This week, I used a couple of National Council of Teachers of Mathematics resources for my Pre-Algebra classes. Additionally, in 6th grade math, I found a wider divide between kids who totally get what we’re doing and kids who are fairly lost. We’re also ramping into building actual robots in robotics!
My goal this week was to teach the distributive property and simplifying expressions in Pre-Algebra. Last year, my ‘lesson’ on the distributive property was 1 slide in a presentation about simplifying expressions. Needless to say, they never had a really deep understanding of it. This year, I used a packet from an NCTM lesson that walked them through the concept of basic area all the way through factoring out terms like 3a from an expression. A lot of ground to cover but I loved how incremental the packet was. Each step was just a little bit more complex than the previous which helped students make those connections! The best part was that they were CONTINUALLY drawing a visual model of the distributive property at work.
The downside was that students were great at recognizing the new patterns and not super at understanding the vocabulary of what they were doing even though I was trying to reiterate it over and over. In the packet, it described an expression written like 3(x+4) as the area of products, while an expression written as 3x + 12 as an area of sums. I kept saying THIS is what we’re doing when we’re doing the distributive property…we’re DISTRIBUTING this leading number into each part of what we find in the parenthesis (we had visual models for this as well). Each time I would say something like ‘apply the distributive property to the expression 5(x+2), I’d get blank stares.’ They’d start getting it if I said ‘this is written as an area of products, can you write it as an area of sums’ but the distributive property isn’t usually described in that manner.
The students were surprisingly positive about the packet. It was a change of pace from taking some notes via a slide show and then doing practice problems that were posted on our website. More tactile. A few shared they preferred taking notes. Most of the slide shows are problems they attempt before we’ve learned the concept, then fleshing out and figuring out if our thinking was on track or not.
The second part of the week was devoted to learning what like terms were and how to combine them to simplify expressions. Found another NCTM lesson on it. They first had this online game they wanted students to play to get introduced to like terms called Ker-plash or something like that. I was super confused when I was playing the game and that’s knowing exactly what like terms are. Really glad I didn’t attempt it because I imagine it would’ve been a pretty frustrating 20-30 minutes in class with no real positive learning outcomes. Give the game a shot. Link is above or just click on the picture below.
Instead I used their resources for playing a couple card games similar to WAR and MEMORY. In war, students compared terms to see if they were like, and if they were, the person with the higher value won those cards. In memory, they had to find the like terms and then add them together correctly to keep them.
Some said it was fun but they didn’t really learn a ton from it, other said that they were pretty unsure what like terms were when they started but the game helped sort of smooth that out for them. We then started working on simplifying a few expressions and bringing the distributive property back into them.
Saved time by having students take about 2 minutes to cut up their own sheet of cards before we started the activity instead of me spending 30 minutes doing it myself.
Glad I found these lessons and will definitely use them again. I usually find lessons that I feel will take a lot of time and don’t really hit exactly what I’m wanting them to learn. These were spot on though.
6TH GRADE MATH
We’re finishing up our number theory unit in 6th grade math (divisibility, GCF, LCM, primes/composites, and order of operations). I have about 3 students who have a ton of background knowledge in it who I’ve noticed are getting bored and distracting to others. Wasn’t sure how to engage them more in these concepts. When they were writing their math reflection journals, one of the students finished way before everyone else and answered all the reflection questions for order of operations. I showed him one of the Pre-Algebra order of operations problems that involved cube roots and exponents of zero and asked if he could figure it out by explore those two parts he hadn’t learned yet and then giving it a go. He was up to the challenge, as was one of the other students who was in the same boat.
We have a placement test for incoming 6th graders to see if they should be in 6th Grade Math or Pre-Algebra (typically 7th grade). Not the greatest placement test and we’re revising it for next year so more students are in the right place.
I’m working on making a short series of movies showcasing what’s happening in robotics. We are finishing up the ‘Intro To Programming’ aspect of the course and will begin actually working with the robots today. I’m excited about the short movies.