Lessons Learned From Distance Learning – CMC South 2021

My colleague and friend Bob Rodinsky and I delivered an amazing presentation today at CMC South Palm Springs. It was Bob’s first presentation, in his 6th year of teaching on his 3rd career after being a successful IBM manager and a real estate agent.

I presented last year at CMC South virtually. It was asynchronous. It went OK. I got some positive feedback. It was a lot of teacher talk. Like distance learning, it was challenging in that there was minimal interaction despite our best efforts as teachers.

My presentation last year was about HyperDocs and how I use that format to teach students complicated tasks. This presentation took some elements from that but focused and expanded on a few of them.

We were the first time slot and rehearsed and refined our presentation up until 1:30. I went around the Hilton and promoted it to others. I was delighted I got the support from Ethan Weker as well as Desmos employee and CL wizard Kurt Salisbury who attended.

Similar to Open Up lessons and presentations, we did a warm-up, two activities, an Are you ready for more, a lesson synthesis, a simple true / false cool-down, and a call to action to get participants thinking about what ideas they would implement.

Bob started us off thanking the participants for choosing to come to our session and we were honored. We talked a little about ourselves and then introduced our learning goal that “participants will learn about digital tools to enhance student learning and focus on choosing when to use digital tools.” Then we introduced our agenda and our warm-up was “What were you unable to do on Zoom that you previously did in person? Did you adapt any of your in person activities for distance learning?”

One interesting idea was a participant said they missed students walking around the room with their phones to use QR codes to do a problem solving scavenger hunt. Many people mentioned the inability to read non-verbal body language. Teachers missed seeing students facial expressions with their cameras off and knowing their emotional state and whether they were having an “a ha” moment or not.

Then we moved to our main topic. Flipgrid implementation. We checked everyone’s understanding by saying give a thumbs up if you’ve used Flipgrid with your students, sideways if you’ve heard of it, and thumbs down if you hadn’t heard of it. Most did thumbs up and some sideways.

Then I lead with this tweet that was well received:

I then talked about I show students how an assessment was graded based on point values and my expectations on what they should explain for each problem that they may have skipped or gotten wrong.

I then checked for understanding to see everyone’s experience with Loom. Many hadn’t heard of it. I called on someone who gave a thumbs up and they explained that Loom is a free easy to use screen recording website. I then showed a screen shot from a students Flipgrid submission where they sketched how they proved two figures were similar or scaled copies using a series of translations and dilations:

We then moved on to another way to use Flipgrid: number talks. I used the border problem made famous by Jo Boaler. To prime everyone for my video explaining how to do it digitally, we did it the old fashioned way by showing everyone the prompt and then annotating on paper their ideas under a document camera.

Then I moved to showing how to use Flipgrid to record a Desmos activity. I threw in a check for understanding and was shocked that some people had never used Desmos yet. I realized I needed to dig deeper into this later in the session.

Intrigued by this animated GIF, I asked if they wanted to see student sample work. They said yes! Check it out here.

Then we moved to Activity 2: The Spiral of Pythagoras. Bob took the lead with this because he is super passionate about it. I showed my hype video that is a 40 second time lapse of the project being completed. It gets slowed down in the next activity.

After Bob talked, I compared how we would model how to complete the project under a document camera in person, but for distance learning I figured out how to record myself doing the project, upload it to Edpuzzle, record a voice over, and insert multiple choice questions along the way to check for understanding. So instead of doing it the analog way of under the document camera, I played the Edpuzzle as everyone in the room followed along and shouted out the answers to the questions. It was pretty successful.

The are you ready for more slide came up with 30 minutes to go. I wondered if we should skip it or go to the lesson synthesis and cool-down. I decided that instead of going straight to the Flipgrid, let’s show the Desmos newbies how to get to the website, create a class code, and then had them join that new code. They did this from their devices or phones and experienced Coin Capture. I assumed everyone knew to click Next on the slides. I realized by circulating this was not the case. I talked about that and then hyped up the amazing Class Gallery screen so that students could create a challenge that needed at least 3 lines: 1 horizontal, vertical, and diagonal line.

With 15 minutes left I launched the synthesis. I said that this would be one of the few times I would read off my slides since it was so important. Here are the 2 major points:

  1. When students use Flipgrid or Loom to record themselves completing test corrections and assignments, it creates permanent and authentic evidence of student learning that can be shared with peers and family.
  2. When teachers use the free tool Edpuzzle, it allows students to perform a complex task anywhere so absent students don’t miss out.

We then did a cool-down which you can see in the following Google slides link. We got great feedback. People said we set a high bar. They said we made the trip to Palm Springs already worth it. Andy requested a picture with Bob and I. It was an awesome feeling.

I am so glad my first time getting on a plane in 2 years and first time back to a math conference resulted in this first day experience. We still have a full day of sessions to attend tomorrow. I am delighted I get to see two amazing speakers tomorrow: Peter Liljedahl whose Thinking Classrooms book I am currently reading, and Geoff Krall whose Necessary Conditions book I have already read. Stay tuned for another blog post where I recap those sessions.

Unit 8.2 Lesson 7

Desbook version

Teaching students the fact that two triangles are similar if two pairs of their corresponding angles are the same can be a tall task. It’s abstract. Being well versed in finding the missing angle of a triangle given two angles helps a lot.

I’ve tried teaching this 8th grade standard using three different curriculums: CPM, Open Up Resources 6-8 Math by Illustrative Mathematics (IM), and Desmos Middle School Math Curriculum. I think we have a winner.

CPM tries to get students to understand the standard by analyzing diagrams and proving the AA Similarity postulate.

IM has students use linguine pasta to break off, tape, and measure on their workbooks. I have yet to get through the whole lesson in a 53 minute class period.

Last year during the pandemic I had the good fortune to use Desmos’ digital/paper curriculum and this lesson truly makes a convincing argument for the minimum number of angles needed to be the same for two triangles to be similar. It harnesses the power of Computation Layer, CL, to aggregate data from the whole class who have created triangles meeting 1 required angle and later to 3 required angles.

I am going to teach this lesson tomorrow, and have had this blog post sitting in my drafts with screencasts already created and converted to GIF to show the truly awesomeness of this lesson. Also, by writing this blog post I am preparing to teach this tomorrow, so I’ll probably update this blog post.

Another advantage to a digital curriculum is updates. I can see that screen 1 is different from the first time I taught this lesson.

Screen 1: Students are cleverly asked to use as few reveals as possible, reviewing that parallel lines create corresponding angles that are congruent so that they can solve for the missing 3rd angle of a triangle.

Screen 2: I remember taking snap shots of students screens here, of students who misunderstood and created similar figures, as well as students that had correctly made two shapes with congruent corresponding angles but were not similar and had them explain how they knew it was correct.

Screen 3: Now students create triangles with three given angles. They predict if all of their peers triangles will be similar to each other.

Screen 4: Students click a button to see the below animation, then discuss with a partner, “are all of the triangles similar?” Notice how the third corresponding sides are parallel.

