Solving equations is one of the MOST important things that I do with middle school students (other than fractions, of course). I want them to learn the “process” of solving equations with simple, one-step equations. Hopefully when we get to multiple step equations they will have a process to fall back on.
I always start with Hands On Equations. I do not use their “number dice” because I want students to physically move EACH unit from each side. So, I use integer counters instead. I also made my own worksheet to go with it because it matches many online equation solving (virtual manipulative) websites. I link to these sites on my Concept Help Pages and don’t want students to be confused.
This year, I also had students do the Khan Academy’s equation solving intuition problem set before we even started the Hands On Equations. (Here is the explanation video – but none of my students needed it). They understood the concept of the balance AND really got a kick out of the little characters (representing the variable) on the Khan site. That also gave me an idea! Khan called the guys “Pants” or “Old Spice Man” but I decided that WE would call them MONSTERS!
I used the Hands On Equation manipulates (which I called TOYS so they loved them before they even saw them) and my own worksheet (below) which they LOVED because I let them draw MONSTERS on it. Of course we needed to get the MONSTER (x) by itself before it gobbled up the poor little integer circles. Seriously. Gold.
OH MY! How 6th graders LOVE monsters. They have begged and begged to do more equation solving – just so they could draw more monsters!
Day 2 we did not get out the “toys” but did do a pass-it equation solving unit where each student got to make up their own one-step equation (and thus their own monster) and then pass it to a friend for the second step. Really, you would have thought that we were playing a game instead of just writing down and solving equations. Day 3 we will work with on one-step equations involving multiplication and division. I made that one a foldable for their notebooks!I still can’t believe what the right “spin” can do to a lesson with 6th graders! Have I said how much I LOVE 6th graders? My worksheets are shared below. 🙂
Foldable for one step equations with multiplication and division.
I Speak Math 
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I love the Monsters idea! That’s awesome!
I love this! I spent most of the day trying to figure out how to help my 6s with equations! Today we made a flipchart focusing on the basic steps, and they practiced tonight. This will be perfect. I love “just in time” learning:) Yay- thanks!!
Julie, what a great idea! You’re always so creative with ways to practice…. I can’t wait to try the monsters with my students! 🙂
Very cool idea. I like the balance metaphor.
I’ve seen others do something similar, but the “monster” would chase away the integers, and when crossing over to the other side, their signs would change. I was never a fan of that method – it doesn’t translate well into mathematical thinking. But I still like the metaphor. I wonder if there is a good mathematical explanation of how the monster could chase the integers away.
FYI, when your posts show up in my google reader, they’re usually the first ones I read. Thanks!
Nathan,
I’m with you 100%. I really hate math “tricks” like the crossing over to the other side that you mentioned. I like making the variables “monsters” but it must also be mathematically sound. Oh, and thanks for the compliment, so nice! 🙂
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Monster math…another idea I will shamelessly rip off from you. Maybe you should just come teach my classes? Thanks!
Lol! I’m just so glad to help! I’ve “stolen” so many ideas that it feels good to give back. I love our gift community (as Kate calls it). 🙂
Giving this a shot right after MEAPS! Can’t wait to get to real teaching and learning!
Love this–very intuitive, and moves students up the ladder of abstraction nicely. How did you do the monsters with multiplying and dividing–and could you share some examples of that? Or did you just go straight algebra at that point?
Thanks, and awesome work.
Thanks! For 2x = 4 I said if two monsters ate 4 integers, how many integers did each monster eat?
For x/2=3, I said if half a monster can eat 3 people, how many people could a whole monster eat? We drew half a monster.
Sometimes I say people instead of integers to make them laugh. 🙂 and I also bought a monster hat and hands to wear for fun. They loved it!
This is a great idea! I am looking forward to trying it out with my class tomorrow!
Awesome! It’s so fun. I had a student even bring me little monsters that she made with wiggly eyes!
This worked out well! Prior to starting, I gave my students a very brief intro to integers, particularly that opposite integers have a value of zero. Then I introduced the class to the monsters. It was love at first sight! After modeling and some guided instruction, the class worked on a handout. Today, I sat my entire class in the hall and had them pass the equations. It took some time to get into the rhythm, but it worked out great. I love that it provided the students time to discuss the equations and their solutions, particularly if a student arrived at an incorrect answer. Thanks!
I’m so glad your students loved it too! 🙂
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How did you explain adding a positive integer circle for every negative integer circle (like in problem 4 on the first worksheet)? There are all the typical ways of doing so, but I’m wondering how you tied it into the story of monsters eating them. Thanks for the great idea! Hoping my small group will understand this concept better than what they got in class.
I like to use math vocabulary so I would just say, “How can we get rid of a negative one?” And then tell them to use the inverse operation to make a zero pair.
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This is great, and I can imagine using it in my class. Do you know about DragonBox?? (iPad App) I’ve used it with many students and find it quite helpful! really links the “dragons” with the “monsters” and “getting the (variable) alone”
I’d love to download your worksheets and foldable, but I don’t have a Scribd account. Do you have another method for sharing documents?
This is such a great idea!! I will definitely use this at my tutoring session this evening 🙂 Thank you so much for sharing!
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Thank you so much for sharing! I cannot wait to try the Monster Method with my students! I always say we want the variable alone, but I think turning the variable into a monster will help them visualize this concept.