Clothesline Math: Geometry Style! Vertical and Linear Angle Relationships

I am committed to adding in more number sense practice in all my classes this year. We are regularly doing number talks, brain teasers, estimations, strategy chats, and other quick but routine plugs for flexible thinking. But my main focus this year is going to be adding the clothesline. I have used clothesline math in algebra for the last few years, but mostly only once or twice when we introduce slope. This year I want to use it in all 6 classes both for specific content and as part of other warm ups (estimation, number talks, etc). I saw Chris Shore talk at TMC17 and made it my one thing.  He does a great job explaining the underlying idea/structure and providing resources at the aforementioned link, but I’m going to try to capture student language/moves/misconceptions from specific activities this year. (If you want to read my very first clothesline attempt: Clothesline: Slopes)

Setting the Stage:  The day before, we draw lots of intersecting lines, measured angles, and started making claims about angle relationships yesterday. Most (but not all) students were there and had at least some introduction to the words: vertical angles, linear pairs, traversal, alternate interior, alternative exterior, corresponding, and co-interior.

Style: Quick warm up/ try now when entering class.

How it went: Students were either handed one of the four cards (a, b,c ,d) and told to place on the clothesline with a best guess OR were asked to quickly sketch a number line and place a,b,c,d, on it at the tables. (Each table as a whiteboard stuck in the middle). Board placers joined their tables when they finished:

First placement

A minute after class started, I asked if any of the four students had a mathematical reason why they placed card where they did on the line.

Student B: My angle was smaller, and therefore closer to 180*.

Student C: But we don’t have degrees on it. Do we need a protractor? Continue reading “Clothesline Math: Geometry Style! Vertical and Linear Angle Relationships”


First Day! #Teach180

I am excited to be back in the classroom with actual students today. I’ve spent a lot of time this summer prepping, rethinking routines, and setting up a fun safe place for learning. I am also starting year 4 here (a record, by a long shot for a reformed wanderer.) so I want to really refocus my practice. I’m going to try to do a #teach180 with pictures on twitter and then recap weekly (or so) here. I’m also getting out of my comfort zone a bit and taking on more active roles in state math curriculum and education policy, speaking at the NW math conference, pushing myself and others in a social justice direction and otherwise really making Seattle my professional home.

Anyhow, day 1 was awesome. It was so good to see the students again. We played a Breakout game in 4 of my classes (there was 50% success rate), did some check ins and group chats in advisory, and in 1st period which was shortened due to getting scheduled and reacquainted with school, tried a few leveled warm ups to get in the habit of doing math. Also debuted the math play table and had a few students take advantage when they were hanging around or needed to cool off from another class/event.  We are up and rolling!

TMC17: First Thoughts

TMC17 is come and gone. My friends in the south (and elsewhere?) have already started school again, but TMC happens to land equidistant from the end of our school year and the beginning of the next.  In theory, this should be great and allow me to take full advantage of all the awesome stuff I saw/learned/heard/osmosified and create all these new plans by school start. In reality, life always happens and sometime in September or October (maybe #1TMCthing check in day) I’ll run into my notes and get an excited spark to try something new again.

But this year, I took away two different lessons that don’t require any paper prep so that’s where I want to focus on attention. I am most certainly not an eloquent writer, so bare with me:

  1. Word choice matters. And there are many amazing teachers who really are thinking about how simple word choices affect students and colleagues. It might not seem like a huge change, but sometimes that littlest choices make the biggest changes.  Some examples:

Continue reading “TMC17: First Thoughts”

Systems of Equations Unit Plan

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.


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

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

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:


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

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”