Screen 5 & 6: Then they do the same process but with one angle being the same. Notice how students can adjust the scale factor with a slider to see what happens with the 2nd and third angles:

This is a powerful place to have a discussion before they work on their card sort:

Here you can see it’s really important to stress that triangles are special in that if their angles are the same, they are similar. You can see that the two parallelograms have corresponding angles that are congruent, but no side lengths are given so there’s not enough information. The rectangles are interesting because the side lengths are 1 apart so they’ll really have to think about a constant scale factor between or within the side’s shapes. The two triangles with one corresponding angle clearly are not enough information. Finally, the last pair of triangles, the warm-up and main idea of the lesson comes back that we must check the third angle of a triangle to see if all three corresponding angles are the same.

The are you ready for more? is pretty nifty here. Students drag a triangle on top of another to see if the third side is always parallel. Then they can keep pressing the button to generate more pairs of triangles.

Lesson Synthesis: Here we can clearly see that no third angle must be calculated if students understand that 2 pairs of corresponding congruent angles are necessary for two triangles to be similar. Many students last year calculated the third angle just to be sure, which I will point out with a snapshot. I will challenge them further to figure out the scale factor. I’ve noticed that a lot of students are rusty with 6th and 7th grade concepts, like finding the missing factor. I will emphasize, that 2 * ? = 5 ,and to find the question mark, we can use the opposite of division and do 5 divided by 2 or write it as a fraction 5/2. We know this is small to big because the fraction is greater than 1. (Lots of leading questioning here). Also asking what the scale factor is other way from small to big (the reciprocal).

Cool-down: For the cool-down I’ll take some snap shots of student work to show class the next day.

I am excited to teach this lesson tomorrow. It’s a tough standard to teach, and I think Desmos has presented it in a solid way that activates prior knowledge at the beginning and student discussions ensure they are understanding the visual phenomenon in front of them. Bravo Desmos team.

My 1st Ignite Presentation

I was an #OpenUpMath community coach for 2 years and Brooke Powers invited me to present an Ignite to close out the Open Up Resources HIVE conference. I’ve always wanted to do one. This one was virtual which made the decision easier to accept because standing up in front of a large room of people is more challenging.

If you don’t know what an Ignite is, it’s a 5 minute presentation where there’s 20 slides that auto advance after 15 seconds. Huge thank you to Robert Kaplinsky for writing a tremendous blog post on how to prepare for it. I am fairly scatterbrained, and this allowed me to add a bit of focus to my presentation. It’s still not that focused because I basically presented about a bunch of ideas I’ve borrowed from others and created myself that have been successful and I plan to continue to do every year I teach.

In this blog post I’m sharing the recording of it and also a link to the slides in case you want to click on the links to get more information. Some of the ideas I’ve presented whole sessions about like the 3D printing.

My 1st Ignite recording – Watch Video

If you’d like to take a look at the Google Slides, this link will make a copy of it for you on your Google Drive.

I think overall it went well. The presentation on my screen was 1 second off of the projected one and it still worked out.


The video is now fixed, thank you Howie Hua and Jenna Laib for alerting me to this. To properly create a video recording of a recorded Zoom session, I suggest downloading the Loom app and following these directions to mute your microphone and for the app to only use your system audio.

I will say that a 5 minute presentation took a total of about 5 hours to prepare for. I highly recommend thoroughly reading Robert Kaplinsky’s blog post because it’s surprising how little you can say in 15 seconds and it will help you shorten your message to the absolute essentials. Like he suggests, get your script finished in 20 slides, then copy and paste each slide and auto present it and read it off the slides to get your timing done. THEN work on copying and pasting images and bullet points from the left hand side of your column. Thanks Brooke for the opportunity.

2020-2021 Teacher Report Card

As part of a sub plan in the last week of school, I assigned my students to give me a “Teacher Report Card” with about  This is one of the suggestions offered in the book Classroom Chef by Matt Vaudrey and John Stevens. Here’s my previous report card blog post from the 2018-2019 year. It looks like I skipped out on giving it when the pandemic started in March and we finished the year in distance learning.

I asked my 4 8th grade math classes to complete it asynchronously, and not all students responded. I got 87 responses.

Here are my averages and results of 87 student submissions. To get averages on google sheets you can use something like: “=AVERAGE(P3:P145)”. I tried to sort these numerically but that resulted in some reference errors.

4.797619048 …respects each student
… makes me feel important.
… tries to see the student’s point of view.
…encourages me to be responsible.
… has a great sense of humor.
… treats me as an individual.
… does a good job of treating all students the same.
…answers questions completely.
4.694117647 …says his words clearly.
… uses language that we can understand.
4.428571429 … explains topics clearly.
… tells us our learning goals.
… keeps the class under control without being too tough.
… seems to enjoy teaching.
… provides time for review of material.
1.530120482 …has bad breath.
4.541176471 …listens to our ideas.
…leads good class discussions.
… tries new teaching methods.
… gives good, fair assignments.
…has a good pace (not too fast or too slow).
… gives fair punishments.
…encourages different opinions.
…gives enough time for assignments.
…has interesting lessons.
4.623529412 …grades fairly.
…gives tests that reflect the material in the unit.
… dresses professionally.
4.658823529 …praises good work.

I’m kind of shocked that interesting lessons got a low relative rating. The Desmos curriculum is extremely interesting… Like every year, pace was a relatively low rating. Gives fair punishments was relatively low, I didn’t feel there was a need to give punishments, I didn’t see any behavior that warranted it besides one class in hybrid that  had a few students who were off task frequently. Tries new teaching methods also rightfully got a low rating, to keep the class predictable I strictly used Desmos. I used Flipgrid to have the make screen recordings of Class Gallery screens as projects as well as for test corrections. Last year I used Edpuzzle for the Wheel of Theodorus project but this year I didn’t get to it. I also didn’t get to my 2 way frequency table project that integrated Google forms so I definitely didn’t diversify my tool box much. Then again, that was purposeful too.

There were also these open response questions. I am going to put my comments in brackets [] Bolded comments I am proud of:

Sometimes, the teacher __________, but not always.

Is a little slow
Calls on people who don’t raise their hand
is slow
Calls on you and asks for an explanation about your answer
makes a few jokes
posts assignments in classroom after the due date
goes too slow
laughs at my jokes in private chat
Goes off on something random, like a meme someone put in the chat
can take a lot of time on one problem
Has funny dad jokes
has bad wifi
calls on me
doesn’t give a lot of test
Leaves the Zoom meeting
calls on me
wants to learn modern slang words that we use and its really funny
speeds through certain slides
is strict
can go fast while teaching
goes through the screens too quickly
calls on you when you didn’t raise your hand
is not here
tells us about things from his life 😀
is wrong
gets mad
makes mistakes
has to leave because of internet problems or his family
reiterates question answers a lot
lets the class out early
turns grumpy
goes over cool-downs when class starts
is tough
I dont know
gives easy homework
Gets angry
dont give paper
is with a drink in class
makes the lesson less interesting
I dont know
gets a little agitated
doesn’t always spend enough time teaching a way of solving
doesn’t attend classes [I gave this as an asynchronous assignment]
is hard
looks nice
Is at school
there is no one thing that teacher only does sometimes
plays fun math games with us
will fit in jokes in his lesson that are fun
tells the class funny stories
Would make funny comments
wears a tie
takes too long explaining a problem
can’t really think of one, maybe makes funny comments, entertaining? not very sure.
Doesn’t explain for everybody to understand and makes it hard to ask questions about things I don’t get
is not busy
makes jokes
Stays on parts of the lesson for a bit too long
doesnt look at chats
gives tests
is funny
no answer for this one
misses class
(no idea)
A little too slow for my preference
Gets mad.
doesnt give to much time
i don’t know
is helpful
moves too fast

Sometimes, the teacher lets the class __________, but not always.

