks to this post.  My students were able to figure out Scratch on their own thanks to the hyper doc in that post.  Many of my students that tried this absolutely LOVED coding!  This is definitely something I plan on incorporating more of in my classroom.

The following is part of what students create in the introduction hyper doc.

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These next three are things that students created in this lesson.

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We were testing in 7th grade.  I overheard one of my students encouraging the girl sitting next to him to be positive about the test.  From their conversation, I gathered that the girl often says she will do poorly on the test.  He told her she can’t be positive about doing poorly either, since she often says things such as, “I am positive I won’t do well on this.”  His then went on to say because a positive and a negative is still a negative.  I had to smile at this.  I loved that he was encouraging this student, and even incorporated math in his encouragement.  🙂

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Last week I had my students create their own marbleslides.  (See this post and this one.)  This is one of my absolute favorite things I do with my students.  Here are a few of their creations.  Be on the lookout for a post on this in the future with more of their creations.

One student asked, “Why are you being so nice and letting us play games all hour?”  I don’t know if he was implying that I’m usually not nice… 😉  I had some examples from last year up when he asked that, and my response was, “Look at all the math that is involved in this!  I am more than happy to let you play with this all day!”

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Merry Christmas and Happy Holidays, MTBoS

As 2018 comes to a close and I’ve been thinking about everything that’s happened over the past year, it really stood out to me how many awesome MTBoS people I got to see in real life this year and how much of my improvement as a teacher can be attributed to the MTBoS.

It is such a cool experience to meet people in real life that you’re friends with online and to continue online friendships in person, and I have been so blessed to have so many opportunities to meet up with many of you throughout the year.

I’ve also had the opposite happen this year -people I knew in real life first have been introduced to the MTBoS.  It’s been so fun to see people that I’ve known from high school or my undergrad jump into the MTBoS!

Looking at the pictures below, I am blown away.  When I started teaching I never saw myself doing those things, let alone all of them in one year!  I cannot wait to see what the next year has in store.

I hope you all have a restful break and are able to recharge.  Merry Christmas!


TMC in Cleveland!

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(TMC Posts:  One  Two)


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Math on a Stick

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MTBoS in my Classroom

 

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Activities for Before Christmas Break

The week before Christmas break is always crazy, and I tend to have plans A, B, and C ready to go because I never know what to expect.  For the most part, I try to keep things as normal as possible for as long as possible, while at the same time knowing things may not pan out as I hope.  I usually leave the last day before break somewhat open so I have some wiggle room if something else comes up and I would need to push a test to that day or if a student was gone and needs to take a test, etc.

Even on that last day, I usually have several different options ready to go that I could use in case something else would fall through.

Here are a couple of my favorite things to do with students the last day before Christmas break.

1. Sara Van Der Werf’s 5×5 Activity.

I have used this activity for the past 3 years, and it is an absolute favorite.  Read all about it here on Sara’s blog.  It’s not super mathy, but there’s addition involved.  In short, as I call out numbers, students place them in a 5×5 grid with the goal of earning the most points.  You earn points by having the same number in adjacent boxes.  Read all the details in Sara’s post.  I am always amazed at how quiet and into the game students get.  I will intentionally pause extra long sometimes before calling out the next number just to see if students will stay quiet -they do.  🙂

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2.  Flextangles

I stumbled on this last year, and it is a keeper.  I honestly had no idea how this would go over with my 7th grade boys, but they really seemed to enjoy it.  I had students asking if they could work on this in their free time long after the day we did it in class.


I had some extra time with some of my students in a class this week, and on a whim, I decided to try Function Carnival.  I had never used it with students before, but I thought this would be a good group of students to test it out on.  They loved it!

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It was the perfect activity to use a couple days before break because it was fun and engaging for students, and there was still a ton of great math conversations happening amongst my students.

I’ve already used these Desmos activities in a few of my classes, but may pull them out this week again if needed.  (That’s the one downside to teaching students multiple times -I can’t use all my activities the first time I have them, because I will have them again within the next two years and need to save some of my favorites.)

  • Trees and Tents (one and two)
  • Wolves and Sheep
  • Jay Chow creates awesome Desmos Breakout activities.  This is above where my students are at, but if i taught high school, I would definitely consider using this.

I may also pull out several of the different things I’ve put out on my Play Table, or some of the board games I have in my room (Rush Hour and Blokus are some of my students’ favorites).

I also just found out you can play Otrio online!  I have the game, but I honestly hadn’t had a chance to play it until now.

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Game about Squares is another great one!

