Introduction and the Amazing Expanding Expression

Hello #MTBoS!  My name is Sebastian Speer and I teach at a private school in northwest Florida.  I teach accelerated 6th, 7th, and 8th grade math courses.  I have always been interested in teaching and working in education, but I took a circuitous path to getting to math education.

My undergraduate degree is actually in music and I am a classically trained clarinet player.  I realized teaching band was not for me, and I ended up working jobs in a high school and a university after I finished my undergrad.  I have always had a propensity for math, and through those jobs I saw how important the understanding of math was to students’ futures, so I decided to look into becoming a math teacher.  A few years of graduate classes later and here I am in my first year of teaching.  My favorite thing about teaching is the “ah ha” moments when you see a student go from “I totally don’t get this,” to “It all makes sense now.”


Amazing Expanding Expression

I am writing this post, at least partially, for mission one on Explore Math TwitterBlogoSphere, so I am also going to include what I consider to be a “rich task” that I did with my 6th and 7th grade students this year.  I call it the Amazing Expanding Expression.  I use this to work with Order of Operations, so that they can see how extra operations change the value of an expression, as opposed to simply being told they did the order wrong on static expressions on a worksheet.

I begin by writing an expression on the board (the first time we start it’s almost always 4+3.  I don’t know why, but I almost always use 4, 3, and 7 as my examples).  I ask if anyone can evaluate that expression, and then I call on someone.  As long as they give the correct answer, they get to come up and add or change something.  They can put in parentheses, exponents, multiplication, division, addition, or subtraction.  I then ask for any volunteers to solve that expression.

We keep going in turns until the expression just becomes too difficult to deal with.  I then just write a new 2 term expression and we go again.  If someone adds something very strange (divide by 4.736 has come up before), and the other students get stuck, I will usually solve it on the board, and then take my turn in changing or adding something (usually altering it to make it more accessible to more students).

This activity allows students to see how the order of operations affects our answer.  If someone answered 3+4 and added x10 at the end, I will sometimes get the answer of 70 from a student raising their hand.  Another student can correct them by showing how you have to do 4×10 first and you will get 43.

I also like to let them use their calculators on this sometimes, because the people not using calculators often get the correct answers, while those with calculators often get the wrong answer, and this can reinforce my rule of brain first, calculator second.

I look forward to putting more activities and ideas up here and getting feedback.  I am excited to see how this whole MathTwitterBlogoSphere thing can help me become a better teacher.


7 comments on “Introduction and the Amazing Expanding Expression

  1. mrscoxey says:

    Sebastian, I love this idea! I am going to steal it and use it as my opener in a few weeks for our order of operations lesson. Thank you for sharing!

  2. Chris Smith says:

    Hi, thanks for your post. There are a lot of us Maths teachers who also like music- I play in a ceilidh band here in Scotland .

    I love simple lesson ideas and the Amazing Expanding Expression has lots of appeal. It is student driven which is a nice motivator. It involves no real preparation which in the busy-ness of teaching is a massive bonus. It provides discussion points which leads to greater understanding as students articulate their strategies and solutions.

    Hope you have a great year 🙂

  3. I love this idea- I think I will use it with my remediation group of 7th and 8th graders. They certainly struggle with order of operations. I love activities that don’t involve worksheets and yet still seem like they would engage the whole class.

  4. debboden says:

    HI Chris!
    I really like this idea, and plan to use it this week as an Interactive Warm up! I’ve done the Order of Ops problems where you have a problem without any parenthesis then a solution, and the students need to figure out where to put the parenthesis, which is fun, but I think the students will love being able to come up and change the expressions themselves! thanks!

  5. Hi, Chris, my pupils should know the order of operations already but sometimes they actually don’t. So I will keep your Amazing Expanding Expression in mind for some resque activity. Thank you, it is a great idea. francesca

  6. @JustinAion says:

    This is an awesome task! I can see a lot of extensions of this going forward as content get more complicated as well!

    Keep up the good work!

  7. Hello! I love this idea – thanks for sharing.

    I also started as a musician, saxophone performance/music ed major. I spent two years as a middle school band director/general music teacher before switching over to math.

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