Go to the bathroom
Go in break out rooms to discuss for a short amount of time
out early
Go in breakout rooms
Chill and have a little bit of fun
fool around a bit
I don’t go to in person class so I don’t know how to answer this
mess around
recommend him new shows/movies
Do asynchronous, get our work done and get some free time.
just talk
talk to each other
leave class early when we’re done with a lesson
Join break out room
Play math games
join breakout rooms
idk what to put here lol
get out early
play educational games like that card game that i forgot the name to. [SET]
do breakout rooms
teach him new terms like chad and pog [funny inside jokes]
do group discussions
play games
play Set
play games
go early
work on homework
im not sure
play set
have fun
i dont know
takes breaks
Work on their own
end early
discuss with each other
work together
I dont know
have discussions
out early
be unfocused for period of time
watch a video instead
have fun
go outside
go in breakout rooms (they stink no one ever talks) [not consistent]
out a few minutes early
talk a bit when done
play sets
relax and have a good time
play SET
time to think about the problem
do independent work by ourselves
roam freely
play Set with Friends when there is extra time
Play set once we finish the lesson
out early
get loud
get dismissed early
do some fun games like uh i forgot
play set
talk in groups
i dont know
discuss stuff
be quiet
solve on our own

What do you like BEST about the class?

I like how all the student are polite
I like that Mr. Joyce actually spends the class time working and teaching the students. I had walked into my sister’s class one time and saw that her teacher just assigns the desmos assignments, and leaves the students to learn by handbook. I was informed that she never works with the students.
Mr. Joyce, he is funny
I like how mr Joyce makes us have time to complete each screen
I like having a lot of time to do different problems during class and I also like how you go in depth for topics that may be confusing to others and myself.
Slow pace so everybody can be finished
You can make up late work
You focus on and celebrate accomplishments rather than failures, which makes me feel pretty good about myself. [YES!]
Its pretty chill, nothing too stressful
I liked when we played set because it was fun and I was really good.
it’s lively
solitary ti- I mean, talking with friends about the lesson
we don’t need our cameras on
The teacher is nice
I like the best about this class that when you don’t do good in your test you can get a better score
I like how I get to learn different concepts of math instead of 1 concept.
good teacher
I like when the teacher puts pictures of peoples work up because it helps me see different ways of math and tends to explain the math problems very clearly. He also interacts with the students as well as giving them extra support.
i like that you’re always happy to help a student in need
Math is easy for me, and Mr. Joyce is a fun teacher, which is the least you would expect from a math teacher.
No one judges your answers
Mr. Joyce’s bad but funny jokes
I like the easy going vibe that the class has
how fun it could be
The atmosphere, everyone is calm and it’s like hanging out with friends, just a chill vibe.
it’s math
the teacher really cares about the students grade
The way the teacher explains each problem.
The teacher
I like that its super to easy to share what I believe to be the answer to the question, ecouraging to class participation well.
its very fun
the fun desmos gamrs
its always fun and the lessons always have a different situation in them not just the basic book ones.
The teacher makes sure to give people time to write down and copy what he did.
That we have a teacher that actually wants us to learn
How we work in unison
I like that the class is respectful of each other and their responses.
I like to
We can do corrections for assignments or tests.
Being able to learn math, even though we are all in different places.
I like that Mr Joyce is very chill and layback, in my opinion a teacher who is tense makes me feel uneasy.
How I was able to learn new things about math and how after some time, it became easier as I learned more
It’s fun
he doesn’t push us to hard
I honestly just like math and Mr. Joyce teaches it the best
I like that Mr. Joyce actually listens to me in chat, unlike a few other teachers.
you feel relaxed when you finish your work
when the teacher tells us stories that he experienced in his life
I like how the class is very fun to be in. Such as how they would have mini contests on who is the faster to join a lesson. [one period raced to see who was at the top of the class summary screen]
How I understand the math better and how he doesn’t like to embarrass someone.
I like how the class is educational, yet not too strict. It has a good environment for students and gives fair punishments if needed. I like how there are corrections for tests and explains practice problems through videos which I find very helpful and appreciative.
I like the community and the fun activities we do.
The class is funny
getting called on for a right answer
Understanding the lesson and raising my hand = I have an answer for you guys
Mr. Joyces way to make math fun
The teacher is nice and he helps me better understand things that i’m stuck on
probably out of all the classes, this were the class socializes/bonds the most
its fun
I like how the work is easy to understand, but I get distracted so I don’t always get it done on time. [I gave grace and no penalty for late assignments, which lead to groups of students turning in stuff in big batches]
The other students
learning with Desmos
the set thing, that is fun but not sure how to play it very good
i like how we all get along very well, and how we have a good enviorment for everyone.
The work isn’t too challenging, but when it is, mr. Joyce makes sure to explain it so it makes sense.
The interaction with each other.
The way math was being taught
the environment [I’m really proud of students feeling that the environment was safe to make mistakes and share in. As you can see more of these came at the end of response lists because my 6th period was bonded quite closely!]
mr joyce is nice
he is a good teacher
he is doing his best so that we can learn in detail.
The teacher lectures are particularly interesting。
everyone is always positive

How does the teacher make you FEEL?

He makes me feel special and he is very nice and supportive
The teacher makes me feel like a part of class and I appreciate that he always answers my questions, whether it is related to the lesson or not.
he makes me want to learn and fell like i can share my ideas.
The teacher makes me feel like a student.
I dont know
He actually makes me feel smart, which is rare for me.
eh idk
I feel smart when I am in the class and I am always excited to learn something new.
i don’t know
very good
The teacher makes me feel like I could be confident in my good work.
Heś a very chill person and being in his classroom is a safespace for students
i can ask questions
He makes me feel happy, and he is always trying to interact with students, which is a good thing.
He makes me feel like I’m learning things
like a student? idk
Mr. Joyce is always positive, he doesn´t stress me out. He doesn´t put you on the spot, put picks you if you have a good answer which I appreciate very much. 🙂
like a student
He is chill
Comforting, very supportive
I feel normal around the teacher
The teacher makes me feel happy and upbeat.
He makes me feel relaxed and at ease.
I feel happy in this class, and I’m happy to learn in this class
He makes me feel like I’m doing fine in class.
happy/excited because he’s very funny
The teacher makes me feel good
He makes me feel like I am doing a good job when working on assignments.
The teacher makes me feel more calm on how he doesn’t embarrass someone.
The teacher makes me feel productive during class and always tries to explain every subject in lessons. Overall, I think this class was good and wasn’t too difficult or simple, nice difficulty level.
The teacher is nice and enthusiastic. He makes me feel good.
like I was one of the smart people in the class
Excited to learn
He makes me feel good when i get a correct answer or i am creative with my solving of it.
very nice and fun. good teacher and never makes you feel like youre behind
makes me feel like im learning
He gives me self confidence.
annoyed [bummer]
Makes me feel ready to learn new math stuff
good! hes definitely has left an impact on me.
acomplished when I do a good job or get a question correct.
Good, safe,
I felt great.
he makes me feel safe that i am slow at math as if i am not being judged.

