It’s nice to be back in a unit that we’ve taught many times before (this is, I think, the only unit we teach every year).
A stray Google comment by Curriculum Partner on 2 year’s ago lesson plan reminds us that our original reading guide was somewhat clunky. We go through and revise the questions to focus on one workable problem each.
Kiddos are still stymied by the idea of getting X alone (as we call isolating the variable) and most of them refer to it as “making the equation easier”. Which, true, but still confusing.
Another reading guide today to start thinking about issues and who supports what (with a little bit of mathematics to justify) and how we can convince voters who typically don’t vote, to vote. Lots of tricky language here. But a good exercise in reading and differentation (we straight up printed a news article for our kiddos who know more English to read).
Photo: Reading guide on who supports which issues and by how much. I don’t claim, at all, to be a teacher of history here.
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:
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.
Every few months, I meet with other beginning math and science teachers to discuss teaching and what it looks like for us (though the Knowles Science Teaching Fellowship). Recently, this has meant collecting data on our classrooms, presenting it to two other fellows, then discussing it.
The lesson I discussed was an exploration of the Pythagorean Theorem. Students read a reading guide and used Pythagorean Tangrams to see if the two smaller area squares added up to the bigger area square. (photos below)
Part of our assignment was to think about the Standards for Mathematical Practices, which, admittedly, I didn’t.
A couple of thoughts:
- Students sometimes got stuck when trying to put together the two smaller squares to make the big square and I’d have to show them a hint or first step.This felt useful in terms of keeping the kiddos moving and not letting them get stuck on anything that was probably not hugely important (though if it wasn’t hugely important…) In general, I think I need to try and push students to struggle with math without giving up before asking for help. It feels like such a fine line between getting them engaged and than letting them be independent.
- We also established that the students may not have understood the goal of the activity. Do they fully understand what it means when they make the two smaller squares equal the big square? Do they think that putting together the two smaller squares means that this will work for all squares?
- It’s interesting to see how students explain and justify. One student says “I don’t know how to explain” which is frustrating because they probably could explain, but at least shows that they know they need to explain. It’s also interesting to see how students explain something tricky like “why do we need to write the small 2.” (This maybe feels like a “guess what the teacher is thinking” question)
- In thinking about standards for mathematical practices, I go back and forth about which ones are “most important” (they’re all important, which makes it difficult for me to try and focus). So I might try and get our department (four people) to pick a math practice to focus on across courses next year. We’ll see.
Photos 1 and 2: Student A
Photos 3 and 4: Student BPhotos 5 and 6: Student C
As part of our unit project (graphing cost, revenue and profit for different number of items), we spent Thursday learning about cost, revenue and profit. This is much condensed from the last time this project was taught 2 years ago (when it spanned about 3 months).
We learned about cost, revenue and profit through a reading guide. Teachers at our school write reading guides as scaffolded mini-articles where students read a passage together, then complete certain tasks after reading. This plays nicely into our focus on supporting reading this year. Usually, the tasks involve language functions like making predictions and inferences, but since our class is a math class, we usually do math tasks (calculate profit, calculate revenue, etc).
Photo: “We are working. Go (back) to your group.”
Reading guides can be tricky. Students are supposed to read and stay with their groups. One of my classes is particularly antsy and there were students who were constantly getting up and asking friends at other tables how to solve problems. While I admire their commitment to finishing a task, one of my groupwork goals is for students to learn to work and talk with their group (rather than just their friends).
Intervention #1: I taught groups that were often visited by wanderers how to say “We are working. Go (back) to your group.” (I was slightly flustered and forgot to add the word “back” when I wrote it on the board). I like this phrase. It emphasizes that the group is working. It emphasizes the behavior the wayward student should do. It isn’t quite as prickly as “go away” (which one of the kiddos constantly yells at other students. Sigh). It helps students who are doing the right thing actively redirect their peers in a more positive way. We’ll see if it works.
Intervention #2: During the reading guide, I did a participation quiz, meaning that students earn points based on positive groupwork behaviors (reading in English, working together in the middle of the table, leaning in) and lose points if they leave their group or are not working. With 10 minutes to go (and realizing that many students were wandering), I showed groups the scores they were currently earning (and actually took points away from one group while they talked over me). I then crossed out the scores they were earning and told them they could raise their scores by following the positive group behaviors we had talked about earlier. To my surprise, students stayed in their seats for the rest of the period.
Reading guide on patterns getting bigger. What do you notice? What do you wonder?