100 Numbers Task Version 2

Last year I used Sara Van Der Werf’s 100 Numbers task at the start of the year and LOVED it.  Absolutely loved it!  I can see myself using this in the first week of school for the rest of my career.  You can read Sara’s post here on why and how she uses it with her students.  I can almost guarantee your classroom will look exactly like Sara’s in her blog post.

This activity is awesome!  It has numbers so it seems mathy, even though it really isn’t.  It’s low risk and engages all students –every group ends up being a productive group simply by the nature of the task.  This allows us to have a conversation about what group work should look like in class throughout the entire year.  We’re also able to talk about how math is the study of patterns and that as mathematicians we notice patterns, describe patterns, and generalize patterns.  (I made a poster on that idea.  The blog post is here, and here’s Sara’s post on that topic.)

As I’m starting to put together plans for the first week of school, I plan on using this activity again.  The only problem is one of my classes is a group of students I had last year who have already done the activity.  I still want to review what good group work looks like as well as reiterate that math is the study of patterns, so I still want to do this activity with them again.  I thought about using the same sheet and having students count backwards like I had seen Sara do at a PD session one time.   Then I saw someone post on Twitter about creating different expressions for the numbers.  Brilliant!

I came up with this:

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I kept a pattern, but switched it up a bit from the original version.  If you divide the page into 4 quadrants and start in the upper left and move clockwise around, it goes 2-1-1 and then repeats the 2-1-1 in order to keep the total number of expressions in each quadrant the same.  You can sort of see this below.  The yellow is the first 4 numbers, purple is the next 4, green, and then blue.

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I would LOVE feedback on this.  I like it, but I think there’s room for improvement.  Below are some questions I have.

  • Is it too much?  Too busy?  Obviously the expressions take up more space than a single number so there is more on a page.  Is it too overwhelming?  Would I be better off going up to 50? or 75?
  • I had originally planned on using all operations, but when I finished I ended up only using addition and multiplication.  I decided this was ok because students will only have to focus on two operations, but is even 2 too many?  Would it be better to just have one operation?

I won’t have a chance to try this out with students for a few weeks, but if anyone uses it, I would love to hear how it goes.

Here’s the pdf version of what I made.

 

 

 

Quote Posters 2017-2018

In the past 24 hours my excitement for the start of the school year has grown exponentially.  Up until yesterday afternoon, I wasn’t ready for the school year to start and for summer to be over.  I took a couple math courses this summer and finished up my last final yesterday, and as soon as I got home from working on that I was ready to start thinking about the school year.

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I really enjoy creating things for my classroom.  I like that I’m being productive, but it doesn’t feel like work.  Last year I shared some quote posters I had made in this post.  Every year I like to create a few new ones.   Last night when I got home, finding quotes for new posters was one of the first things on my list of things to do for school.

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I thought I’d share what I made in case anyone else wants to use them in their classroom.  Here is the link to download the posters, and again here is the link to last year’s post where you can download the other posters I’ve made.

TMC17

I recently got back from Twitter Math Camp (TMC), and in the words of David Butler, “That was unreasonably awesome.”  Yes.  Yes it was.  I’m having a hard time putting into words what I’m feeling after this conference.  I feel I can’t adequately describe my experiences.  It is so unlike any other conference or PD I’ve attended.

Everyone was there to learn and grow.  Everyone.  As David Butler said, “Everyone is worthy to present.”  Whether you had written a book, a curriculum, were presenting, a veteran teacher, or a newbie.  We were all there to learn and grow from each other.  As Jonathan said in his recap, “Everyone gave a crap.”

Just to forewarn you this post contains a ton of pictures and a ton of links -so I can find everything later! 🙂

Desmos

On Wednesday I was able to spend the day learning from the Desmos staff.  I am looking forward to spending time playing around with some of the new features they shared with us.  Meeting Eli Luberoff, the founder of Desmos, was definitely a highlight for me.

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Morning Session

I attended the Rich Tasks morning session with Cal Armstrong, Peg Cagle, and Bill Thill.  It was sort of a spur of the moment decision to go to their session, but I’m so glad I did.  I have been wanting to implement more rich tasks into my classroom, but was unsure how to go about doing this.

Day One:  We were given the following task.  It is similar to Fawn Nguyen‘s Visual Patterns.  After we complied a list of all of our responses, we paired up with someone who wanted to look into the same thing and start playing with the problem.  Julie and I had a great conversation as we worked through the task.

I’m not sure yet how I would use something like this in my own classroom, but it was a lot of fun to be given so much freedom when working on this activity.