How can the class be improved?

Maybe less conversations
(Overall, not just this class) I feel that the classes should be divided based off capability. As one teacher, Mr Joyce can only teach at one pace. However, with such pace, some students are being pulled back while others are being pulled forward. [honest feedback. More differentiation needed!]
For me I would not let my students make up all the work because when I as a student hear this i would not do my work and just do it later. Then I end up doing it all at the end. [true, hard to strike a balance between grace & deadlines]
Try not to pack in too many lessons in one day because sometimes it hard to understand all the material were being taught.
Unsure, very good class
I feel like some of the lessons would be more interesting in person but you can’t really help that
not as slow
I don’t think there’s a room for improvement here.
I don’t know
I don’t know
i’m not sure
in no way
students talking more so they can get along and help each other
do more math
If the teacher can help them he they need it
Class can be improved by allowing any student to answer the question. If they get it wrong, then the class can fix it together. [good feedback, afraid during distance learning they wouldn’t raise hand again or just ignore me next time I called on them]
Its good
I like the class as it is but idk how it can change to be better
uhh it’s great at the moment
Maybe if we went faster through the lesson and played more fun games and stuff instead of just the lesson, then it will be more fun.
I don’t know
Maybe more time to look at the problems but it’s mostly because we usually don’t have enough class time.
Sometimes Mr. Joyce moves too quickly and I think the material can be explained more thoroughly
i cant think of any ways
I didn’t see anything wrong with this class, it was very fun and i was actually able to learn something about math this year, so thank you. 🙂
it’s fine as it is
its pretty good the way it is
Maybe each slide can be explained quicker. [common theme: I’m either too fast or too slow]
it can’t, it is already awesome
Maybe go at a faster pace for in class lessons, sometimes I’m waiting for a while after, but understand that others may be slower. [again, this student though shows empathy]
More multiple choice, because along with the right answer I can see the thinking process of why the other entries are wrong
I’m not sure
paying attention
im not sure
he can calm down in little situations like someone on their phone.
Some rules
maybe a better discipline way [So, I didn’t do as much consequences or classroom discipline because the classes were so quiet. I assume these answers are from students who came to hybrid class and opened other tabs, distracted themselves and others, gchatted others, etc.]
People work together and speak more
more talking
Thereś no need for improvement.
I dont know.
It can’t. Mr. Joyce is a great teacher.
I think it is perfect!
Spend a little more time to explain solutions or explain slower sometimes
I don’t know
nothing needs improvement
not sure
the best
Let the kids answer more questions
I think that the class is perfect the way it is
Go at a faster pace on the lessons.
I don’t really know.
I actually do not know
Maybe if more people talked since usually it is the same people who get the correct answers.
I can’t really think of anything to be improved.
By paying attention and following directions.
The class can be improved by maybe explaining a bit better to make students understand. I think the class was very academic and can’t really think of much improvements.
I know things are different for this year, but I would have liked there to be more explanation on certain topics, or for him to check in with people with a quiz or something to see if they got it. And if we didn’t get it so teach the topic again or explain it in a new way. Also later on the classes were rushed and less fun. It was easier to learn when we just did one lesson per day. This helped me understand it better. Now it is harder to understand things because it has been going way too fast for me to understand . I know that there was some things we had to get through, but I didn’t like how that affected my learning and understanding. [This was honest feedback from a student who was successful all year. I am surprised at this because I feel with the faster pace at the end they were still successful, but I was clearly wrong there.]
Nothing the class is perfect
not sure
I don’t know
if the people on zoom were able to come into class so they can also experience it [I wish this too. No surprise, students on Zoom were more often a screen behind, not writing anything, while students in class could be more actively participating and monitored.]
Maybe we can spend a little more time on perfecting how we do a type of problem or when we learn a new skill.
not much other than giving a bit more time for certain questions and look at zoom chats more frequently
it could be slower
I think the class can be improved if there was more engagement. (requiring cameras on) [first student to suggest I should have required cameras on. But, if you require cameras on, what’s the consequence for having them off? I refuse to take points away, and I don’t want to waste my breath asking students to turn it on…?]
nothing honeslty
He can learn some patience and stop yelling so much, people that don’t have proper patience [Ah yes, this is the student that was very upset with me that they got called out for gchatting with students across room, opening other tabs to look at guitars, and I lost my cool with them. One of the few times this year. I gave 2 warnings before giving a consequence. Then the rest of the year they basically gave up on me.]
Doesn’t need much improvement, I think the class is already good
better expo markers to use and draw with.
I don’t know, I really understood everything we learned, and I enjoy being in class.
Make the due dates more clear.
the class should be bore interesting to make students want to learn and have fun
I don’t know
nothing really
study math
we don t need to we are good
You can try to get students to communicate more。
dont know

How were you able to raise your grade in this class?

I tried my best and mr Joyce helped me a lot!
Make up any assignments if I was in any way marked down.
Yes. Thank god
Work harder
By redoing my homework and communicating with you.
Doing the work
turn in things that are marked as 0
correcting practice problems
Correcting tests and homework.
doing work
Doing missing work
by participating
you can raise your grade by doing all your missing assignments
We learn math.
I was able to raise my grade in this class by doing my homework and classwork and making a Flipgrid for any corrections.
flipgrid, correcting stuff, and do homework
i didn’t
doing past work and emailing the teacher about it.
Corrections and getting work done.
He gave us opportunities to make up for missing homework.
Do test corrections and missing work
make up assignments
I was able to pay better attention and that improved my grade.
correcting practice problems
trying harder but class in zoom is very hard
I did my practice problems carefully.
by doing my assignments, trying to do it right the first time, etc.
Corrections were super helpful
remake of Homework and tests
re doing my home work for a better grade.
Focus more and show work more
turning in late work
Just completing the practice problems
easy homework and test corretions
Finish a few missing assingments
Participating, Homework, and being repectful
I used the corrections and made videos
I was able to.
Redoing assignments
By doing work
do my homework
i struggled to pay attention then got back to it
Test corrections
I always had an A so basically I just turn it all my assignments with effort.
Correct the tests, do the homework, and pay attention in class. That’s how to get a good grade.
I don’t know
by turning in missing or incomplete assignments
Redoing some homework and test corrections.
Work hard, do your best, and be responsible.
By correcting my practice problems and tests I took. Also, I pay attention to Mr. Joyce in class and videos he does for corrections, I understand that too to know how to do the problem next time.
Some ways that I did to raise my grades were to participate in class, do the work, and make corrections on my tests.
Mr. Joyce provided different resources for us to use and get full credit if we redid things.
Paying attention in class
keep doing work in class
Well participation and tellling the class the correct answers
do my missing work
By turning in late practice problems
correcting tests
doing work
I was able to re-do my missing assignments. Then I emaild my teacher and he allowed me to get some points back.
doing more work/cathc up
With test corrections
not rlly, i don’t get good grades unfortunatley =(
yes, after zoom.
By completing incomplete homework
Making up practice problems and homework.
he ALWAYS lets us do our assisments
with time
study math
the offender teaches well, but I don’t understand, that’s why it’s usually bad
Do more practice
dont know

If you chose to stay in distance learning for the whole year, why did you make that choice?

