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”.