Second Breakfast: Day 72 Or Which Came First? Equality or Congruence

This is the second day in a row that I thought to myself “Oh I should blog about that after the last class” and then when I sit down to write I have forgotten it. I guess I will need to start writing quick reminder notes to myself while teaching because I cannot remember what I wanted to say about Foundations at all.

On the bright side, a student in geometry asked a very interesting question, which I would like to pose to the internet because I was not certain about the answer.

I started teaching similarity today and I was connecting it back to congruence and equality as they are topic we have already investigated. A student raised his hand and asked “Do you think congruence came before equality?”

Man, what a great question.

I told him that I would need to look up some materials and think about it, but that I think you could make the argument that congruence as a concept did come before equality given how the Greeks conceptualized number and area.

And now that I am sitting here writing this and thinking “What about math, such as it was, before the Ancient Greeks” and I thought of the theory that ancient peoples would count livestock by piling stones and using a 1-to-1 correspondence. Which is also like a congruence rather than an equality.

But I am curious to here what more knowledgeable people think. Please tell me!

Thanks for reading.


Second Breakfast: Day 71

I introduced slope-intercept form today by having Foundations students graph a given equation using Desmos and then identifying the slope and y-intercept. They repeated this for 6 graphs. Then I asked them about any patterns they noticed.

It didn’t click.

I will have to redesign the task for next time.

I asked very pointed questions to first block and they finally got it. But second block still didn’t get it and still didn’t get it.

I moved on to some small direct instruction with notes on slope-intercept form.

I like the strategy of discovery activity and then class summary but it doesn’t always work. Sometimes my task design isn’t good and other times it works for some students and not others.

Tomorrow I will reinforce with practice.


Second Breakfast: Day 70 Or Is Oatmeal A Soup

I underplanned Foundations today. That hasn’t happened in a while. I scrambled with some Kahoots and turned out terribly because I didn’t have time to vet / edit them and some of the Kahoots out there are just plain old bad. I managed to correct the problem by the time second block rolled around, but it was a little dicey near the end of first block as I tried to find a new task for the students to do. They behaved surprisingly well.

I stole a great warm up from Sarah Carter (@mathequalslove) that went great in all of my classes. I am pleased that I have convinced most of my students to buy into debate in math class. I still have some work to do in getting everyone immediately on task at the beginning of class, but once they got started they did a great job. And speaking of debates in math class, a first block student cracked me up this morning by walking buy, holding out a packet of instant oatmeal, winking, and saying “Soup!”

I was confused at first, but then I walked in to find my first block arguing about whether oatmeal was a soup all on their own.

It was so great.

Thanks for reading.


Second Breakfast: Day 69 Or Doing What You Can And It’s Okay

Now sometimes you just have to do what you can and it’s okay.

I used a Visual Pattern from Fawn Nguyen’s website for the warm-up (Again. Thanks, Fawn. You’re the best.), but I was struggling to come up with the energy this Monday morning to moderate a whole-class discussion on the correct answer. I was tired. It’s okay.

Class behavior wasn’t bad, but  I decided that it was okay every once in a while to let the students try the warm up and then move on to the next thing to do without a whole class summary. It’s okay.

Even though they were a little slower to start Quizlet than I would prefer, they eventually did it and worked together. I don’t have to be riding them hard to be maximally efficient with classtime every day if I’m a little slow on a Monday. It’s okay.

We practiced slope a whole bunch afterwards using a worksheet. Because the kids need to practice slope. We already did a conceptual exercise last week. It’s okay to use a worksheet to practice the skill. It’s really okay.

I went through some answers in second block and we didn’t have time to show the work on every single problem. It’s okay.

In geometry I met individually with every single student because the last unit test scores were




and this conferencing took up longer than I wanted. And that’s okay.

I lectured on kites and trapezoids from the whiteboard without making a slide deck or interactive google forms because I didn’t have time to prepare them this week. It’s okay.

Sometimes you just do what you can do.

It’s okay.



Second Breakfast: Day 68 Or Mt. Doom Remix

Last year when I taught slope for the first time I introduced the concept using a silly drawing of Mt. Doom. This year I tried to remember how the lesson went last time and make some adjustments. I think it went better this time.

Here I must once again this year tip my hat to Dan Meyer for his “Math Class Needs A Makeover” video, since this lesson approach to slope is very obviously a rip-off of his ski slopes deconstruction.

I started by setting the scene from Lord Of The Rings (for the students who were unfamiliar) and recited the One Ring incantation in the Black Speech of Mordor (they were, sadly, not impressed). Then I showed them the following clip of Sam and Frodo on Mt. Doom.