Because it’s easier, and it’s nice to be at home especially in the winter when it’s cold. Also it’s just better in general and I feel like that teachers care about u more. But also I feel like the teachers take advantage that you are at home so they give you many many assignments.
I visit my grandparents pretty often and I didn’t want to contract COVID for the safety of those around me.
None of my friends went back [I saw this was reason a lot of high schoolers chose to stay distance learning too.]
To stay safe from the coronavirus
I didn’t choose to stay in distance learning for the whole year.
Can’t wear masks for too long on hot days, gives something like a rash to face.
becuase i didn’t want to start going back to school in the middle/ towards the end of the year. I just didn’t find it practical
not to socilize
It was better for my mental health. I’m doing really well right now in online school with both grades and mental health, unlike when I was in person and both of those weren’t doing so well.
because i have an excuse to sit down and look at a screen for 4 hours
I didn’t stay for the whole year, i go thurs-fri
I did not stay in distance learning
i didn’t choose distance learning
I came to class so I didn’t get bored
my parents didn’t let me go back to school
I want to stay in distance because my parent want me to
I made a choice to stay in distance learning for the whole year because my parents aren’t able to drop off and pick me up from school.
because my mom said
i didnt
i went back to school which i feel helped me personally not be as distracted at home
I didn’t because it is boring to stay at home.
I felt more comfortable staying at home, than going back to school while we were still in the pandemic.
I was worried about covid
my mom was worried about the upcoming cases and how taylor would handle it
I did not, I was very happy i chose to go back in person.
am at home.
i thought it would be better but it wasnt
Just to stay safe.
I didn’t but if I did, it was because I didn’t want to socialize and wear a mask all the time.
I went in person.
I choose to stay in distance learning because I was supposed to be out of the country for a month during back to school which would reflect on my attendance. Distanced learning meant I could also be healthy from COVID.
im not sure
Online made math not fun for me, but when I came back it improved
to keep my family safe.
my parents didn’t were scared I was gonna be more exposed to covid
Mostly because I feel more comfortable at home rather than at school
The only valid reason would be because im lazy, in person would be much better. [Glad they were honest with themselves here.]
i was in school compa
Feel more focused at home.
If I did chose to stay in distance learning for the whole year, it would be because I haven’t been vaccinated.
Im in person.
My parents told me that in person is like distance learning. I thought “then, what’s the point?” [It’s true, we used laptops at school, so that students could work on Desmos from home and at a school. It was the best option I thought.]
I am an antisocial kid so I dont like interactions, especially with teachers.
Doesn’t apply, went to school for some classes
Because it’s good to interaction with other people and not be at home all day
I don’t have to get up early
no I didn’t
Because I was home the whole year I didn’t want to change.
I’m in the comfort of my home. aka snacks in class
I don’t want to get infected or my parents.
Because I don’t have to walk home every day for over 2 and a hlaf a mile every day.
The reason why I made the choice of staying in distance learning was because I love learning in my home with my family. [looks like a parent or 2 were able to provide home support and were able to juggle working from home themselves too]
I think that I felt safer since Covid was a serious thing.
I didn’t but since this is a required question in this survey, I gotta put something in here so I’ll say that I really enjoyed in real life learning and had a terrific time in this class.
I didn’t chose to stay in Distance Learning for the whole year because I went to school in person. Also, they might stay in Distance Learning maybe they have a lot of siblings and might be late to school or maybe because of the virus which is Covid-19.
I chose that choice because I felt safer at home during the pandemic. The timing was also uncertain during the time. The covid rates were higher than now which made me want to do online more. There are also vaccines now so if it was now, I would go back to school since it does feel better to be back in school and see people.
I didn’t chose to stay in distance learning for the whole year.
For personal safety
i did hybrid
I feel I should do some more homework
i did not because i wanted to say hi to my friends and get better grades
I did hybrid learning
a lot more convenient (as in not having to drive to school everyday) and since the school year was already ending in a few months (referring to spring when school was opening back up) it wouldnt have made much of a difference if I went.
its better
My parents were a little afraid when the option arose of whether choosing distance learning of in-person learning. Near the end of the year were okay with the option of in-person. I didn’t get to go in-person though.
I went to school to not get distracted like i did before on zoom
More flexible schedule between my parents and I
I don’t know, I just think it’s easier to stay at home.
Worried about getting covid and spreading it to others.
So I can learn more math on my own
it was more safe
i live 2 hours away from taylor
I did not do it
it was easier
study math
i didn t chose to stay at home
Ask the teacher more questions if I don’t know.
protecting my family and i

Anything else you want to tell me?

You are a very good math teacher!
I really enjoyed this year, thank you!
Your a really good teacher. I had so much fun in class this year.
Even if the class is behind its really hard to keep up and understand two lessons, so maybe just keep it to 1 lesson every class instead of adding on another lesson.
I have never never been with you in person so i don’t know how your breath smells
Honestly, you’re probably the best teacher I’ve ever had. I really enjoy coming to your class. You’ve improved my mental health quite a bit. I’ve never liked math but this year it was really fun. I really can’t thank you enough.
Thank you for being an amazing teacher!
i’m considering a stem career, probably something with space
nope your a good teacher
You are the best teacher ever
Thank you bring my 8th grade math teacher.
nah but you’re a great teacher
thank you for being one of the best teachers i’ve had throughout these past 3 years in middle school. i really appreciate how i can be open with you; how i feel like i could tell you anything. i like your sense of humor, the way you treat your students, and overall your teaching put together. again, thank you for being such a great teacher. you actually made me like math.
I think you are a great teacher, keep it up, just go a little bit faster.
Thanks for being a great teacher!
mr.joyce good math teacher
If the 1-5 rating scale looks suspicious or like i didn’t care about this, then I want you to know I chose honestly.
Mr. Joyce, I really enjoyed your class. For 6th and 7th grade I didn’t really learn much with my other math teachers but you made math interesting for me. and I really appreciate your teaching methods, You made me feel smart. Thank you for that.
(and also I know the late assignments may have been annoying for you but I truly appreciate you being patient with me. 😀 )
I can now go into highschool less stressed than I was, I was terribly worried about the math content in highschool but now I realize that math is just harder one step at a time, and I just have to look at it a certain way to understand it.

