Feb 12

Using systems of equations to find the optimum room arrangement

I recently read Malyn’s post: Why teach simultaneous equations? The point of her post is more about discovering the purpose for teaching a specific topic and its importance in a student’s life.

After I read her post, the first thing I did was Google simultaneous equations. I had a gut feeling she was talking about what I call systems of equations, and a quick look at a couple of results verified my thought. I left a comment to her about how I use systems of equations to help me map out group numbers in my classes. I actually find many ways throughout the year to use these types of equations to solve things. Perhaps that really magnifies the nerd in me!

For instance, this past week I was rearranging seating assignments in my classroom. I have 8 four-person groups in my room, and I have a class of 29 students. I wanted a mix of three and four people groups. For me, the quickest way to figure this out was to use a system of equations. So I set up the following equations:

x + y = 8

3x +4y = 29

Using this, I was able to see that I could have 3 three person groups and 5 four person groups. Perhaps that was obvious to you without doing the math, but it really helped me! Now I feel that I have a good arrangement of students around the room with as nearly equal number of students per group as possible with the number of lab tables and the number of students in the class.

Most of my other classes are a little bit easier to plan out, for instance my class of 28 students uses seven of the tables groups and leaves one vacant, and my class of 32 students uses all of the available space!

To me, it’s really easy to justify why I teach what I do. (Of course, I teach Earth science, and we all live on Earth, so it should be really easy to explain the importance of my subject!) I find ways to use things I learned in school in ways I never imagined I would use them. Plus, my students have no idea what they want to do or what they will do when they “grow up”. It’s great that I can prepare them with information they may need one day. And as in Malyn’s case, you really never can say how important knowing about simultaneous equations might be one day – or what creative uses you may find for them!


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  1. Denise Krebs

    Janelle, thanks for explaining this. I try to brush upon my math, so I can help students in study hall. It is always good for me to see equations, instead of my just figuring it out and not knowing the equation. This wqs helpful.

    1. Janelle

      I’m glad it was helpful to you, Denise. Malyn suggested I share this in a post, so it’s thanks to her I wrote about it. I find I’m always using math for something that I wouldn’t have expected.

      My sixth grade homeroom kids are often asking me for math help. I’m glad I am good with math because most of my kids are in gifted accelerated 6th grade math, and I have a few in gifted accelerated 7th or 8th grade math! Sometimes I still have to think a few moments to make sure I’m giving them the correct information.

  2. Malyn

    Thanks for the mention Janelle but MORE importantly, thank you for posting so quickly on my suggestion. You’re really such a nerd (and I say that knowing it’ll be taken as a compliment). 🙂

    Funny how I never thought to use equations to do groupings. The point with equations are the flexibility afforded by the variables (called pronumerals here, honestly, I think variables make far better sense!). Imagine if you had say 3023 delegates (totally random) at a conference you wanted to split into groups. I think that’s lost to most kids which is a shame….Developers /programmers definitely appreciate them.

    Also, my post wasn’t so much about questioning the relevance of any singular topic but the importance of exercising our critical thinking – just as we expect our students to.

    Moreover, I wanted to apply a new (moral philosophy and ethics) framework I just learned, i.e. that everything we do (or not) is a choice which can be justified via an awareness of the deliberative process – values-based decision-making in action. Using equations to help you with groupings is a choice you made because you value the mental challenge. Respecting the fact that others go through some deliberative process themselves hopefully help us respect their individuality, if not the validity of their choices. Sounds deep but really when we reflect on our practice, that’s what we do – it’s extending understanding to others that’s more challenging.


    1. Janelle

      Thanks, Malyn! You’re right; being called a nerd is a huge compliment! 🙂

      Thanks for clarifying the critical thinking exercise. I think this might be a good thing to have students to work through after doing or not doing an assignment. Of course, with 11-year-olds, they often really don’t know why they have done something – except that it was the first thing to pop into their mind!

  3. Malyn

    You hit the nail on the head there. In one of our PD days, a clinical psychologist mentioned that synaptic pruning starts at about the age of 10. So kids (and adults) have to work harder to keep them going. As teachers, we must give kids opportunities to exercise their mental muscles.

    Even when we get them to do critical thinking on curricular content, we must not assume they can abstract and make generalizations and apply such skills into other areas of their lives. It’s something we have to facilitate.

    I think that you’re in a perfect position to adapt the ‘scientific method’ into other areas of their lives. This is not too far off from the values-based decision making I was talking about. For example, ask them what their parents give them for breakfast and carry on; there’s still a bit of science there but the point is to use the scientific method (which ever way you’ve taught it) on something other than what you’re currently teaching. I just hope they don’t carry out dangerous experiments to test out hypotheses such as “what if I only eat junk every morning or skip breakfast?”

    It’s kind of weird how this conversation has gone but I’m glad it’s still going.

    btw, if you do act on this suggestion, please, please, please blog about it.


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