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I would love to hear your favorite activities to do with middle schoolers in the day or days leading up to Christmas break!

Function Notation Same/Different

I have seen other people use the prompt “What is the same?  What is different?” around Twitter (Check out #samediffmath), but I’d never formally used it in my classroom.  I have asked those questions before on the fly, but I’d never created something to put in front of my students where those questions were the main focus.

As I was driving to school Friday and was thinking about what I was teaching that day, I had this thought to create one for function notation.  Function notation is something that some students struggle with, and it sort of surprises me every year because it is so similar to things they’ve already done.  Here’s what I came up with.

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I printed these out on half sheets of paper and had my students do a Stand and Talk with them.

Here are some of the responses I got for “What is the same?”

  • Both have an answer of 57
  • The last 5 rows are the same.
  • Both replace the x with 4.
  • Both have 3x^2 + 2x + 1

For “What is different?” we talked about how on the right it has f(x) and asks to find f(4), and on the left instead it says “evaluate…for x = 4”

We talked about how so much of the problems are the same, but if I just gave my students the top row, they would know how to do the left one, but would feel completely lost with the right one.

In my second class, I explained how these questions are asking something very, very similar but the notation is different.  I thought of the example of in elementary school if they were given 5 × 3, they would know exactly what to do.  However, if they were given 5 • 3, they wouldn’t, even though it is asking the same thing.  As I was explaining that, I could see some students making the connection to the two problems we were looking at.

I LOVED using these prompts intentionally in my classroom, and I’m looking forward to finding more ways to incorporate this into my classes.

(Here are some of the other things I’ve done with function notation.)

Good Things: Volume 8

Volume 1 | Volume 2 | Volume 3 | Volume 4| Volume 5 | Volume 6 | Volume 7

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Several weeks ago, we got to watch our middle school play.  I love seeing my students excel outside of the classroom.  They did a great job with the play Transyl-Mania!

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I still have students asking if they can work on Desmos Mini Golf Marbleslides months after we did it in class.  It makes my heart happy that they not only remember doing this activity, but enjoy it enough to want to work on it in their spare time in class.

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I overheard some of my 8th grade girls talking about one of their pens (a Flair pen).  The girl said that I inspired her to get the pens because I have them.  It was cute.  I did nothing to “inspire” her other than use them in class.

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I had my students create their own equation puzzles, and they crushed it!  They came up with so many creative puzzles!

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My response to a student’s question was, “We’re all in this together.”  Without missing a beat, a student broke out into High School Musical.

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I used Julie Reulbach’s method to introduce equations to my 6th graders.  This is one of my favorite things I do with them.

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We were going over a few examples of equations in class, and I had several students with their hands raised before I even asked a question.  I pointed this out, and ended by saying that maybe they do know what I’m going to ask.  They then proceeded to go through the example and ask the guiding questions that I would have through the entire problem.

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Not entirely math or school related, but I put my Christmas tree up last weekend.  I know it’s early, but I wasn’t sure what my weekends would look like the next couple weeks, and I LOVE having the tree up and wanted to enjoy it as much as possible.  Christmas ornaments have always been super special in my family.  It started when I was a little girl and every year my aunt would make an ornament each year for everyone and my grandma on the other side would also paint a ceramic ornament each year.  My aunt and my grandma have both passed away, so those ornaments are now extra special.  My mom always gets ornaments to remember special events, whether it’s a trip throughout the year or a big event that happened that year.  I’ve started doing this too.  I smiled when I put up my TMC ornaments

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My mom, cousin, and I have carried on the tradition of making an ornament each year.  I was pretty excited that Target came out with holiday building blocks.  I’ve spent a lot of time this past year playing with different mathy toys with my cousin’s daughters, so I thought this would be the perfect ornament for this year.  I’m happy with how they turned out.

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Another non-math Good Thing, but I saw this planner, and knew I’d found my planner for next year.

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Basketball season has started.  I’m convinced that God made basketball a winter sport because he knew Minnesotans needed it to get through our awful winters.  Basketball is a huge thing in my family since my dad still coaches.  Part of the reason I look forward to it every year is because it means time with family in the gym.  I also love that my middle schoolers ask whenever they have games if I’ll be there doing clock.  I love that it matters to them that I’m there.

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Middle schoolers’ giggles.  I love the sound of innocent middle school giggles.  I’ve got a group of students who have been coming to my room after lunch to play with the stuff on my play table and just hang out in a quieter space than the lunch room.  This week they made up their own HedBanz game.  I loved the sound of their giggles every day in my room.  On Friday, I had a group of boys first hour get the giggles as they were working.  It was a great way to start the day.

