Admittedly, I’m not backwards planning this summer unit as well as I’d like to. We spend Fridays working on a summative-esque project page. Last week, we used real data to make graphs. This week was supposed to be more of a focus on using linear functions to make predictions, but we ended spending a worthwhile day making a table and then a graph from a situation. (I also wish we’d done something with equations, but that’s for another time).
Photo: Student work. This kiddo was rather stymied because the (correctly scaled) axes made her graph too small to see the change over time. So we worked to redraw the axes (growing by 5 instead of 10).
What do you observe? What do you wonder?
In our abbreviated summer program, we’re going through linear functions. Kiddos are great at tables and pretty good at graphs. So now it’s on to using equations to generate those representations.
I feel like we could probably push more on what the different parts of the equation mean (slope, y-intercept) and I almost wish we were doing more with really big numbers (to make using an equation worth it rather than just counting or multiplying), but it feels important to build intuition around how to use linear functions and equations.
Photo: Student work. What do you observe? wWhat do you wonder?
One thing I’m finding, 3 weeks (to the day) into summer school, is that when in doubt, lean on your routines (I’m fairly certain I read this in Carl Oliver’s blog, to give credit where credit is due). We have about 5 weeks with 50 minute classes, so there is not much time to teach or to plan (let alone condense everything into a cohesive, project-based unit that may or may not sync with the biology class next door).
It’s taken me a while to remember this, and to get back into it.
I do recall that one of the structures that was most successful from our linear functions unit is the multiple representations paper (It says “Different Representations” on the actual paper and that is how the kiddos largely refer to it. Change it? Leave it? The eternal dilemma…)
For some reason, the kiddos love this one. There’s enough to talk about, there are different sections, and (added benefit of teaching summer school to some awesome multilinguals, many of whom I taught some portion of the year to) enough kiddos know something about the things that we’re seeing that most kiddos have some access to the content but still need to practice what goes where in the table or why we don’t just put the y-numbers from the table on the y-axis.
I’m also fairly certain that only our school talks about “Figure X” as I had to stop class and review it every time. It’s sometimes a bit too complicated for my tastes, anyway (but makes a nice stretch point).
Photo: Different Representations Paper
What do you notice? What do you wonder?
Week 3 of Summer School, though I don’t know if the first 3 day week actually counts.
In what is maybe not the most cohesive move, we start a new unit on linear functions and graphing this week (Goodbye area and volume). I largely pull from our linear functions unit from this year which largely pulls on CPM (credit where credit is due).
Photo: Student Work on PatternsEduardo has been in my class for 2 years, which makes me somewhat wonder why he’s in my summer school class, but also thankful that he’s there to help support other kiddos as we go. He catches on to the patterns quick (and also has a helpful habit of saying “Wait, we learned this already”, which gives me some hope that what I teach may stick around for longer than the 65 minutes I usually see kiddos) and is quick to point out that the sentence structures for the opening are the same for this entire week (thanks, Estimation180).
He also carries over some unusual conceptions from the school year (that many other kiddos carry), including how to generalize figures with more squares. Admittedly not the most useful skill and probably not Common Core-approved, but it reminds me that I need to push kiddos to explain what the square represents and ground them in familiar concepts like base and height.
What do you notice? What do you wonder?
While this blog has helped me to reflect on my work, as well as to keep an archive of sorts, I fear that the thing I will remember most about today’s lesson is that a lot of the kiddos summarized the jobs they had to do for the Video Project instead of just writing their names like we wanted them to. Apparently no amount of mental wishing made this happen. English Language Development for the win (when just plain efficiency would have done).
Photo: Picking roles within the group to ensure that people get to do a range of videos explaining how to solve equations with algebra tiles:What do you notice? What do you wonder?
Friday is a short day. I always forget how long it takes to make posters, but how worthwhile it is and how weirdly groupworthy (there’s that word again) it is.
Another short day for the Halloween Dance and some vertical alignment and portfolios planning. We put the kiddos into partners (generally the same partner from yesterday) and had them read an equation, identify slope and y-intercept and then make a graph.
As it’s practice, it still takes a bit of time. I noticed that one of the kiddos was in a mood and needed a bit of alone time. So I had him sit and do a reflection. On his own, he asked how to do the first one and tried to solve problems, which was about as much as he usually does. So I think I’m ok with that decision.
After the surprise challenge of yesterday’s representations and equations, I was looking forward to having the kiddos make posters about linear representations. And it turned out to be a pretty cool day. I ended up taking photos of all the posters (for another learning community that I’m part of) but the one that stuck with me most was the scratch paper that some kiddos used to try and explain their idea to other kiddos. So much good conversation and group work (mostly). And lots of learning/releaning of important concepts.What do you notice? What do you wonder?
Partner task where students use a representation (words, table, graph, pattern) to generate an equation. We pulled this from the curriculum 2 years ago, which was probably pulled from the District curriculum. We also added on the “Next, make the…” new representation, which was probably unnecessary.What do you notice? What do you wonder?
Today was the first day we looked at linear equations as a class. Curriculum partner and I set it up as a station rotation where students looked at an equation and another representation (table, graph or figures) and then had to make additional representations. Didn’t get them quite as far as we wanted (trying to balance taking time at each station versus seeing a variety of equations), but we’ll be looking at linear equations in our third unit, so we have time.
Photo: Multiplication beats Addition
The kiddos had to figure out how many squares were in Figures 25 and 43. Some students still insist on adding the numbers until they get to the 25th or 43rd figure. In a (rare) fortunately-timed teacher move, I watched one student (who was largely absent last year but has turned it around this year) repeatedly add 2 to the number of squares in the 4th figure, aiming to get to the number of squares in the 30th figure. I waited until they got to the 20th calculation and then wrote the multiplication problem on the other side of the paper. “Yeah, I guess we should have used multiplication,” they admitted once they saw the answer.
Side note #1: Curriculum partner likes to talk about how lazy math teachers are. Multiplication is definitely easier than addition.
Side note #2: we’re preparing for assessments for the end of our first unit: group quiz tomorrow (graded on participation with an eye to having students practice for the individual quiz), written reflection on Thursday and individual quiz on Friday. Any guesses as to the average student grade?