Systems of Equations Unit Plan

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During this years MTBoS blogging initiative, I used the share the love prompt to capture some of the things I wanted to use and remember for teaching the quadratics unit. I am going to try to continue doing something similar to keep links and ideas for other units as well. I am really terrible about keeping all the activities I have used in the past or new things I want to try so this way I have an electronic record and I can share idea with other math people:

We are knee deep into a systems of equations unit in one of my Algebra classes. So far we’ve done the Systems of Equations Launch which I wrote about here. Which led into graphing systems. At the bottom of that post I wrote how I would adapt it next year by adding in some lines that never cross or end up being the same. Since I hadn’t done that with the launch, I used that idea for the warm-up the next day.

I projected a Desmos graph with a few different lines and told them that the battleship path was the red line. They were tasked with estimating mine placement for the other 4 lines.

systems

This quickly brought up the “missing” orange line and the inability to lay a mine on the green path. We discussed possible numbers of solutions to a linear system then I had them sketch ideas for a system that could have two solutions.  Afterwards they did some more practice with graphing to find solutions. And ended by having the students create scenarios were you’d care about the intersection and then write up a problem which would fit that story. I collected them. Some will turn into warm ups or lagged review and some will end up  on quizzes or the end of unit assessment.  I’ve been working over the last few years to incorporate student generated problems. They seem to get excited about the possibility and its improved their problem writing because they want me to use theirs. Continue reading “Systems of Equations Unit Plan” →

Pythagorean Theorem and the Distance Formula: Live 3 Act

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I was reading twitter when I found Mr. Orr’s 3 Act Task Corner to Corner task. I had just taught the Pythagorean Theorem the day before and the distance formula was on tap for the day. I had a giant thing of string from Algebra’s battleship task, so I thought….why not recreate the scenario in class.

I taped a piece of string from one corner on the floor to the kitty corner  one on the ceiling.  I have tables and a relatively small class ~15 students so I was able to push tables to the sides for the day. When I greeted the class at the door, I asked them to watch their heads. That got a few chuckles until they saw the giant string. Instead of giggles, I got excited chatter. Many were variations on”What is Ms Micaela up to now?”,  but many students were asking each other math-y questions as well. The bell hadn’t rung, I was still greeting in the hall, and already I overheard the question I wanted.

img_0769 Continue reading “Pythagorean Theorem and the Distance Formula: Live 3 Act” →

Systems of Equations Launch

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After wrapping up our linear functions unit, the students had one day off. When they returned to class on Thursday, each table had been turned into a mini command center. Big sheets of graphing paper were stuck down to the table and an assortment of string, scissors, tape, rulers and three colored dots were at each table.

When students were sorted into teams, they were handed the mission sheet:

Battleship.png

I told them they could only use the supplies on the table and at the end of the activity, I’d need a report on where the mines should be laid in the form of coordinates.  And they were off! (Side note, the original question had more information, basically telling them how to solve, so I just erased it which is way the type is a bit crazy. I’ll type up a nicer version for next time with the additions I add at the end of this post).

After we stopped, I took the coordinates and posted each teams on the board. No groups had the exact same answers. They wanted to know if they “won” but I told them they’d have to wait. Continue reading “Systems of Equations Launch” →

Quadratics: Sharing the Love MTBoS Blogging Initiative

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Explore the MTBoS prompt for the week is to share the love and the resources from other great bloggers. I wanted to do that by collecting some of the blog posts that will help inform the next unit I’ll be teaching (added, bonus, I’ll be able to find them easily when the planning begins in earnest). Algebra 1 starts semester 2 off right with a unit on quadratics. It is usually one of the more challenging ones for my students, but I have grown to really enjoy teaching it both here and in my third year math class which also has a quadratics unit with a bit more depth. Continue reading “Quadratics: Sharing the Love MTBoS Blogging Initiative” →

Soft Skills: MTBoS Blogging Inititative

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Soft Skills. According to the Collins English dictionary these are “desirable qualities for certain forms of employment that do not depend on acquired knowledge: they include common sense, the ability to deal with people, and a positive flexible attitude[1]”  I like this definition. Mostly because I can say I at least have two soft skills…just not the social people one. Reading Sam Shah’s post from the Virtual Conference made me think a lot about the idea of what soft skills, especially regarding connecting with students looks like. I agree with him that we have some amazing people in the MTBoS that do powerful work and really connect with students.

I don’t buy that you have to be good at conversation and sweet emails to be that person. My bet is that Sam and his readers are all much better at connecting that they realize and also, that their brand of student connection might reach students that the more obvious outward teachers don’t. This might be partially a biased opinion. I am not great at social skills. I am awkward around people. I am terrible at talking about feelings. I am not a ‘friend’ to the students in the way many of the teachers at my school seem to be. I am definitely not bubbly.  I don’t understand even 5% of the references students and adults make to things I should probably know. But that doesn’t mean I don’t have a connection with students. My students know that I care about them, or at least that I respect them and have high expectations for them. I wouldn’t hold those if I didn’t care. I tell them this. And often students who are also feel different feel better knowing that they can count on me without going through the exhausting social protocols. Continue reading “Soft Skills: MTBoS Blogging Inititative” →

Student Grouping: My Favorite

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My biggest focus as a teach this year is to support and grow student discourse and empower my students to own the classroom. I have always considered getting students to work together and have great discussions a strength, but I’m using that to my advantage not to be afraid to try out crazy ideas since I already have some tools that work. I’m hoping that by June I’ll have more tools and more confidence to share these tools with others.

