Dan Meyer has a collection of blog posts called “If (insert math concept) is the asprin, how do we create the headache.” I felt I was shoving asprin down my Pre-Algebra students throats as they were saying ‘I don’t have a headache but I do now!’ during our lesson on modeling one-step equations. Additionally, in 6th grade math, I feel I’ve got a wider gap between students with a lot of background knowledge on the current concept and students with no background knowledge. It’s challenging. But we had fun auctions in class this week!
One-step equations can be intuitive when working with whole numbers, which makes having students model it visually on a scale difficult; why make an easy thing hard? Well…to try and make the harder things easy later on.
We started out by playing with this Khan Academy module where you’re balancing a scale to figure out the weight of a monster. A few of the reflection comments were as follows:
I had to get the monster on one-side by himself because I wanted to know what HIS weight was, not the weight of him AND 4 other blocks.
When I took 4 blocks off one side, I had to take 4 off the other side or else it wouldn’t stay balanced.
Awesome start! This gave us a great lead into how to visually model solving one-step equations with addition, multiplication, and division. This is where I started losing them.
We were using -1’s to show x – 4 = 8.
How can you have a -1 block?
I told them it was like an anti-gravity pound. Because that makes sense. They were kind of getting the multiplication and division modeling. For division, I had a monster cut in half and the other side of the scale has 12 lbs.
I then gave them a worksheet where they had to model one equation for each operation. They were pushing back quite a bit.
I know that you said that the modeling would help us understand it down the road but I feel just more confused and it isn’t helping.
I get what you’re trying to do but I think you should trust us to allow us to do the work in our head if we know we can and then show our work algebraically if we can’t do it in our head.
I told them I’m saving them from trying to guess and check when their variable is something like 4.28 or 12/13. Perhaps I should’ve shown them a problem that was ‘impossible’ first (3.52x = 4) to help create that headache and then show them the beauty of working to isolate the variable and performing the same operation on both sides to maintain equality and balance.
6TH GRADE MATH
We’re delving into fraction operations with mixed fractions. I’m at a cross. I don’t want to just show students the algorithms for working with mixed numbers, but it’s so hard and time-consuming to help them conceptually see what’s happening. I read through THIS research on teaching fractions and it gave some very helpful tips, but it’s not easy stuff. Reading through some of it made me realize that I don’t have the deepest conceptual understanding…at least in the sense that there were some visual models they provided that I really didn’t get until examining it for quite a while and felt it’d be really confusing for my students.
I really did like some of the models that were provided. Hadn’t ever really thought of using an area model to show multiplication of fractions. Their intersection is the area.
I went through the same struggle earlier in the year when teaching my Pre-Algebra students when doing all operations with positive and negative mixed numbers. It’s not too bad when moding multiplication and division of benchmark fractions, but to conceptually and visually understand -4 2/5 ÷ 7 1/3 isn’t as easy. It’s easy to do the algorithm though and see if you’re answer is reasonable.
This week we did classroom economy stuff for the first time in a while. Bonus money day, pay day, rent day, quite a few folks are saving enough to buy their desks, discussion on tax day in April (flat $500 tax for everyone), opportunities to have ‘deductions’ by donating to the auction, and having class auctions. I use some resources from My Classroom Economy but have modified it a bit so it’s not as time consuming in my class. I want to make a video series for the classroom economy but I think I’ll wait until next year so I can show the steps from the beginning. I guess it’d be more ideal to have it before next year so people would be able to plan it before the year starts. Hm.
I’m making movies in robotics now because it’s fun 🙂 Check out last weeks. Will be filming some more today and experimenting with some new time-lapse techniques.