I´m gonna miss you, Thanks for being an awesome teacher and an awesome person, Mr. Joyce. 🙂

Nothing really.
to have a great summer break
no, but thank you!
i loved your class 🙂
Thank you for this amazing year teaching us math!
I hope you don’t retire next year. Your a great dad.
Nope you are perfect Mr Joyce thank you for an AMAZING year!! 😀
N/A, I think you did a great job teaching aside from a few moments. Thanks for making math fun for me again!
I love your teaching and I wish I could have a teacher like you in high school.
Thanks for being my math teacher, it was pretty good.
Have fun teaching next year.
nope not really.
I would like to say that I really enjoyed your class and learned a lot of cool things and that my enthusiasm for math has not dampened at all and to keep doing a great job.
I want to tell you that you are the best math teacher I had of all my middle school year, best than 6 and 7th grade because I can understand a lot by you.
Not really, but have a great summer!
Overall I enjoyed this class, even though somethings weren’t perfect.
Nothing else
Nope great year! Also I like raising my hand if I understand so you can call me all you want!
I think everything was pretty much covered.
the bad breath question i just put 1 since ive never met you in person so i cant say. good teacher overall though
nothing else
Stop yelling at everyone just calm down your temper, no one has a good day when you get all angry, take a deep breath and talk to us like humans, and stop being so aggressive, seriously calm down [Ah yes, this student again. It’s clear that one time of being upset with a student can erase any previous good will. I will apologize in my closing email for the year with this student.]
You did good teaching
although all of my answers are mostly 5’s, I truly mean it. You’re genuinely one of my favorites, and I really enjoyed my time doing hybrid in your class. thanks for having me!
not really
You have great dad jokes!
i like math but i don’t understand english because i am not good
You are the good teacher.

I also asked two multiple choice questions and here are the pie graphs from those:

On my practice problems I…


The context of this, is for every Desmos lesson I assign an accompanying practice problem set. The last slide checks their work. I recorded a screencast for every single set so they can fast forward through to problems they got incorrect and get an explanation.

After my 8th grade year of math my attitude towards math…


In summary, this years feedback mentioned a lot less about me yelling or losing my temper. That’s something I have always worked on improving. I think it’s easier to get upset when you have a full class of students in person, and it doesn’t happen often in distance learning or hybrid because it’s usually so quiet. It can be quite frustrating though when students don’t reply to private Zoom chats, ghost you, or write in an answer but refuse to unmute and read it to the class.

I am very proud of the comments talking about the “chill” environment I provided and how it felt like a community. Those are difficult things to create, especially through Zoom.

Once again some of my lowest rating were pace. Though my colleague did mention, that it’s a positive if you’re getting a mixture of feedback on it. Like, if they’re all saying I’m going too slow, then I’m going too slow for sure. If they all said I was going too fast, then it was too fast for everybody. I think a cure for this would have been doing more pacing of multiple Desmos screens rather than going one screen at a time for pretty much all of it. My 3rd period had 23 students, and 5 actively participating and understanding. I would wait for the 6th 7th or 8th students to finish so I could get them to share and then move on and not keep calling on the same people.

This whole idea was suggested in his book Classroom Chef. It’s scary to give this out. They also suggest giving it in the middle and the end of the year to act on the feedback. This year I only gave it at the end.  Also, students may or may not realize it’s anonymous because there’s no field for them to put their name in. As the survey says at the beginning, be honest. Our students know us best. They’re with us everyday. We need to listen to their feedback. And I’m going to #pushsend and share this with the world because I can look back on it later and see if I’ve made the choices to refine my craft.

HyperDocs to Enhance Classroom & Distance Learning

In this blog post you will find a recording of my presentation from the CMC South 2020 virtual conference as well as my slides that includes links to all of the resources. This blog post will be updated with a link to the article I wrote summarizing this presentation in the March 2021 issue of the CMC Communicator.

Here is a link to my 50 minute Loom video asynchronous digital presentation of the ideas from the slides.

Click here for a link to make a copy of the Google slides.

Math Elective & Desbook Grade 7 Unit 1

As some of you know I teach 4 Math 8 classes (using the Desmos Middle School Math curriculum inspired by IM/Open Up) and 1 Math “Elective” with a majority of one of my Math 8 classes mixed with some 7th and 8th graders who are in RSP Math. I’ve previously blogged about how I taught students how to play the card game SET with an amazing activity made by Greta.

I have also used other freely available activities with my elective class such as Mini Golf Marbleslides to review plotting coordinates, Pop Music, Electricity Generation, & E-Cigarettes from the Desmos / New York Times “What’s Going on in this graph?” series, The (Awesome) Coordinate Plane, Polygraph: Points, Polygraph: Shaded Rectangles (fractions), Des-Farm (great activity for Grade 6 on ratios), Balloon Float (happens to be from Grade 7 Unit 2), Click Battle, and Area of Rectangles by Nathan Kraft to name a few.

We’ve also explored some engaging topics using Jenna Laib’s SlowRevealGraphs.com.

We have also done one collaboration with a local 5th grade class on Zoom where we investigated Fraction Talks, one of my favorite activities that I’ve blogged about before.

I couldn’t resist digging into some of the Math 7 curriculum with mt elective. This blog post is to share about some of the lessons.

Desmos’ Grade 7 Unit 1 launches with an activity called Scaling Machines that is freely available.

Lesson 2 is Scaling Robots. This one is awesome. Students warm up by creating their own robot face by dragging sliders that control height, width, eye distance, and the antenna. Here’s what they came up with:

Then students are given a table with their robot measurements and are asked to create a scaled copy giving a height that is double their robot’s height for the “Copy Robot.” Then it offers some visual feedback so students self-assess how they did. Slick. Students then analyze a table of a student’s work and answers if they made a scaled copy. After they adjust the values to fix it and make a scaled copy. We laughed at a students work that used a scale factor of 1000, making the copy impossible to see, but they could still see the green checkmark positive feedback. Another slick screen is another common Desmos strategy: pick the parameters you want to change to plan how you will fix a scaled copy, and then execute your plan. It was really cool to take snapshots of all of the different solution pathways. Loved it.

Lesson 3 is “Make it Scale.” This lesson inspired me to figure out how to make animated GIFs of the activity. In short, I used Loom to capture a portion of the screen and then I used ezgif.com to take that MP4 and convert it.

The activity starts with an awesome Which One Doesn’t Belong prompt. Then students select a rose, whale, diamond, or bee to sketch a scaled copy of. I like how the color selecter on this next screen then limits the color options to only the colors necessary. At first they sketch it without a grid, and we discuss the strategies they used. Then they are given a grid and of course accuracy increases a bunch.

The rose.
An 8th grader said they thought of the diamond as a reflection to make sure the left side mirrored the right side. Great connection.
I told students that the bee was the most challenging. A student talked about getting the height of the triangle on the right side of the wing and then realized they had to double the distance the triangle went to the right also.

After that they make a sketch of a trapezoid but get to select their scale factor with a slider. Really cool built-in differentiation. In my 8th grade class I also encourage this differentiation. One example is when students dilate a shape and select the scale factor that suits their level of understanding. If you feel you haven’t mastered it, do a scale factor of 2. If you can handle more, try 1/2 or another fraction. If you want a bigger challenge try 1.5.

I have taught the 7th grade Open Up Curriculum a few years back and it’s cool that they have still included some of the same cool-downs.

In lesson 4 students do Scale Factor Challenges where they get feedback on how to undo a dilation or go in reverse. They also sketch and get feedback on how their sketch scales.

Lesson 5 is Tiles where they again personalize their learning by picking the colors and placement of them on a mosaic that they then scale. The goal of this lesson is for students to see that when you use a scale factor, the area gets multiplied by the scale factor twice, or the scale factor squared.