One simple idea that I used recently might be my favorite way to small group students. I use MARS Formative Assessment Lessons  in my classes quite often. In the high school tasks, a hallmark of the structure is a card sort where students pair up or sort two types of cards, then add a third set, then a fourth and so on. A recent example had students given a large set of cards to sort function or not. Then using only functions, linear or not. And then finally finding rates of change. Another example has students matching words with equations, then added graphs and then tables. The tasks take care to ensure students are paying attention to detail and have blank cards students need to create to finish sets. The FALs also come with great teacher moves, possible questions/misunderstandings and responses. Continue reading “Student Grouping: My Favorite” →

Adapting for Discourse

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In one of my classes (Bridge to College) there are sets of developed lesson plans that address the standards for the course. Because of agreements with the community colleges in our state, I do have to stick fairly closely to the outline provided. Luckily, the lessons themselves are pretty well thought out and have a huge focus on the practice standards and the idea of more than one right way to solve problems approach that I like to employ in my other classes.

I do, however, take the opportunity to make small additions or adjustments to further the opportunity for student discourse. Continue reading “Adapting for Discourse” →

Bridge to College 4: Collaboration

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Part 4 of a year long series: The first 3 here.

Not a long post today, but its been longer than I’d like between posts. There is a push in Bridge to make sure students have a chance to develop skills that will serve them in life after high school. One of those skills is creating a collaborative peer group to support learning in college or the ability to work on a team.

Students were asked to think back to a successful group they’d been apart so far this year and brainstorm why they though it worked. They shared those out and are in blue on the poster below. They also had to think to when their group struggled or weren’t as successful and what might have been the reason. When we shared those answers, they had to come up with a solution or the opposite positive of the issue. Those are in green on the poster. When they work in groups and are giving self-reflections or if I’m giving feedback we reference the poster. “We compared ideas and strategies at a level 3 today, but probably told instead of helped when someone got stuck. I’d give us a 2 there today.” “I saw you guys justifying your work and providing constructive criticism! Be mindful of where your whole group is pace-wise though.” It was their words and their ideas. Harder to argue about cell phone use when they said it was impeding their learning.  Continue reading “Bridge to College 4: Collaboration” →

Bridge to College Part 3

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This is part 3 in a year long reflection of one specific class period. Part 1 and Part 2 can be found here: All Bridge to College.

Some of my favorite lessons have all been from the MARS Shell Classroom Challenges. The structure is predictable and they are all built to encourage meaningful student to student discourse and yet they are easy to implement and run. I have used them in two ways, to see where students are and begin to develop conceptual understanding near the beginning of a topic or as an end of the unit recap/group work quiz. Part of the students grade in this class comes from their work on mathematical communication both written and verbal. I am also trying to build up the idea of peer support. When my students leave high school, part of their success in higher education might depend on whether or not they ask for help from their professor or their fellow students.

The following work is from the Sorting Equations and Identities Lesson.  When I assign group work, I travel around with a clipboard to take notes. This particular lesson, each group seemed to approach the task differently and there work styles were different. One group really wanted to do a lot of rough draft work and then put together a clean, well explained poster. Others wanted a more informal capture. The groups with the least writing were also struggling more with talking to each other. Some looked at structure of the equations only, some solved to see what happened. Instead of answering questions, I asked groups to explain pieces to each other.

 

Finally, they each individually took a quick assessment. The group that struggled the most at talking to each other also struggled the most on the assessment.  I wanted to check in to see what was the issue. Did they all have a conceptual gap which prevented productive discussion? Nope, just struggled with motivation to talk. I showed them quiz results and asked them to talk to each other for 10 minutes and retake quiz with no additional guidance from me. All the quiz scores went up. Then we had a quick chat about why group work can be valuable and I extracted promises or increased participation in the future.

I want to address the idea of collaboration and learning with the full group in the future. I think the next time we assess I’ll have them all try alone and I won’t even grade/look until the end of the next step. Then talk to each other for 5-10 minutes and then re-assess on a clean quiz with no instruction/input from me. My assumption is that scores will go up. If that hold true, as a group we’ll talk through why that happens and what strategies that implies for future problem solving.

Sticky Whiteboards

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I jumped on board the VNPS (vertical non-permanent surface) bandwagon this year and have loved the result, but I also installed contact paper style sticky white board material on all the tables and that has made a MAJOR impact in student work. Students definitely need time to get up and think together, but they also need a quiet, semi-private place to think, make mistakes and move forward.

The stuff is relatively cheap, can easily be peeled off, and seems to clean as easy or easier than my actual white board. But most importantly, the students are so much more willing to try new strategies, make mistakes and then keep trying. Other students are more likely to help each other by adding there own thoughts and even basic practice seems more efficient and productive. As opposed to having actual little boards that have to be taken out, these live on the desks. Markers and erasers are left out on the tables and students can use them whenever. I’ve pushed the idea of rough draft math thinking as a great use of the boards, but we do independent practice and group work there too.  I even caught a student inventing his own problems while waiting for class to begin.

One roll cost be about $6 on Amazon and it was enough for 3 tables (~18x26ish on each one). Its a simple idea, but probably my favorite thing that is different about this year.