Then I passed out the first page of this small handout. (I had four graphs to a sheet. It was big enough too see and write on, but small enough to be economical with my prints.) I emphasized that what I was interested in was the REASONING for picking a certain section to be the most steep and not necessarily a looking the “correct” section of the mountain.

I gave the students some time to think and talk about this. Of course, there was some off-task behaviors, but most of the students in both blocks of Foundations discussed with classmates and wrote down an answer. I even got some good reasons out of them (although I had to coach/coax/coerce them into actually writing the reasons down instead of just saying them outloud to classmates or me). In fact in several cases the students really debated amongst themselves about why the tiny vertical portion was the steepest. They related it back to literally climbing a mountain so I was happy with the time that I spent explaining LOTR and watching the video clip. (Besides, it’s LOTR.) The only downside was that they got a little sidetracked worrying about carrying someone on your back (which made the vertical portion “impossible”.) But then again, this emphasized the extreme slope of that part of the graph.

As has been the pattern all semester, I got better engagement and discussion out of my first block than my second block, but both blocks did well. I was pleased and they seemed to get it. And even better, some students labeled points or asked about names without any prompting from me. Once I had given them a chance to work individually and we moved to whole class discussion, this was the first thing I brought up. I called on the students who had asked about labels or written labels and had them share what they did with the class. I prodded the rest of the class about why that was useful and then had everyone label using the same scheme.

After I was sure we all had a labeling scheme I asked the students to share which section they chose and why. Generally classes were split between the first segment (from point 1 to point 2) and the fifth segment (from point 5 to point 6), but students struggled to say anything past “It’s vertical” or “It’s nearly vertical”.

Still! That’s exactly what I wanted.

I then followed up by giving them the second sheet and emphasizing that it was the exact same picture with some helpful additions. (I don’t know if I quite created enough of a “headache” here for which a graph would be the aspirin. Maybe next time I will force the students to rank the slopes from greatest to least and submit there answers. This may create a greater need for more information.) But overall I was pleased.

Once I had the second graph I upped the amount of guidance I was giving to help them figure out how to use the graph to make an argument. I don’t know if this was too much help or not, but they seemed to get it. I drew a table on the board with “Segment Name”, “Up”, and  “Down” and asked the class to identify the pieces and then use the numbers to compare.

I was tempted to print the document front-to-back to save paper, but I knew that if I did that, I would have students who would start on the wrong side and make it difficult, so I am glad I spent the extra 11 sheets and classtime to hand out two different slips. Next time I think I will give less help during this portion, but I was happy with how much better this activity flowed and connected for the students this time around compared to last year.

I moved from this intro into notes on the definition and formula for slope and then we did some practice problems.

Also I just noticed that I introduced the topic of slope a full 10 days later this year. I wonder how much of that is the new pacing guide we have for the district and how much is me being behind.


Thanks for reading.






Second Breakfast: Day 67

It seems that invariably if I do not write my daily post before I leave work then it does not get written the day of.

I spent my planning (and past the final bell) talking with one of my administrators about how I have been feeling discouraged at work lately. It helped. I am really thankful to be at a school with such supportive and open leadership.

Other than that, yesterday went mostly well for being the first day back from bronchitis right after a long Thanksgiving break. There were a few hiccups and, but some learning got done. I don’t really have time to go into more detail than that this morning because I need to get started on today’s work.

Thanks for reading.


Second Breakfast: Days 65-66 Or Bronchitis

So I did it again.

I tried to force myself to go to work sick, felt awful, and then the next day had to stay home.

That is the second time I have done that. I probably should have just stayed home on Monday, but I felt bad because we just came up Thanksgiving break and I was irrationally concerned that it would look like I was just trying to extend my holiday.

On Tuesday I requested a sick day and went to the doctor. After a blood test (blegh) and a chest x-ray (with the rudest x-ray tech I have ever met) the doctor told me that because of my asthma my cold has turned into bronchitis and they want to make sure it does not turn into pneumonia.

So I was told not to go in to work today (Wednesday) either. One because I needed to rest and Two because apparently I was still contagious. (Oops, sorry kids from Monday.)

On Tuesday because of the last minute decision to stay home and rest and then go to the doctor, I did not have a lot of work prepared for my students. But today I am concerned about them getting too far behind so I am writing Google Slide Decks from home and creating forms to go with them so that the students can still try to learn something new while I am not there. I do not know how well it will go without me there to answer questions, but I feel better about that than assigning them Algebra Nation busy work again.

I am concerned about my classes getting behind and I am really feeling nervous about the pressure to stay “on pace” with the district and department and I would have felt that way even if I didn’t stay home sick.

I now really understand what Sweet Brown said about getting bronchitis.