One of the many changes we’re making to our curriculum is thinking about how to represent negative numbers. We’ve used CPM‘s Algebra Tiles a lot, but this is the first year that we’ll really explore negative tiles, but also the idea of opposite.
Side note: last time we taught this unit, we used the Interactive Math Program’s hot and cold cubes (hot cubes cause an increase, cold cubes cause a decrease). Which I think was a neat idea, except that CPM’s negative tiles are red, which confused students when we talked about hot cubes causing an increase. This was not helped by a school-wide evacuation in the middle of one of our lessons. We had planned a summative project entitled “Mystery Soup” (how many hot and cold cubes are there? Maybe?) but with all the confusion and our eventual movement away from hot and cold cubes, we all seem to have forgotten what “Mystery Soup” refers to.
At any rate, watching the kiddos think about and represent negatives and opposites has been interesting. This group thought of different ways to show an expression with negatives using tiles. Any time we can get kiddos to talk together, but show their own way of thinking is pretty cool:
Curriculum partner and I sensed that 10th graders and students who had seen more simplifying with Algebra Tiles were getting restless, so we split the kiddos into homogenous groupings. We always try to frame this as letting students challenge themselves with students who need similar challenges.
FASCINATING to watch some of our newer students who frequently hide in the shadows start to step it up (and also to see 10th graders using tiles and expressions in a more meaningful way).
Photo: “We don’t speak any English!” said one newbie (in Spanish). But that didn’t stop them from a) using the tiles and b) saying the names of the tiles in English.
Spent about 45 minutes after school with the Littlest Advisee, revising a quiz. It’s a slow process that (currently) involves me reviewing the problems they missed and then them showing me they can do the problem (with help). If they can do the problem, I’ll give them half credit (up from 0, in this case). If they can do a different version of the same problem, on a different day, I’ll bump their score up as if they had just taken the test.
Spent another few minutes helping one of last year’s kiddos with his homework. Compound interest. What is that even? #PleaseHelpCantMath
Bowtie Tuesday. Because yes:
I keep forgetting (or just denying) that Afternoon Me is the Worst Me (as the cool kids say).
We did a reading guide, which went slowly in some classes, just right in some classes/groups, and was a struggle in others. Now wishing I had been harsher and a bit more vocal with the participation quiz aspect.
Student work (from the afternoon, but still some solid work)
At any rate, I liked the opening. We showed them a bunch of windows and asked them how many there were. Almost every kiddo was talking or writing:
Teacher confession: after 1 class, a colleague pointed out that there were different numbers of small windows in each cluster, so my initial calculation of 900 was far greater than what many students calculated as about 768 windows.
Also, we cleaned almost all of the papers (except notes) out of the math section of our binders. Maybe this is the organized year. (Dinna hold yer breath.)
The last time we taught this course, Curriculum Partner and I realized that there was power in making the kiddos explain problems to each other. So we gave them the steps to different problems, have them solve them and have them explain to each other. Quite a bit of English spoken and kiddos mostly seem excited to be talking to each other.
We also had them do an explanation quiz where they draw figures based off of Figure X and vice versa. The kiddos work in groups, complete a problem, then call the teacher. I quiz a kiddo at random. If the kiddo can explain correctly, they move on. If not, they get a chance to revise and retry. First explanation quiz of the year, so a bit rough, but a good start.
Photo: Kiddos explain parts of Figure X to each other. I’m not sure where the sandwich thingy came from.
So, we’ve been making the kiddos draw patterns for a bit. Last time we taught this course, we decided we wanted to make the kiddos create their own patterns. And we wanted to do it with stations. Fond memories of this lesson (though in hindsight, many of them went the “Figure One has 1 square, Figure 2 has 2 squares” route. While it does help them make the connection, it’s super boring. Ya heard that, kiddos? Booooring).
Photo: One group knocking it out of the park. You can’t see it, but Black Fingernails is basically teaching 2 total newcomers how to speak English and how to make patterns at the same time.
Context: The Mathematics Twitter Blog-o-Sphere – a group of mathematics teachers who share their practice on the internet – is dedicating the month of August to writing a blog aday. It’s spearheaded by DruinOK. If you’re looking for ideas (and who isn’t?), prompts are here.
The beginning of the year is always a new start, but it’s a big start. Bigger than I remember at the end of the year. While some of our kiddos from last year (especially the ones who arrived at the tail end) are showing tremendous growth in English and leadership, going through all of our structures, which will soon be familiar enough, always takes longer than I expect.
Today, Curriculum Partner and I introduced reading guides. The reading guide is a structure that we use a lot, but for many of our kiddos who have never seen it (or saw it briefly without perhaps fully internalizing it), this is a big step. The kiddos are supposed to take turns reading sentences and then work on related mathematics problems together. Today’s reading guide focused on patterns and extending them.
Photo: Typical work sample from today. What do you notice? What do you wonder?
We did our first community circle in advisory. Circles look a little different this year as a result of a training I went to this summer. Kiddos actually go around in a circle, which makes when they’re speaking easier to predict. We also talked a lot more about norms, so kiddos were a bit more respectful than usual.
Photo #2: Things that make kiddos feel safe and successful. What do you notice? What do you wonder?
Context: The Mathematics Twitter Blog-o-Sphere – a group of mathematics teachers who share their practice on the internet – is dedicating the month of August to writing a blog a day. It’s spearheaded by DruinOK. If you’re looking for ideas (and who isn’t?), prompts are here.
If yesterday was the first day of actual content, today was the first day of actual relevant content. (And groupwork absolutely counts as content, it’s just not as much in the content standards. Perhaps “timely” is a better word than “relevant”).
Our first unit uses pile patterns to look at linear relationships (side note: “patterns” is confusing enough for emerging bilinguals, so I’m dropping the “pile” and just saying “patterns”). It’s pretty visual and therefore accessible, which makes it a great starting unit. We also did our first participation quiz today. Kiddos work together on a group task while I monitor and try to highlight group behaviors that help move them forward (like pointing at specific parts of the pattern, working with their group in the middle of the table, leaning in so they can work together, etc). (Similar to Class Dojo, but on paper and thus subject to me getting distracted)
We’re off to a decent start, though I wish I had done some more explicit modeling on how to show patterns. Kiddos seem to be able to find the pattern relatively quickly, but showing their thinking around the pattern is tricky. Counting the number of squares in each part feels helpful.
Photo: Our opening and some patterns. What do you notice? What do you wonder?
Objectives and opening:
I didn’t take photos of my participation quiz notes, but we’re doing it again tomorrow! (So wait until then?)