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Day Two: We watched a few videos of teachers from around the world teaching and discussed their teacher moves and the reasoning behind the tasks they were using with their students.  Peg said a couple of things that day that stood out to me.

  • “Focusing on your goals doesn’t please everyone, but we have to keep in mind why we’re doing what we’re doing.” -Peg Cagle
  • “You can’t build on your strengths if you don’t own them and recognize them.” -Peg Cagle

Day Three:  The last day of our time together they focused on how to take every day tasks and make them richer.  They shared with us several prompts that could be used with a worksheet that would result in a richer task and students thinking more deeply about the problems.

  • Which 3 problems would be hardest for you and which 3 would be easiest?  Why?
  • Which 3 problems do you think will be the most challenging to the most students in our class and why?
  • Which 3 problems do you think would be most useful to a student preparing for an assessment on this material and why?
  • Which problems will students make mistakes on and what will those mistakes be?

I LOVE these prompts!  One of the things I love about these prompts is that it will likely slow students down.  They will have to analyze the problems and almost start doing them in their head before they actually start working out the problems on paper.  Peg also shared the following, which gave me something to think about:  We typically put the easier questions at the beginning of an assignment.  Students work on those problems in class with their groups and then have the more challenging problems for homework.  What if we switched the order of the problems so that the students had the easier problems for homework?

Peg also shared this with us to close our time together, “Remember that there is no single right answer about which task to use or how to implement it.  The right answer is whatever best supports your students in making progress towards your identified mathematical learning goal.”

And lastly she shared this, “Good to Great:  Any change in our practice is likely to begin with a drop in productivity.  Expect that things will get worse before they get better.  Give yourself and your students time to re-acclimate.”

As I was thinking about this session, something hit me.  Implementing a new routine in my classroom is sort of like teaching new math concepts.  I wouldn’t just jump in and start teaching solving systems of linear equations by graphing to my students if we hadn’t done anything with graphing lines before.  When it comes to implementing more rich tasks in my classroom, I need to start smaller and build up so that my students can use their experience and skills working with the smaller rich tasks on the bigger ones.  So, my #1TMCthing is to incorporate more rich tasks into my classroom this year.  I plan to start by using some of the prompts given to us on the last day and see where things go from there.

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More Math

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  • I went to Annie Fetter‘s session titled “Sense Making:  Is it at the Core of Your Classrooms?”  (You can download Annie’s slideshow here.)
    • Math is really about relationships, but kids think it’s about numbers.
    • Ask about ideas, not answers.  “Tell me something about problem 7?” instead of “What is the answer to problem 7?” because everyone in the room can tell me something about problem 7, even if they don’t know the answer.
    • Ways to become a better listener:  Ask questions that you don’t know the answer to.
    • Annie was the second person to mention recording your teaching for 10 minute segments by putting your phone in your pocket and recording yourself.
  • I missed Norma Gordon‘s session on Smudged Math, but I plan on going through the resources she shared on the TMC Wiki.
  • I also missed Pam‘s session on asking good questions.  Her presentation is here.
  • Several of the “My Favorites” sessions that were shared were based on blog posts I had read by these people, but it’s always fun to hear them talk about it in person.
  • I loved Pam Wilson‘s Make a Difference Monday

Don’t let anyone tell you that you aren’t a great teacher.  Ever.  And don’t tell yourself that.  Ever.  -Lisa Henry & Sam Shah

People

When I went to TMC last year in Minneapolis, one of the things that stood out to me most was the relationships people at TMC had with each other.  It was SO evident that these people didn’t just see each other one week out of the year and that was it.  These people had formed true friendships with each other.  Because I hadn’t really been super active on Twitter prior to TMC last year, I didn’t really know anyone apart from a few MN teachers.  I remember shyly walking up to Casey on the last day of our morning session and asking if I she wanted me to sign her book.

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Shortly after TMC last year, I wrote this post, which prompted Casey to adopt me as her little sister.  She has been a constant source of encouragement and made me feel like I had something to contribute to the MTBoS (Math Twitter Blogosphere) community.

Over the past year I have participated more in conversations with people on Twitter.  I so wished I had done that prior to TMC last year so that I could meet all of these people who were helping me out so much in person.  So needless to say I could not wait to meet everyone in person at TMC this year.

One night several of us when to The Varsity, which claims to be the world’s largest drive in.  It was one of my highlights of the week.

There were several of us from Minnesota that made the trip to Atlanta!

And a few last pictures.

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Notice/Wonder

Last summer I watched Annie Fetter’s Notice/Wonder video at a training led by Sara Van Der Werf.  I instantly knew this was something that I needed to be using in my classroom, and I was able to use the questions “What do you notice?” and “What do you wonder?” while tutoring over the summer to try it out before the school year.  Right away, I was amazed by how those two questions changed things for me while tutoring, but I was unsure how to implement it into a classroom setting compared to a one-on-one tutoring session.