In lesson 6 students are introduced to scale. One cool part is in the warm-up students calibrate their screen by holding up a ruler to a caterpillar that is 4 centimeters long and adjusting a slider. Nice touch. Students scroll through different small and large shapes and make the connection between scale factor being how many times bigger a shape is than another shape while scale compares a real life measurement to a grid square.

I had a short 30 minute period on Monday so we did Paint, which was recently released and is the first lesson of Unit 2. Be sure to ready the #desmosified Blog series about the thought that was put into beefing up the IM/Open Up lesson.

I did this because the last lesson of Unit 1 was Scaling Buildings and knew I would need a full 80 minute period to get the most out of it. This lesson is really thought out well. I love it. It starts with a scale drawing of the Arc de Triomphe in France that is 50 meters tall. It’s on a grid, and students are asked to find the scale, or the value in meters of one unit. Really great lead up. The illustrations of famous buildings in this activity is amazing. Students were able to give input on ones they knew about and it even motivated me to Google some of them for real photos in real life. Some students are able to guess and check some of the answers because they use a slider to adjust the height of the building after given a scale drawing on the left.

I am thoroughly enjoying digging into the Grade 7 curriculum, the Desmos team has put a lot of thought, effort, and ingenuity into it.

Desbook U1L7 Are they the same?

This lesson is where students start to develop their definition of congruence. It starts out with the similar warm-up from the original Open Up lesson where students select all of the left hands. Then they are shown pairs of figures and must select all the pairs that are the same. Then in teacher view I looked at which were the most popular and like the lesson plan suggests hear arguments for why they are or aren’t the same for each pair. This shows the need for a more precise word or definition of “the same.” It leads to the definition that two figures are congruent if you they can be lined up after a sequence of rigid transformations. I then asked students, “what can be different about two congruent figures?” They came up with location (which can be fixed with a translation) and orientation (which can be fixed with a reflection or rotation).

On the next screen students take a closer look at pair B to say what is and is not the same about it. Students figure that they are the same shape, same angles, but are not the exact same size.

In activity 2 students look at six polyominoes. Again, they are asked what is the same and what is different about them. Students said they had the same area, but the square that is sticking out is not always in the same place as the others.

Then students are asked to select all of the polyominoes congruent to A. I could see on my summary view a check mark for those that had all of them clicked. Then to review the requirements for congruence we worked together to give all the details necessary to write a sequence of rigid transformations to make them line up. Students need practice including the center of rotation.

The lesson is synthesized by referring back to the pairs of shapes in activity 1 and asking, “How can you determine if two shapes are congruent?” Some students sketched C on the shapes that were congruent and NC on the shapes that were not congruent. I pointed out students who mentioned that you could use rigid transformations to line them up, and if you could do that, all of the other requirements would be true like the same shape, area, side lengths, and angles.

The cool-down asked students to see if two ovals were congruent. They were slightly different and they needed to measure and compare using the sketch tool to see this. It’s a great lesson and I like how they used polyominoes.

Desbook U1L6: Connecting the Dots

So far, this is one of my favorite lessons from Unit 1. It really works on challenging students to precisely describe a sequence of rigid transformations. I have read the first few chapters of Amanda Jansen’s Rough Draft Math (thanks Open Up Resources for the free copy for attending the amazing HIVE conference) in that I asked students to write a rough draft and then together combine our ideas into a more polished draft. I did this by taking snapshots and then annotating the graphs and adding more text. It was also my way of using the MLR Stronger, Clearer, Each Time. In an ideal world I would have done breakout rooms for students to share and revise in but we did it whole class instead. Goals for the future!

On the warm-up students are asked to move the moveable point to the center of rotation and describe the rotation. These interactive screens are really cool. It allows for some guess and check and allows students to articulate how they figured it out. I pointed out a student that said, “I put the dot on 2,1” to show that not only did they find the center but they reported the coordinates, and reminded them to write it with parentheses around it. Sometimes the self checking practice problems screens mark it wrong if they don’t put parentheses and it is an important convention. I pointed out a student who correctly said 90 degrees, and finally ended with a student who mentioned 90 degrees and the direction, counterclockwise.

On the next screen they had to describe this sequence. As you can see below, I took a snapshot of a student who correctly sketched the triangle ABC reflected. I also recognized that the person didn’t just say move the shape, they said reflect it and the translate it. I then prompted the class to say what further details must we provide for a reflection? A student said the x axis. So I drew that horizontal line and labeled it x. They said they knew that because the x coordinates did not change and it all lined up. I then said how can we be more specific for the translation? They then said you should say 7 units to the right and I showed how I counted the grid squares with the dots. I then set a timer for 1 minute for students to do their second draft of their sequence.

Sequence #1 required a transformation.

While the sequence below was a little more complex, I did want to honor it in that it was also a correct method. This conversation involved talking about labeling the center of rotation with a letter and mentioning it in the sequence as well as labeling it on the graph. Again, while they did draw their line of reflection, I mentioned that it’s good to once again label it on the graph and mention it in the sequence.

Adding labels to the graph.

Here is the next sequence students had to work on. I honored an uncommon approach before reviewing the most common approach.

This student saw it as a reflection over the diagonal line M.

To synthesize describing sequences, we went over the requirements for each transformation. As you can see, the approach below was rotating 90 degrees clockwise around the origin, and then reflecting. Eventually these ideas will be integrated into a unit anchor chart they can refer to.

On screen 4 students are shown a diamond preimage and image. The student Amari says it’s a reflection and students have to agree Yes or No and justify. Most students said no, because the corresponding points were in the incorrect place. They said they were in the correct place if it was a reflection.

On screen 5, students move the 4 points of a quadrilateral to show a 180 degree rotation around the origin. Students had a tough time articulating how they correctly placed the points. I tried to watch my teacher view and take snap shots of students that were reflecting over one axis, then the other to aid in their explanations. I wanted to reinforce that although it’s challenging to visualize, we can think of this type of rotation as a reflection over each axis.

Then came my favorite screen, the Class Gallery. Students were to create a challenge and then solve each others. It’s really cool to see students motivated to solve problems that their classmates create. Julie Reulbach wrote a blog post that has a link to an activity collection that has activities with this Class Gallery feature. It’s literally one of the coolest Desmos features.

As I suggested in this tweet, my goal was to create a Flipgrid prompt so that students would record themselves creating their own challenge and solving one of their classmates. I recorded myself using the website Loom demonstrating how to do a screencast recording using Flipgrid. I encouraged students that the goal of the project was to verbally explain how you knew where to place the transformed points in your challenge and how you knew how to solve someone else’s. No pun intended, but this was a real challenge. I’d love to share some of the examples but the videos use their real names, but I can at least show you the prompt I used to attach to the Flipgrid prompt and it gives you a sneak peek into the activity:

The lesson synthesis is so simple but so complex at the same time: “What information do you need to precisely describe a transformation?” This allowed me to snapshot students who could contribute some of the requirements for each transformation that I went over earlier in the blog post.

The cooldown gives a sketch screen where students translate point A, and give the coordinates of the image. Then they reflect A over an axis and rotate 180 degrees using the origin and give the coordinates of the image for both.