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I had an 8th grader come to me before class Friday morning.  She told me she was going to be leaving early and wondered if she could take the test first hour during her study period.  When I brought the test to the teacher, the teacher was unaware that she was leaving and had asked to work on the test early.  That means she took it upon herself to plan ahead and take initiative to get the test taken!!!  I LOVE when I start to see middle schoolers take responsibility.

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I had the warm-up on the board Friday, most of my students were working.  I was getting ready to go prompt one student to get started when he said, “I suppose I should probably do something.”  Again, I love when I start to see students monitor their own behavior!

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Every Friday we do Hats for Hearts and the proceeds go to one of our secretaries who is battling cancer.  Students pay $1 and get a sticker to put on their hat, which tells us as teachers that they are able to wear their hat for the day.  One student had a sticker on his shirt and wasn’t wearing a hat.  I asked if he just gave money to the cause.  He did.  I love the hearts of these kids!

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Our high school play this fall was Clue.  Clue was the game I always played with my grandma when I would go to her house growing up.  We are nearing the 1-year anniversary of her passing away.  Every time I saw the posters for the play up around school, I thought of her.  In my 5 years at my school, the middle schoolers have never gotten to go to the performance of the high school play during the school year.  This year we did, and I don’t think that was a coincidence.  I thought of her throughout the entire performance.

You really do need a play table in your classroom!

When Sara Van Der Werf first wrote about her play table a couple years ago, I loved the idea, but at the same time I was hesitant to do this in my own classroom.  If you haven’t heard of the idea of a play table before, I recommend you go read Sara’s post that I’ve linked above.  In short, Sara has a table in her classroom where she keeps a mathy toy out for students to play with, but her post includes a lot more specifics of how she has this set up.

There were a couple reasons I was hesitant.

1) Time.  Sara mentioned that the main times when students play with the things on the table are during downtime in class, between classes, and before/after school.  We don’t have super long passing times, so I didn’t envision students having time to play between classes.  Because I teach all middle schoolers whose main way of getting to school is the bus, I couldn’t really picture any students playing after school and with breakfast served at school in the morning, I wasn’t sure if mornings would be an option for them either.  I plan things for my students to be doing from the time they walk into my room to the time the bell rings.  I wasn’t sure how this would work into that and couldn’t picture what it would look like with middle schoolers to have them play with this during downtime in class.  This sort of ties into my next hesitation.

2)  Behavior.  With middle schoolers, I wasn’t sure how having a play table would go behavior-wise.  If some students finished their work and started playing during class, would this be a distraction for other?  (Would it be any more of a distraction than some of the other stuff that happens in class?) Would the play table prevent students from getting to work right away at the start of class with whatever task I had on the board for them?  These unknowns were part of the reason it took me a while to set this up in my classroom.

3) Space.  The other reason I didn’t start a play table immediately after reading Sara’s post was space.  I didn’t have a table for this, and I didn’t know where in my room I would put it.


Fast-forward a year.  I now have bigger class sizes than ever before.  I had to get more student desks over the summer to have enough seats for everyone.  Bigger class sizes also means more potential behavior issues, but I added a play table to my classroom this year.

Another teacher had an extra table at the beginning of the year, and I snagged it up.  At the time, I was still on the fence about adding a play table.  Around that time, was Math on a Stick -a math playground at Minnesota’s State Fair headed up by the amazing Christopher Danielson.  I volunteered at Math on a Stick three different times right before school started.  You can read about my experience this summer here.   Watching the awesomeness at Math on a Stick convinced me that I needed a small piece of this in my classroom.


Here are a couple things I’ve noticed/learned so far with the play table.

  • One good thing about waiting a year to start my own play table was it gave me time to build up a collection of mathy toys.  After seeing Sara’s, I started picking up different things when I saw them on sale on Amazon, at garage sales, or at Goodwill.  It’s nice now that I have several, that I’m not in a panic to try to find something new for my students when I’m ready to switch up the toy.
  • I’ve followed Sara’s advice and only have one type of “toy” out at a time.
  • On average, I’m switching what I put out every two weeks.  I’ve noticed that the first week a new toy is out, I have the “regular” students play with it -the ones that always come check it out, regardless of what’s out.  The second week, I see students who may not play with this stuff as much at the play table.  I also see more creativity the second week.
  • Before school and right after lunch are when 95% of the “play” happens, which means only about two classes are using the play table, but I am ok with that.
  • I haves some students who come to my room early on Monday just to see the new toy for the week, and I now have a group of students who will come to my room 15+ minutes early after lunch to play.

