# 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.

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”.

# Two of My Favorite First Week Things

In the past, my thoughts on the first week of school have been something along the lines of, “Let’s get through these first few days of class meetings and abnormal schedules, smile a lot despite the chaos and exhaustion, find some mathy thing that you can use to highlight a skill students will need this year, and then once the schedule is as close to normal as it’s going to get, jump into the first unit.”  I’ve ended up doing a random assortment of disconnected activities.  The activities have been “one and done”.  If I wanted to highlight group work, I’d find some activity, use it, and move on to the next thing never returning to the idea of group work.

I cringe at those thoughts now.  I’d never thought of doing a “Unit 0” the first week of school with goals to teach students some of the non-math skills they will need to be successful the rest of the year and then follow up with those skills throughout the week with specific activities.  Thank you #MTBoS!  Sara has several posted first week ideas herehere, and here.  Basically just go read Sara’s entire blog right now.  I’m serious.  She is one of the most intentional teachers I’ve ever met -at least she’s very verbal about sharing her intentions in person and on her blog.

This is what Sara said in this post:  “Here is a quick litmus test for you about the potential quality of the task for your students –If someone were to ask you about the item and you can’t talk a lot about why you selected this item – then it probably should not be in your lesson.  Good teaching has intention.  Student success on the tasks we give requires us to plan.  Don’t just take a problem from the book your school assigned you without asking why you are using it.”

After running Sara’s litmus test idea on the first week activities I’ve done in the past, here are two things I can talk a lot about why I use them.  They are things I’ve done the first day that I come back to later on in the year that I really love.  What I like about these two things is that they are small ways to show my students that I notice them, that I listen to them, and then I follow it up by actually doing something with that information.

Numbers About Me:  My first year teaching I used Sarah’s Numbers About Me.  At first, my main purpose for it at first was get to know my students, and then it morphed into something more.  After collecting them, I typed up students’ responses.  About 6-8 weeks into the the school year, I pulled it out and used the information to write word problems.  The reactions I got from students were priceless!  “Did you know that there’s really a girl in our grade named _________, and she really does have (insert number and noun)?!”   “Did you know that (student) really did (insert some accomplishment that involved a number)?!”  And “So.  I hear there’s a problem about me today.”  It’s so fun listening to them as they try to figure out how I knew all that stuff!  I think part of the reason they get so excited is that I wait long enough to do this so that they’ve forgotten they gave me the information in the first place.  For whatever reason, I usually only do this once.  I’ve thought about using each student’s name in a problem throughout the course of the year, but I just haven’t followed through with it yet.  Maybe this is the year.

# Quote Posters

I start school crazy late this year because my school is in the middle of a building project.  After seeing so many blog posts and Tweets this week from all of you back with students, I’m anxious to get back at it, but I’ve got to wait until September 12th to have a classroom full of students!  In the meantime, I’m enjoying reading all your first week ideas and am taking notes of what I want to steal from you all for when it’s finally time for my first week.

This post is simply my attempt to organize some of the quote posters I’ve made over the years so that they’re in one place -right now they’re in about twelve different folders on my computer.  Because let’s be real, who actually has an organized computer?  If you do, PLEASE teach me your ways because I. certainly. do. not.  It’s a mess.

I have always loved quotes.  Over the years, I have found countless quotes I want to use in my classroom.  A couple years ago I started putting up a quote of the week on the whiteboard below the agenda for the day.

Honestly, I do it more for myself than the students.  I put up a new quote every Friday before I leave for the weekend.  Sometimes I pick one that resonates with me personally -something to encourage me throughout the upcoming week.  Other times I pick out a quote in hopes to encourage a student or a group of students based on something I noticed that week or something I know will be coming up the following week.

Here is the link to most of the quote posters I have made.  I print them off on colored card stock and laminate them.  If I find more in random folders on my computer or make more in the future, I’ll try to remember to add them to that folder, but no guarantees.

# Co-Teaching

Pam Wilson blogged/tweeted about co-teaching last week. I enjoyed reading Tina’s post and am looking forward to going through the rest of the responses Pam’s gotten to get some new ideas. I have some experience with this and thought I would join in on the conversation.