When I first started using it, I wasn’t sure how to do it.  I wondered if there was a “right” or “wrong” way to do it, so I was more hesitant to use it in my classroom.  As I started using it more, it gradually became a common routine, both formal and informal, in my classroom.  I was curious to see the how I used Notice/Wonder over the course of the year, so I went through my files from the year and pulled out the images I was intentional about using with Notice/Wonder.  As I look back on the images from this past year, I would put most of them into one of the following categories.

  1. Students noticed/wondered about a problem before beginning to work on it.
  2. Students noticed/wondered things about several similar but slightly different images, and then we discussed how these slight differences impacted the math we were talking about.
  3. Students noticed/wondered things about a new concept on connected it to what they already knew.
  4. Students noticed patterns and/or put new concepts into groups.

The first two usually happen more in the middle of a unit, while the last two were typically how I started a unit.

The routine in my classroom for this is that students work individually for a few minutes writing their answers down.  I typically tell them something like, “Write down 7 things you notice and 5 things you wonder.”  Sometimes when they finish, I do a stand and talk (read about them here– scroll down to #4) before going over their responses as a class, other times we go right into a whole class discussion.

I saw this on Twitter a while back, and I like this idea rather than giving students a specific number of things to notice or wonder.

Here are some things I noticed about how I used this over the course of the year.

  • I was surprised by how often students were able to connect the new concepts to what they already know.  This was HUGE for me as a teacher because it helped me to realize I don’t always have to start from ground zero when introducing new concepts.  It also helped my students see how math builds off of itself.
  • When students noticed the differences among what we were talking about and made the connections I wanted them to make, it stuck better than if I would have just told them.
  • It gave me as the teacher a ton of insight into where my students were at with the math.  Some students would comment on the size or color of what was on the board.  Other students would connect it to what they had learned in the past.  The vocab they used when talking about it also gave me clues as to where I needed to go with what we were talking about.

As the year went on I found myself asking “What do you notice?” much more informally in class.  I would use it when I put a problem slightly different than what students had seen before, or if we were working on a problem and students were hesitant to participate.  Asking them what they noticed was a much safer way for them to participate than jumping into the problem right away.

I also found that I asked students what they noticed MUCH more often than “What do you wonder?”

Is every Notice/Wonder I do awesome?  No.  Are there more effective things I could be doing?  Most likely.  But this is where I’m at right now with this.  It’s made a HUGE impact on myself and my students, and I’ve seen growth in myself when it comes to using this in class compared to the start of the year.  After doing Notice/Wonder more often with students, it became easier for me to find new ways to incorporate it into my lessons, and I saw an improvement in the images I used with my students.

**Update:  I had this post written and saved in my drafts before going to another training by Sara Van Der Werf where she talked a lot about Notice/Wonder and was encouraged to have her validate many of the ways that I’ve been using this in my classroom.   I will try to remember to link Sara’s blog post on this training when she posts it.**


Here are some images of how I used Notice/Wonder with my 8th graders.

I used Notice/Wonder the first week of school with Fawn Nguyen’s Noah’s Ark problem to get them to think about the problem before starting.  This idea was completely stolen from Sara, and it was a great way for me to start using this with students.

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This is another example of a time when I had students Notice/Wonder before they actually started solving the problem.  I was especially hoping they would talk about the exponents.

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While grading quizzes, I finally saw where the misconceptions were coming from with some of the mistakes my students were making, so I created a notice/wonder to talk about those and the differences between the following terms.  This ended up being one of my favorites from the year.

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Here are several examples of when I used Notice/Wonder to introduce new concepts.

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I used this one to help students see the differences between the various forms of linear equations.

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Rather than just giving students a new formula like I would have in the past, I used Notice/Wonder.  Students were able to tell me the variables they were familiar with, so the formula didn’t seem completely new to them, and we discussed the variables they hadn’t seen before.

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In our unit on sequences, I used Notice/Wonder a few times in hopes that students would notice patterns and connect the sequence to the formula.

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I felt that I didn’t use Notice/Wonder as well with my 6th graders, but there were a few times throughout the year that it worked well.

I used it at the start of the year to introduce the game Set.

This spring I saw this Tweet.  I’m always encouraged when I see that someone else confirms that something I did in my classroom was a good idea.

After seeing that, I was reminded to use it again to introduce the rules to this Kenken puzzles.

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I used the following image when introducing the idea that there are 180° in a triangle.