Here are the things I’ve put out so far this year.

Hexagons:  Unfortunately, these hexagons are no longer available at Target.  I keep waiting for Target to bring them back.  I was fortunate enough to have a friend give me some of theirs.  This was the very first thing I put out, and I think it took almost a week before a student *finally* became curious enough to start playing with them.  Once one student did, it didn’t take long for several others to start playing too.

As Sara mentioned, one downside to these is that they take more time to break apart.  Like Sara suggests, at least once a day I take apart what students have made so that other students can create.

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Pattern Blocks:  I think I only had these out for a week, and I wish I had kept them out there for two.  They’ll show up again later this year.

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Brain Flakes:  This was one of the toys that got many students hooked on the Play Table.  After putting this out, I started seeing a lot more students playing.

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Hashtag Blocks:  Run! These are currently in my Target’s dollar section for the holidays.  They originally had them for back to school, and I checked Target a lot for them during that time.  There are also Plus Plus Blocks, which are similar, but a lot more expensive.

One downside to these is that they do take a bit more time to break apart than some of the other things I’ve had out.

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Magformers:  These have definitely been the favorite so far this year.  They are also the most expensive, but worth it.  Every once in a while Amazon has them as their Daily Deal.  It was a fun day when students realized these stick to the whiteboards!

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Mosaic Mysteries and Magic Mosaic:  I think the Mosaic Mysteries is a Discovery Toy.  I’m not sure what Magic Mosaic is.  I’ve picked up one of each of these at thrift stores.  At first I wasn’t sure how this would go over because I only have two of the hexagon boards, but I found that students will play with the trapezoid pieces without the board itself.

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I am SO glad I decided to add this to my classroom this year.  It has become one of the highlights of my day to see what my students create.

It’s fun to hear the math that comes up as students are playing.  I often hear students talk about making patterns.  When the hashtag blocks were out I heard one student ask another, “Oh, you’re making a giant pineapple?”  The student replied,  “No, I’m making it to scale with this carrot.”  (We haven’t talked about scale at all this year.)

If you are like I was and have seen things about a play table on Twitter or in the MTBoS community, I can’t encourage you enough to start one of your own!

If you have a play table and have other ideas of things I could put out, please share!

Equations and Inequalities with No Solution or Infinite Solutions

I was looking for something a little bit different than what I had done in the past to introduce equations that have no solution or infinite solutions.  I came across this post from Sarah who blogs at Everybody is a Genius, and it was exactly what I was looking for.  I also liked this because when I had these students as 6th graders, I used scales to introduce them to solving equations, so this wasn’t a new idea for them.

I gave this sheet to students and told them to fill in the boxes to keep the scales balanced, and that for each scale, the number in the box must be the same.  Students have done a few different Open Middle problems this year, so some students struggled with the idea that they could no reuse numbers since they are used to not being able to reuse them for those problems, but they eventually understood what to do.

Equation Scales

As I was walking around, exactly what I hoped would happen, happened.  Students got two number 3 and I heard, “What?  This doesn’t make sense.”  “This is impossible.”

As we went over what students came up with, we discussed how in #1 and #4, we could pick any number we wanted, in #2 and #5 only one number works, and in #3, and #6 no numbers work.  Then we took some notes on this.  In the notes sheet I handed out to students, I included a picture of the scale and we wrote out the equation and showed what was happening to the scale as we did the algebra.

I liked that introducing this topic this way to students gave students a visual to help them understand these types of equations.


The next day we did some practice at the whiteboards.  I always include some problems that have one solution (especially ones where x = 0) because some students want to start saying every single equation either has no solution or infinite solutions, even though I stress that this only happens when the variables are eliminated.

Sarah Carter has created a nice Open Middle style problem to go with this topic.  Here students can use the numbers -4 to 4.

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Last week we worked on solving inequalities with infinite solutions and no solution.  I really liked what I did last year for this, so I did something similar this year.  I started the day by having students solve an equation that had no solution.  Then, I asked students which inequalities would make that true and which would make it false.

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We briefly discussed which would make it true and which would make it false, and that was pretty much the only instruction I gave students that day.  They had little to no trouble transferring the idea of equations with no solutions or infinite solutions to inequalities.

I shared at the end of this post a Desmos card sort I use as well as another Open Middle style problem on this topic.

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Overall, I’m really happy with how students are doing with these types of problems.  I think that introducing this idea using the scales really helped my students to see what was going on.