Why Perpendicular?

I realized part of the reason I haven’t blogged much this year (despite saying it was one of my main goals!) is because my team is so awesome. There are four regular ed teachers who teach double period Algebra 1, and we’ve done it in various combinations for several years now. This year, we’re newly combined and changing up the way we teach some things.

My contributions are often sharing awesome things I found (but that others wrote)–great for my students but not really anything to blog about. I’ve been loving Math Equals Love INB pages. I’ve implemented way more Desmos activities. I’m not standing still–just not very original I guess.

Anyhow, last week we did parallel and perpendicular lines. We started with parallel and a fairly routine look at parallel lines, focusing on identifying slopes and writing equations of lines that were parallel through a given point (largely to practice writing equations). I (badly) started introducing perpendicular at the end of the period, and homework focused on parallel lines. That day, C (one of my awesome team members) came in to talk through what he had just tried in his class: he gave his kids dot grid paper and had them determine where perpendicular slopes came from.

He tried writing up an activity sheet for me (which he is graciously letting me share below) BUT I didn’t use it either. I tried out what he discussed the next day in my class–and after using his sheet myself to practice decided to instead give dot grids in dry erase pockets. That way, students aren’t limited to a certain number of points (which may mean you have to start at only one of a couple places to be able to complete a square.

When students entered, the Do Now was posted on the board: Make as many squares as you can on a 3 by 3 dot grid.


And as the bell rang, each student got a dry erase dot grid, marker and eraser. My morning class got the idea; my afternoon class (which OF COURSE C was observing so we could talk through this) did not listen at all. Some kids were trying to make squares on an entire sheet of dot paper (whhhhhhy???). Finally, we got the idea and I had students submit in a poll how many squares they got. I should have been clearer that I would have students come up to show their squares, which hopefully would have made them count a bit better! For a 3 by 3 dot grid, the max is 6, but none of my students got more than 5. I showed them the 6th and then told them to use 4 by 4 dots to make as many squares as they could. Again, the maximum a student found was 18, but you can get as many as 20.

Warm up over, we took out our notebooks as well. I had students draw a segment with a slope of 1/3 on their dot grid–and then complete a square. Some students could not figure out how to do this, so I was glad for the dry erase. When we all had it, I had them copy the square into their notebook, and then make a square with a slope of 3/4 (which was tricky so I would maybe switch that for something easier?) on the dot paper. We followed the same process for -1/4 and -2/3 (I may have one of these be an integer slope for next year).


Then I asked them what they noticed about the slopes. After they discussed with partners, we shared out and used those ideas to build our definition of opposite reciprocal slopes. Previously, I’ve usually just said that perpendicular slopes are opposite reciprocals and practiced finding them–but I didn’t feel like students understood WHY that happened. This took a little more time, although not as much as I would have thought, and I think students have a much clearer idea of what makes two slopes perpendicular to each other. I still did Quick Poll them on the calculators to practice finding the slopes, and I want to add more in about differentiating between the two–when I just asked for perpendicular students were generally fine, but asking for one OR the other led to way more wrong answers. Maybe something where they have to circle or underline or write the symbol would help? I thought about having them find both the parallel and perpendicular, but the problem seems to be deciding WHICH one to find.

From there, we practiced more writing equations with Math Mats.

Let me know if you try this out–it’s still very much a work in progress, so we would love any feedback you may have.


Rearranging Linear Equation Strips

My first foray into equation strips was Miss Calcul8’s radical equation strips. I loved these–its a new and unfamiliar format of equations, but it helps students to see the parallels with solving any other kind of equation. Having all of the steps written out is a little like training wheels, so students feel more confident. I was even inspired to do more Equation Strips for both exponential and logarithmic equations.

I’m back to my Algebra 1 roots now though, and wrapping up linear equations. We had a lot of discussion around standard form–I come down firmly on waiting to teach students to convert standard form to slope intercept form. I recognize that standard form isn’t always friendly, but I’ve found in my Advanced Algebra classes that many students can’t graph at all from standard form. So they take forever switching over from standard to slope intercept form (possibly making some sign errors along the way) and THEN  graph.

