“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.

“One Incorrect” Worksheets

One of the things that’s a constant struggle for me every year is giving students access to answer keys for homework problems.  I want homework to be useful to students.  I want them to be able to check their work to know if they’re doing it right, but I go back on forth with whether I should just give students answers or worked out solutions.  I am also terrible at remembering to upload answer keys to Google Drive for students.  If anyone has a system that works for them, please share!

Last week in two of my classes, I assigned a worksheet like this:

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I was introduced to this type of a worksheet this summer by Sara Van Der Werf.  She had us do the one below at one of her PD sessions this summer.  It was this activity from Don Steward.  All but one of the expressions simplifies to 5n + 3, and you need to find the expression that doesn’t and show that all the others do.  I like it because students know that 7 of the answers will be the expression in the middle.  I don’t have to worry about remembering an answer key for students!

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I created similar versions for evaluating expressions and order of operations with integers that I used last week in two different classes.  It was easier to make 7 problems that all evaluated or simplified to the same answer than I anticipated.  For the problem that doesn’t work, I tried to create a problem that if students make a common error, the expression still equals what’s in the middle.  For example a problem might have -62 and if students say it is 36 the final answer will equal what’s in the center.

So far, I am really liking how well students have been working together on them.  For whatever reason, it seems that students are more engaged and are more willing to go back and find their own mistakes rather than asking me for help right away when they know that 7 of the answers are the same.  I’m not really sure how this is any different than having the answers in the back of the book, but I’ll take it!

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I’m using this one this week for simplifying expressions because I was looking for slightly different types of problems than what I found on Don’s website.

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You can find pdf files for the worksheets here.  I don’t know that the Publisher files would be of any use to anyone since I created the equations in Word and copied them to Publisher and used a random font for the other text, but if you want them let me know.  I can upload those too.

If anyone has created something similar to this or ends up creating similar things, I would love to share resources!

 

Commit and Capture: An Order of Operations Activity

 

This post and my previous post on another order of operations activity may seem sort of random with all of the other start of year blog posts out there, but they are results of me reflecting on what I do in my classroom as I’m trying to be more intentional about the things I put in front of students -more specifically, I’m trying to think big picture.  Being intentional seems to be a reoccurring theme for be this summer.  Today I finally had several pieces come together and feel like I can put into words what I’ve been trying to process in regards to this…but that’s a post for another day.

Commit and Capture is an Open Middle type problem.  Like the last order of operations activity I wrote about, I used it more often my first year teaching than I did the past couple years.  Again, I’m not exactly sure why because it’s great.  It will be making more frequent appearances in my classroom this year.

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Commit and Capture is one of several activities I got when I went to a session by John from Box Cars and One-Eyed Jacks at a conference a few years ago.

To play, I write 3-4 expressions on the board, either from the sheet above or I’ll create my own.  In pairs, students write down the expressions from the board.  I roll a die, usually 10-sided but it could be whatever you want, and call out numbers one at a time.  The goal is to get the greatest answer possible for each expression.  I call out numbers one at a time.  As I’m doing this, students must agree with their partner on where to put the number -they can put the number in any box in any of the expressions.  Once students have a number written down, they cannot erase it.  They also can’t write down all the numbers on the side of their paper and wait until the end to put them in the boxes.

I’ve always had students work in pairs because I love the conversations they have as they decide where to put numbers!  There are so many different things they think about during this activity.  They are looking to get the greatest value for not just one expression, but for several.  They also have to consider their chances with the die and the number of boxes left.  For example, if there are only two boxes left and they’re looking for a high number.  If I roll a 6, do they use that as their high number or take their chances that the final number will be higher?

A heads up if you decide to try this in your classroom, regardless of how many times I tell students they can put the numbers I call out in any of the boxes they want, there’s almost always at least one group that thinks they have to fill in all the boxes in the first expression before moving on to the second expression.  I even do a quick example before hand and model how it works, but no.  There’s still always that one group that misses memo.

I haven’t tried these, but here are a few variations I’ve thought of.

  • Have students try to get the lowest answer rather than the highest.
  • Have students add their answers for each expression to get one number.  (I’ve always kept them separate and had a winner for each expression.)

I couldn’t find the exact handout from the session I went to on their website, but here is a similar one.  I’ve also used Betweeners, Order in the Court, and Balanced Equations all found on that handout.  Balanced Equations is another one of my favorites.  You can find several other handouts here from other conferences they’ve done.

 

Number Muncher: An Order of Operations Game

One of my favorite activities/games I started using my first year teaching is something my students named “Number Muncher”.  It’s an old Discovery Toys game I had from when I was younger.  (Thanks mom for instilling my love of mathy games young!)  I couldn’t remember what it was called but knew it needed a name, so I decided to have my students name it.  I made a list of several of their ideas and had them vote from that list.  Number Muncher it was.  I’ve since learned that it’s actually called Number Jumbler.

I don’t think I fully recognized the value of activity my first year teaching because since then I’ve used it less and less each year, and I don’t know why because it’s SO good.  It’s low floor/high ceiling.  It’s a great way to review order of operations, exponents, properties of multiplication and division, and even fractions.  It allows students of all levels to be successful but also challenges all students.  I’ve mentioned before that I’m working to be more intentional about the tasks I have students do in my classroom, and this one makes the cut.  It will be making a comeback this year!

The goal of the game is to write expressions equal to the middle number using the numbers around the outside.  You don’t have to use all of the numbers, but you can only use the numbers on the outside and can’t use them more than once unless there are duplicates.  (For example, in the picture below, you can only use one 3 but you could use three 6’s.)

Because the numbers are random, some sets of numbers are  much more challenging than others.  I want students to feel success with this game at first, so I try to make sure that the numbers are nicer to work with the first few times we play (i.e. when I write the numbers on the board I change some without students knowing -particularly the middle number.  I think the numbers on that cube are 10, 20, 30, 40, 50, and 60.  I like to keep that one smaller at first.)

I vary how long I give students to work depending on the numbers, but it’s usually around 3-5 minutes.  I usually make it a competition, and whoever comes up with the most correct expressions wins.  Each expression is worth a point, and depending on what math concept I want to encourage students to use, I may give students bonus points for certain expressions.  For example, I may tell them they get 2 points for every expression they come up with using an exponent.

After time is up, we go over several of their answers on the board.  In nearly every one of those conversations, addition and multiplication properties naturally come up as well as whether the parenthesis a student used in an expression were necessary or not and why.

I’ve used this as a warm-up.  Other times I pull it out when we’ve got an extra few minutes at the end of class, or when I’ve got some early finishers.   How else do you think I could use this with students? As I’ve been writing this post, I’ve thought of the following ideas:

  • After students have had individual work time, put them in pairs or groups and give them a few more minutes to work as a group to come up with a collective list.  Then we could have a group winner.
  • Rather than going over students’ solutions on the board as a class, pair students up and have them check each other’s work.  Then maybe as a class we would highlight some of student’s favorite solutions.
  • Play sort of like Scategories and only give points for unique answers.

I know this is similar to some of the other order of operation activities out there, but students love to be the one to roll the purple thing to come up with the numbers.  They think it’s so cool.  I couldn’t find it sold on the Discovery Toy’s website or on Amazon, but I did find a few on eBay if you’re interested in one for your own classroom.  You could also use 7 regular dice and pick one to be the “middle number”.