I have co-taught 2 of my first 3 years of teaching, and all of my co-teaching experience has been with the same person. We work really well together, and she’s been one of my go-to people for A LOT of things since I started teaching. I’ll be honest due to my type-A personality, I don’t know that I could co-teach with just anyone, but I also think co-teaching helps me be more flexible in my teaching and helps me go with the flow more in my classroom.

I should mention that I have not had any training on co-teaching. I’ve read a couple articles online, but that’s it.  When the opportunity to co-teach came up, we jumped on it.  As of right now we are the only people co-teaching in my 6-12 building, so we aren’t able to collaborate with others in our district -it’s been a lot of trial and error figuring out what works best for our students and for us as c0-teachers.  So for what it’s worth, here’s been my experience with it.

• Partway through my first year teaching we started co-teaching one section of 6th grade. Going into it, we knew it would be difficult to find time to plan together and that because of that she might end up being more of a glorified para than a co-teacher. However, we saw it as an opportunity to learn from each other and hoped that it would open doors for more of this to happen in our school in the future.
• Last year, we had the opportunity to co-teach a high school algebra class made up of mostly 9th graders intended to give them a stronger foundation in algebra to prepare them for other high school classes. Many of the 30 students in the class had math anxiety/lacked confidence in math/were on IEPs or 504s, etc.
• This year, assuming everything worked out with the schedule, we will be co-teaching one section of 8th grade algebra.

During our co-teaching experience last year, we started to figure out how to better utilize having two teachers in the classroom. It was huge that we both had a small chunk of time immediately after class to debrief and talk about the next day. There’s still a lot of room for improvement. There were many days where she was still sort of a glorified para. Nothing we did was groundbreaking, but we made progress from when we first co-taught 6th grade.

As I’ve been reflecting on my experience while writing this post what has really stood out to me is how beneficial it was to have someone to reflect with after lessons that was in the classroom and knew our students. I was more willing to try things I otherwise might not have knowing I would have someone in the classroom with me, that I would be able to debrief with that same person afterward, and that together we would move forward regardless of how it went.

Ways we were intentional about creating an environment so students saw both teachers as equals in the class:

• We were both included in the start of the year stuff. Both of our contact information was on the syllabus. We did a “get to know your teachers” Kahoot. I know those are small things, but I think they helped set the stage so that students saw that we shared ownership of the class. I didn’t want students to think that because we were in a math classroom it was only my class, and I also wanted all students to see that she, as the special ed teacher, was in the room to help everyone, not just the students she typically works with. (Sidenote: We also had a conversation with students in the first week about why she was in the room as this was new for them. We talked about how we both brought different things to the class and how all students would benefit from having us both there.)
• We bounced back and forth frequently those first few weeks/months. As I mentioned earlier, we work well together and can tag team on the spot pretty well. From the get-go I wanted students to see that we were sharing the role of teaching the class. As the year progressed she didn’t lead the class as often because she was less familiar with the math; however, we knew that going into the year. Because of that, I tried to be intentional about making sure that she had opportunities to go over problems and teach up front, even if it was just a couple of minutes, right away at the start of the year.
• She participated in parent/teacher conferences with me. We do arena style conferences in the gym. She set up a table next to me so that when our students came, we were both there for the conference.

Ways I benefited from co-teaching with a special-ed teacher:

• I learned how to better work with students with learning disabilities and math/test anxiety. Being able to watch her in action with the same group of students who had such a diverse range of needs all year was huge for me. I was able to pick up on some of the things, big and small, she does as she works with students.
• It forced me to think about why I do things a certain way and verbalize these things to her as well as to students. There are times I do things a specific way because a) I see the big picture and know what students will need beyond what we were doing right then or b) I’ve done things a certain way for so long that I don’t think twice about it. Not having the math background that I do, she made me realize that I do this by asking questions either while we were going over stuff together outside of class or with students as questions came up in class. This really forced me to be aware of why I do what I do, and when appropriate, to share this with students.
• Having someone who knew our students and what we were doing in class to bounce ideas off of and collaborate with was awesome! I know I already mentioned that, but I can’t emphasize it enough. Although I did almost all of the planning for the class, we would frequently talk about things or email throughout the day. Often one of us would have the start of an idea and together we could come up with a plan that would work in our class. Sometimes I was hesitant about trying something we came up with, but knowing that I had another person to back me up and to reflect with after the fact made me more willing to try new stuff.
• It enabled me to make adjustments on the spot more frequently. There were numerous times in the middle of a lesson where we would notice things just weren’t working. When we could, we would quick talk about what we could do right then to adjust and then actually do it instead of waiting for the next day. There were absolutely times when we waited until the next day to adjust, but having another person in the room made it easier to adjust on the fly.