That said, standard form isn’t always the friendliest, and students do need to be able to convert to slope intercept form. For some reason, half of my students find this various straightforward and others find it baffling. Enter: Equation Strips. Each pair gets an envelope and separates the strips by color. Then in their starting color (these problems are all the same in difficulty but for simplicity you may want to tell everyone to start with blue) identify which strip has standard form on it and which has slope intercept form. Those will be your starting and ending strips. Then pairs should order the strips and check in with the teacher. When they’re right, copy the steps into your notebook, mix up the strips and start on the next color.

Rearranging Linear Equation Strips

Set of 6 Rearranging Linear Equation strips between standard form and slope intercept form

I included slope intercept to standard form as well, because I don’t want my students to have the idea that slope intercept is king and everything should be in that form–we should be able to change in both directions. I don’t expect all of my students to do these, but I want especially the faster finishers to recognize that both are important. (Oh and the very last one is super easy, but I left it in case anyone was interested.)

I copied the first sheet on two shades of purple and the second on two shades of blue. Then after cutting them in half, I shifted them by one so that each set got a light purple and a dark purple problem, same with blue and then yellow and pink for the SI problems. And then I realized that I should have done what I did with my radical equation strips and make half sets (so one purple and one blue) and just have pairs trade. Ah well!

I love that I’m not explaining anything and students are exploring on their own when we do these–and when I’ve done them in my Advanced Algebra classes I actually feel like it was faster than me giving notes and doing examples. I do still give some wrap up notes at the end for their reference, but they already have their examples done!

Where else could I use some equation strips? I want to make more now!

Midpoint Reflection

Semester 1 will be in the books in just a few more days. My goals have gone…ok.

I wanted to improve physical organization–making sure I actually use all the awesome stuff I have. This has been my biggest win. I looked at lots of different ideas and settled on one scrapbook box per topic to hold all my activities for that unit. I think I will slowly transition away from binders eventually, but I’m not there yet. I’ve also managed to review my files by topic as we go, which has been a big win. This is so much better, and when I have some free time on our PD day for end of semester Friday, will be even more in place.

I…barely blogged. So that is really going to be my focus this year. I think even if I just review what I did (you know, other peoples cool stuff) I want to make it a point to get back into the habit.

My third goal was to let my students struggle more. I think this will need to be slower to be genuine, but I’m making some progress here. I’m also using Desmos more (I just got my own Chrome cart) and I like what that does for my students. Definitely a work in progress but I’m pretty pleased with what I’ve done in a transition year.

So for next semester, I really really really need to blog. Here goes nothing!


In an effort to focus better this year, I set myself three goals to work on. One of those is to physically organize all my stuff.

I’m definitely the type who can’t throw anything out and I save all my activities so as not to have to recreate them. That means I have, in no particular order:

  • Activities, in various sizes of envelopes/paperclipped together, or even in boxes
  • Files, labelled by topic and with spare copies in them
  • Binders, poorly kept up at this point, ostensibly with one copy of everything in it (I have…many binders)
  • Books, from resource masters to activity books to teachers editions

And that’s not even touching my computer, which used to be organized but now definitely has a fair number of duplicates. Compounding things is Google Drive (with which I have a mental block–it’s getting comical. I think I’ve finally shared something right only to have my pro-Google colleague email and ask for permission). There are also the activities I’ve read about on blogs that I want to try sometime but rarely do because I just taught that or it isn’t for three months and I don’t remember it in time.

I read through many of the Organization posts and determined I should probably start from scratch.

I can’t bring myself to get rid of the copies but I can move things over (I have an empty file cabinet) and move them back when they are in a state I actually want to deal with. I read about people who use big binders and little unit binders and boxes and more.

Unfortunately, I don’t think unit binders will work for me, as I’m not sure we’re final enough in what we’re using. I like the idea of keeping everything for a given unit in one place though, so I’m considering doing a box for each unit, with both activities and a single copy of each assignment and trying to do the same electronically.

It doesn’t feel like a perfect solution but it sounds a great deal better than what I’m currently doing–now I just need to get it started. (Or, you know, change my mind again.) I have the boxes, I just need to find the time.


I read somewhere you should only attempt to change 10% of your practice at once. It makes sense. I think back to my first few years teaching–I was trying to change and refine everything. Cringing at how poorly some things worked, I changed in the middle of the year, trying again and again to get things right.