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A few days later I put up these images to talk about the interior angles of polygons.

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Twitter: More than Just a Place to Steal Resources

Yesterday I shared some of my favorite Tweets from the 2016-2017 school year.  They were mainly of things I want to remember to use/steal for next school year.  That was why I first got involved on Twitter.  I was looking for great ideas to steal from others, but as I was going through Tweets, I started realizing how much getting involved on Twitter has helped me as a teacher beyond the resources I find to use in my classroom.  I realized that my “Twitter Friends” not only make me a better teacher through the resources they share, but they also encourage me.  They help me see that I’m not the only one that has days where I question what I’m doing.  They validate those feelings and encourage me to keep going.  They remind me that the work we do as teachers is so incredibly important, even when we don’t feel like we’re making a difference.  They also challenge me to think critically about my teaching.  That was an added bonus of getting involved in the #MTBoS that I didn’t know would happen when I was first looking for stuff to steal.

So here are some of those Tweets.



Here are a few Tweets that have made me think about my teaching.


It is also encouraging to see that other teachers have lessons that flop, don’t have great ways to teach concepts, or still don’t fully understand some of the concepts we’re supposed to teach.  More importantly, it’s a great reminder that it’s ok to admit those things and ask for help.


So thanks MTBoS for becoming so much more than just a place to go to steal resources.

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Favorite Tweets of the 2016-2017 School Year

One of the things on my to-do list this summer was to go through my Twitter “likes” and clean it up a bit.  As I was doing this, I was surprised to see that it’s really only been a little over a year since I started using Twitter to find math resources.  It’s now the first place I go when looking for ideas to use in my classroom, and I don’t remember teaching before I found the MTBoS (Math Twitter Blog-o-Sphere).


Here are some of my favorite “likes” from the past year or so.  They are things I liked with the intention of using, or modifying and using, in my classroom but haven’t yet.  So here’s to trying to remember to use some of this for next year.


Here are a few that just made me smile and think “Oh my gosh!  You too?!”

I try to beat the Chick-fil-a system by saving my extra packets of sauce so I can have Chick-fil-a without laving my house.

 


Seeing Dan Meyer say that it’s ok to have times like this made me smile.


Yep.

Weekends and summers.  God had to have created them with teachers in mind.

Happy summer!

Add ‘Em Up

I read about Sara Van Der Werf’s Add ‘Em Up activity on her blog a while back.  I remember reading her blog and seeing the pictures of this awesome activity and thinking, “Ok, this is great, but is it really like this in real life?  Yeah, it works for Sara.  But she’s THE Sara Van Der Werf. Would my classroom really look like this too?!”

Then I heard her talk about it last summer a few times at PD she was running.  I was slightly more convinced that I could pull this off, but I wasn’t fully there yet.  I remembered this activity when I was looking for something other than a worksheet to do with one of my classes, and I decided this would be a good class to test it out on.

This is what I saw in my classroom in nearly all of my groups!

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My classroom really does look like Sara described in her blog when I do this activity with my students.  It has become one of my favorite ways to review concepts with my students.  I love that it’s minimal prep for me.  I create 4 problems, get big sheets of paper, and I’m good to go!  I’ve learned to just keep several big sheets of paper in my classroom so I am prepared at all times to do this with a class.  I also love that my students just naturally start working together while doing this activity.

Sara explains in detail how the activity works in her blog post, but here’s a brief overview of how I’ve done it in my classroom.  I highly recommend that you read through her post if you decide to use this in your classroom.  Re-reading Sara’s post was a good refresher for me.  She does several things I have left out when I do the activity with students.

  • Put students into groups of 4.
  • Give students a big sheet of paper to work the problems on and have them divide it into four sections with a circle in the middle.
  • Each student solves one of the four problems given to the group in their section.  Once all students have an answer, they add up the four answers and that number goes in the middle circle.
  • When students finish, I tell them whether or not the number in the middle is correct.  I love that they don’t know which problem(s) of the four are incorrect, just that something is wrong.  Students automatically start helping each other to find their mistake.  It’s great!

Here is the link to download the activities I created this year.  Please let me know if you find any mistakes in my work.  The following activities can be found in the link above.

6th Grade Activities:

  • Evaluate expressions
  • Solving one step equations with decimals
  • Greatest common factor and least common multiple
  • Solving multi-step equations (includes equations with variables on both sides)
  • Solving multi-step equations using the distributive property

8th Grade Activities:

  • Solving equations review (includes quadratics, absolute value, square root, and equations with no solution/infinite solution -I just had students tell me which problem(s) had no solution or infinite solutions when they gave me the number in the box.)
  • Function notation