Here are some of the ways that we utilized two teachers in the classroom:

• We grouped students based on their responses to an exit/entrance ticket. We usually had 3 groups -those that got it right, those that understood the overall concept but made a minor error, and those that needed some additional support. We had something prepared for each group, usually nothing fancy. One of us would focus on the group that needed some additional support/instruction. The other would get the remaining two groups started, work with the group that made small errors, and then would bounce around wherever needed. On average, we maybe did this 2 times a month; however, it worked well for us and probably could have been used more frequently.
• We split students based on their preferences and each took a group. Some students preferred activities/games while others preferred whiteboards/worksheets. We had both prepared and let students pick how they wanted to practice a skill. We maybe did this 4 times throughout the course of the year.
• If a student had been absent, one of us pulled them aside to get them caught up. We would often do this at the beginning of the class, and sometimes by the time we started the new stuff for the day, the student was ready to participate. This happened at most once a week, so we didn’t do this every time a student was gone. It depended on the individual student and what was missed. We knew our students. We knew who would be able to pick up on what they missed from a friend or by participating in class and who needed to work with one of us before feeling that they could be successful moving forward.
• During work time if there was a group of students that felt they would benefit from going over stuff in a small group, one of us could work with them while the other was free to circulate the room. This happened quite a bit during work time, probably 2-3 times per week.
• We had an extra adult in the room to monitor behavior and hold students accountable for staying on task while the other took care of attendance, passing back papers, etc. I know this may be an obvious and minor thing, but in the overall scheme of the class this was HUGE. Many of our students still needed an extra little push of encouragement with some of the soft skills needed to be a student, and we had AT MOST 45 minutes a day with them. It was so great that one of us could take care of those necessary start-of-class things while the other actively monitored the class and got them started.
• We had another space where students could work. We were able to use her classroom as a space for students to go during tests and work time. If we split into groups and anticipated one activity would be noisier than the other, we would take one group to her room. We used her room as a way minimize distractions by having fewer students in each room and would intentionally separate some students who couldn’t handle being in the same room together.

None of that was anything earth shattering, but if you have questions on any of it, let me know.  Also, if you have any ideas for us as we will hopefully be co-teaching again this year, please share!

# Divisibility Rules Posters

Confession:  This time of the year I spend more time than I should creating things for my classroom.  My first year teaching my walls were pretty bare, and it was sort of depressing.  Since then, I’ve slowly started adding new things to the walls.  I really enjoy making these types of things and don’t have time during the school year to do it.  I tell myself it’s an ok use of time because for 9 months out of the year, I’m in my classroom more than anywhere else.  Totally valid reasoning, right?

Jo Morgan wrote a post on divisibility rules recently, and it was the push I needed to find/create a set of divisibility rule posters for my classroom.   (If you haven’t checked out Jo Morgan’s site, you’re missing out!  Her weekly collection of gems is my favorite.)

I couldn’t find anything that was exactly what I wanted, but I did get enough ideas so that I was able to create my own.

Here is the link to download the pdf and Word Doc of the posters.  You will need the fonts KG Blank Space Sketch, KG Blank Space Solid, KG Wake Me Up, and KG Be Still And Know for the Word Doc.  (I know, I know…kind of an excessive number of fonts.  I’ll admit I have a problem.)

This year I want to be intentional about discussing with students why these divisibility rules work.  There’s a video in Jo Morgan’s post that explains the rules for 3 and 9.  Does anyone have experience explaining these rules to middle schoolers?  Any tips/advice or things you’ve found that work well to help students understand these rules?

Next on my list of things to create was a set of perfect square and perfect cube posters I had seen here earlier this summer, but I was happy to see that Sarah Carter already did.  Thanks, Sarah!