The year I was pregnant was super rough. I had one of my hardest groups (a very small double period at the end of the day with a rowdy combination of students) and did not have an easy pregnancy either. My focus was on staying afloat. I took a year off for maternity leave and last year my focus was on getting back into the swing of things, organizing my three preps, switching rooms, etc.

I have a lot I’d like to work on this year. I’m making a concerted effort to choose only a few things though. I don’t want to be so ambitious nothing quite gets done–I want to truly build new habits that will impact my practice long term. With that in mind, I’m choosing 3 things to focus on for the next year:

  1. Physical organization: restarting my binders and file folders from scratch (my plan is to move things over only as they are used and get rid of the rest at the end of the year), getting my activities organized and sorted, generally trying to actually use all the resources I’ve amassed.
  2. Blogging. As part of the organization, I’ve spent time this summer on our master planning document for Algebra 1. I read through my own blog (as well as many others) and found good ideas I’d forgotten. Writing helps me process and reflect and I enjoy it. There’s another class in my room 1st period so that might be a great time to use for blogging.
  3. Instruction. I *think* this one will be including more inquiry and discovery type activities, but I need to make sure that my team is on board too–we hope to follow each other fairly closely so if they aren’t interested in this as a goal, I’ll need to choose a different instructional goal.

I considered making tech use or grading a goal, but it took a backseat to the things above, and I want to make sure I can focus. I’m hoping that keeping myself focused on these three things will show big improvements!

What are your instructional goals?


I’ve been spending a lot of time thinking about my goals for next year. I’m a big planner. I like figuring out how to do things better. I also tend to get carried away and come up with more things than I can possibly do. I can list ten awesome goals, but I doubt I could actually accomplish them all–and maybe even any of them if I really stretch myself too thin.

This past year my schedule sucked. I had to share a room, move rooms for one class and had three completely different preps. My desk was shoved in front of a closet, there was nowhere to put anything, I was just back from a year’s leave. It was transition.

Right now, I’m teaching Freshman Connection, a four week program where students have 90 minutes each of math & reading and 40 minutes of counseling Monday-Thursday and go on a field trip on Friday. They get familiar with the building, free breakfast and lunch, meet some teachers and students. I teach two 90 minute sections and get an hour of prep. We’re supposed to spend a good chunk of time playing critical thinking and computation games, and I’m a fast planner, so I’ve got a lot of time on my hands.

And so I plan…

I want to choose my areas of focus so I can be intentional and when I start to overwhelm myself in my good-idea-spiral, snap out of it.

This year, I have two preps. One is being reworked (our Algebra 1) but we have an awesome team, all of whom I’ve worked with before. I have my own room, with another teacher using it during my first period prep. Plenty of storage space. It’s time to get things together!

So, what’s been rattling around in my head?

  • We’re semi-standards based but a friend at another school was pushing my thinking on how she does it. What I do now is ok but could definitely improve and be clearer. However, we’re getting a new platform next year, (our current one is terrible for SBG) and I don’t know what it will be like. This is partially philosophical and partially logistical.
  • Google Classroom: In the olden days I did a class blog, but Google Classroom is made for that and more. I will be doing this for sure, but how much do I want to try to use it?
  • TI Navigator: I definitely don’t use this to its fullest potential, but 3 of the 4 teachers on my team will be this year. That added brainstorming can really help us take things to the next level. I especially want to use more quick polls (as assessments) and collect documents from the class, as well as use some of the files TI provides.
  • Google Drive: I do not understand Google Drive. I need to learn. I’m not excited about this one, but my NHS officers keep asking why I didn’t share things that I thought I had. Ugh.

Physical Organization

  • Make sure I can a) use all my amazing resources and b) actually only have amazing resources
  • Determine how best to organize resources. They may be found in: Books. Activities, Files, Binders, Blog posts, Dropbox, NCTM, Desmos and more
  • Make some priorities. My coworker calls it a warchest–decide what books/activities/whatever is worth the chest
  • Make it useable and easy to access–How many locations are acceptable? How much does portability matter?
  • Decide on a Philosophy: Is there one copy of everything in the binders? Ok to look in both binders and files? Should activities be stored by topic WITH papers or separate?
  • Start new binders from scratch–move over anything useful from previous binders.
  • Pre-tab and start all binders with a table of contents. Dumb but true, I have binders with dividers and no labels. Why?!
  • Start new file drawers. Basically, I need a semi-clean slate.


  • Set draft prompts about topics and focus on making sure I write. Tell others for accountability. (Ha, hi!)



  • Be more responsive to student data (pick 2 skills, 2 ? exit slip with must & may, track data). One of my coworkers is amazing at this–I’d like to get some tips from him, and I think Navigator can really help with this as well. More about this one later!
  • Do projects. Our class is newly mixed ability and I think projects can give some great opportunities to differentiate, as well as be used for the whole class.
  • Differentiation. What can we do besides having some students get further on a given activity/problem set/whatever?
  • Write tests first. Backwards planning. We’re all on board with this one!
  • Tell them less: discovery and investigation.
  • Unifying themes/essential questions
  • Circulate and be more aware of whats happening in class. I plan well but sometimes I’m guilty of watching the action instead of really knowing what’s happening in my room. I know I can catch more misconceptions and be more available to students–I just need to set up some structure for myself to make sure I’m doing this!


  • Gather & use data more frequently–using the Navigator and other methods. And just circulating!
  • I was asked to be on our Data Team this year and have been talking with the AP about it a bunch. I hope we can make it practical and useful for teachers! So far, we’ve come up with: make a sheet, keep up on data, self assess, make goals (have exemplars–collect, analyze, respond, plan/generate) (move beyond exit slips, ways to collect data). More on this one later too–I’m getting sick of editing my random thoughts 😛
Logistics Stuff:
  • With my new/old room (it was mine before maternity leave) comes figuring everything out. In addition to wanting to start from zero on my files and binders, I need to decide what goes on shelves, in 7 cabinets, small and large file drawers. I have a lot of stuff! And at least two of those cabinets will be for NHS supplies.
  • Determine how to organize student based supplies (whiteboards/dry erase/erasers, markers, scissors, rulers, glue sticks) (spares like pencils & erasers). And, honestly, what those are. I’ve used a set of three drawers for years, and students come get what they need, but a caddy per group could work (although I do lots of partner work–but isn’t sharing with another pair still more convenient?)
  • How to handle student work/extra copies (will using Google classroom mean I need no extra copies? That would be amazing.)
  • Where to put mental math, calculators and other stuff
  • Decorate, posters, number lines! Sarah Hagan has tons of cute posters so I’m hoping I can copy her and be done with it since I’m not a huge decorator.
  • Finish moving everything over–I had my homeroom get almost all of it in the last ten minutes of school (right after I found out) but my desk is still mostly full and although it looks nice I have no clue where anything is!

So obviously I have some narrowing down to do, but I think I’m just about there. Here’s hoping I can keep this up!

Something Based Grading

We changed up our grading structure this year. Our admin wants to move towards standards based grading, so we’re sort of supposed to be transitioning towards it a little bit this year. Sorry for all the qualifiers, but that’s how it actually is.

I’ve read enough blogs on SBG to feel like I have a vague grasp of what it should look like. Choose standards, assess & reassess on those standards, then final grades are based on the scores on those standards. Its definitely a huge change from how I’ve taught and assessed before, but I would be up for the challenge.

Except we have to use Gradebook, and we have to enter grades at least weekly and Gradebook is very much not designed for this sort of thing. Gradebook will give you a max of 9 categories, and those categories are the only way to have any weights to things.

So we have this crazy system where we have nine topics/standards and then all the assignments under that standard are coded under that standard but weighted differently according to their type (so that the whole grade doesn’t come from homework, for example). And if you feel a little fuzzy about what that looks like, my math teacher friend, consider how my freshman feel. Or their parents. Or, actually, me. I’m pretty sure that despite the weighting homework is getting way too much value. Progress reports are nearly unreadeable because the multipliers muck it up.

And about that homework…I do think some kind of practice is really helpful in math class and although I don’t care about how they do it (and have only ever graded homework for completion), they probably care that I give them credit for that. So how do I balance that with not really wanting that credit to count?

I can make some minor changes this semester, but I do get a clean slate 2nd semester. Any ideas to help me out? What are your favorite SBG [lite] resources?

Making an Effort

Oh, hi.

I have so many things I want to say, but its been so long that I’ve said anything at all that I feel like I have to come back with something brilliant. Or at least good. And then I get stuck picking what to talk about and so I say…nothing.

Which is silly. So, hi. I’m teaching Algebra 1 to students a few grade levels below this year, which means I haven’t actually taught any algebra at all to date. I don’t have any residents this year. I got a real classroom. Oh, and I did indeed get married this summer and we bought a house and moved. And my sister moved cross country and I helped. So we’re basically all caught up.


Caili Helsper Photography

My students this year already think they’re bad at math, and one girl in particular tries so hard to give up. She won’t try anything (and by anything, I even mean writing down a practice problem in her notebook–not doing it, just writing it.) Today I told my students they  needed the first section of their grid (just a bunch of rounding problems) filled out for an exit slip. She did nothing. It’s her M.O. To wait. And I guess it’s always worked. And it isn’t with me and it’s making her so mad. So she couldn’t leave. And we talked. And she cried. She’s a cheerleader who really doesn’t want to miss practice, but she went to the first half of practice and she’s here now. I want her to stay, and so I stay too, even though I’ve finally started to get caught up and I finished grading everything I have right now during lunch (don’t worry, I give an Algebra test and collect Stats homework tomorrow).

And, as if this post isn’t lame enough, here’s what I hope to be writing about soon:

  • Our foray into some mess of pseudo-standards-based-grading (Spoiler: It isn’t pretty.)
  • Maybe more fractions
  • Favorite lessons and practice structures

I missed you internet. It’s good to be back.

Fraction Success

Today is the last day of finals. I gave my regular-level Algebra class the final section of their final exam today, a “Choose 3 of 7” component.

Question 2 asked students to “Order the numbers 3/7, 0.75, 1/7 and 3/5 in ascending order, and explain how you arrived at your answer.”

I forgot to remind them that they can’t use decimals. When we spent so much time teaching fractions earlier in the year, we emphasized that our students needed to be able to work with fractions as fractions. That was the only way to get credit and we worked really hard on it. We felt like it worked, but that was ages ago.

The first question I graded was, “I switched them all to decimals to make it easier, then I ordered them.” Oh, NO. I forgot to say something, they’re all going to do it wrong, I can’t give them credit for that.

And then I kept reading.

This was a CHOICE exam. No one HAD to do fractions. And a third of them did (Ok, to be fair, the kid with a 90.03 chose all 7–better safe than sorry I guess.)

But I read answers like these, with no reminders about decimals:

I arrived at my answer by looking at the fractions and seeing the amount of shares they needed to accomplish a whole and I took the one fraction who the most shares…

I turned .75 into 75 and put it over 100 it gave 3/4, which is bigger than the other fractions. 1/7 & 3/7 have the same size but different shares and 3/5 is bigger than 1/7 and 3/7

For a topic dating back to October, I am so pleased with these answers. I think we managed to change at least some of our students attitudes towards fractions, and lead them to actual understanding of what they’re doing.

I hope to be able to do even more with this next year. Anyone interested in collaborating? My sister is teaching fractions to adults again this summer….


This has become one of our favorite quick activities in my Algebra 1 classes this year–and credit for this one goes out to my resident once again.

Remember at birthday parties, where you would whisper something to the person next to you, and then they would whisper it, and so on? And it changed from “Lesley has a cute shirt with rainbows” into something totally inappropriate.

Kinda like that.

The materials are super simple–get a bunch of paper (maybe from your enormous stack of leftover mental math?) and cut it into fourths. Then get problems, cut on to slips of paper.

You could cycle one problem through the whole group (I’ve done similar before with one whiteboard and called it a drill), but we prefer to have all the students working, so one problem per student will do.

  1. 1. Students in groups of 4
  2. Each student gets 4 blank slips of paper and labels them ABCD
  3. Each group gets four slips of paper, numbered 1-4.
  4. Each student picks up a problem, does it [distributes 2(3x-5)] and then passes it to the next person. They hold on to the original problem.
  5.  Pass once to the right, factor out the common factor (or a different step), put the piece you were given on the bottom and pass it on with a new top.
  6. Repeat a total of four times, until you get your original problem back.
  7. Have the group check how well they did keeping their problem the same.

We’ll be doing it with multiplying binomials/factoring quadratics, and we also tried it with translating between words and algebra. It fits a lot of places and can be a quick single round activity or something a little longer–lots of fun and a new favorite. I highly recommend you try it out!

What’s your favorite quick practice structure?