Like I said, this was one of my favorite lessons of Unit 1 so far. By asking students to create the flipgrid, it helped build community because they could watch each others and listen to each other’s voices. I was also able to post a link to a successful students video as an example of someone meeting the expectations. I also got to use the Google classroom private comment feedback feature to give students comments if their audio didn’t work or any other technical difficulties. I love activities with the Class Gallery. And I also love asking students to record a Flipgrid because it makes me feel more like a teacher and it feels more like a community during distance learning.

Desbook U1L5: Getting Coordinated

In this lesson students apply transformations to points on a grid if they know their coordinates. It starts up with a warm-up where a shape on the left is reflected over a vertical line. Students are asked to place the corresponding points correctly on the shape on the right. The main stumbling block is students placing the points as if it was a translation, and us discussing why the points have to be on the opposite side.

Then students reflect a triangle across a vertical line with no grid, and then with a grid. Then they get a graph overlay to show what they notice about the reflections. As you can see I used the Zoom annotation features to point out the interesting mistake someone made with the grid, clearly misinterpreting where the y axis is and students said the person reflected over the x axis.

I wish on this screen or after this screen there was a chance for students to explain exactly how the grid helped them place the accurate reflection, outlined in green, correctly. Before talking about coordinates, I wanted students to articulate that it helped because you could count how many units the triangle was from the y axis and put it that same distance away on the other side of the axis. I feel the lesson jumped a bit too quickly then to then analyzing what was happening to the coordinates in a reflection on the screen below.

This lesson was definitely inspired by the activity Blue Point Rule where users drag around a point that gets transformed instantly.

In my first class students were rusty with plotting points in the coordinate plane and I did not start my school year with Polygraph Points and reteaching the coordinate plane which showed. The picture above is from one of my later classes.

I annotated how the coordinates of the red pre-image were (4,3). I explicitly stated and typed that 4 is the x coordinate and 3 is the y coordinate. I tried using some #purposefulcolor to show that that 4 comes from 4 spaces to the right of the origin on the x axis and the 3 being 3 units above the origin on the y axis and that point being where they crossed.

Many students did not mention which coordinate stayed the same and some said “it turned negative.” So, I made sure to drag the pre-image to the left side of the y axis to point out that look, now it’s not turning negative… so how else can we describe this? This pushed students to revise and say the x coordinate becomes the opposite while the y coordinate stays the same.

Actually, instead of rephrasing what they said, I’ll pull some direct quotes from my snapshots tab:

  • “The black point is the opposite of the positive point”
  • “you keep the same y coordinate, however change the x coordinate to be either a negative or positive number”
  • “If the original coordinate is (4,2) then the opposite coordinate would be (-4,2). So every opposite coordinate has a negative sign.”
  • “The Y coordinate stays the same, but if the x axis is negative, make it positive and if it is positive, make it negative.”

Then students apply the rule to reflect a triangle across the y axis. I love that they made it a triangle that overlaps the y axis to make it more challenging.

Then students investigate a translation by dragging a point around. Here’s some responses I highlighted:

  • “It moves down 3 units and left 4 units.”
  • “When the red goes to 0,0, the black dot goes to -4, -3. The difference from the red to the black is four across, three down.”

I definitely pointed out this students strategy where they moved the red point to the origin and the coordinates of the translated point really show how the transformation occurred.

They apply this translation to a different triangle and then move on to the most challenging transformation, a 90 degrees counterclockwise rotation around (0,0). Once again, I would like there to be a chance to honor their intuition in how to do this, like turning their head sideways to visualize it, before jumping straight to how the coordinates are effected. I have also had conversations with one of the assessment writers of the IM 6-8 curriculum, Bowen Kerins, about interpreting how deep the standard is here. I recall him saying that they don’t have to memorize a rule but to notice what happens to the coordinates during these transformations.

Here’s what students said about the rotation’s effect on the coordinates:

  • “numbers would be switched and one of the numbers would be a negative”
  • “switch x,y place and y is opposite”
  • “If the red image’s x-axis is 2 and the y-axis is 8, the black image’s x-axis will be the 8 and the y-axis would be 2. In other words, they would be switched.”

After applying the rotation to another triangle, the Lesson Synthesis screen arrives. I like that once again it provides three choices to respond to which allows for a wide ranging discussion. They select either a Rotation 180º clockwise around (0, 0), Reflection across the x-axis, or a Translation right 3 units and up 5 units. After clicking their choice they get a point that reacts to the transformation like the earlier screens and they need to describe what happens to the coordinates. For the reflection Kent said, “the y is the same number but the x is going negative so the number turns negative.” For the translation Liv said, “add 3 to the coordinate on the x axis then, add 5 to the coordinate on the y axis.” For the rotation Charlotte said, “The coordinates are corresponding by switched negatives and positives. the two coordinates move like a straight line, but have different numbers. Examples are if the red coordinates say -7,6 the black coordinate is 7,-6.”

The cool-down is a triangle in the first quadrant with its vertices labeled as the preimage and the image drawn as a reflection using the x axis. There is no grid so they really need to know what’s happening to the coordinates. Students are asked to label the coordinates. I watched my teacher view to remind students to put parentheses around their coordinates with a comma in the middle. Some students did some bizarre things here like making both coordinates negative or putting the coordinates in the wrong place as if they were a translation.

This was a challenging lesson for students and this is the point in the unit where I started making screen recordings reviewing the practice problems to answer questions and to encourage students to correct it after trying it independently.

Desbook U1L4: Moving Day

For this lesson it was supposed to be a paper lesson. Luckily Desmos created a Facebook group for those teachers piloting the curriculum and I asked if anyone had digitized the lesson. One person replied and I used her activity. Thanks Mrs. De La Fuente!

In this lesson students started with a warmup where they noticed and wondered about a square grid compared to an isometric grid. This really needs to be done with paper because when you do this warm-up with the Open Up Resources workbooks students start seeing many different shapes in the isometric grid which provides a rich conversation. The goal either way is to get students to realize that they are all equilateral triangles which means their angles are all 60 degrees each which is crucial to understanding rotations on an isometric grid.

On the next screen students watch an animation of a reflection and are asked to think what the prime (‘) means in terms of transformations. Students think it’s the result of a reflection. I had to clarify that it doesn’t necessarily mean it’s a reflection, it means it could be any type of transformation and is the corresponding point. They were introduced to corresponding sides and points in 7th grade.

In the next activity they are asked to sketch a translation before clicking a button that animates it to check their answer. It was important to keep an eye on teacher view to snapshot students that drew the lines or students that drew the corresponding points first, highlighting 2 ways of approaching it.

Doing a rotation digitally without tracing paper is a tough task! I really miss this from in person learning. A 180 degree rotation can be hard. It’s also important to point out that it’s not the same as a single reflection. I tried to get students to articulate how they can rotate one point and then visualize where the other nearby points are in relation to it.

Then they had to do a reflection over a diagonal line of reflection on an isometric grid and reflect if it was easier or harder than the rotation. Finally they did a 60 degree rotation on isometric grid paper which wa the purpose of the warm-up. The lesson synthesis asked students to think about how grids helped them perform each of the transformations. It was a short lesson so we were able to start on some of the practice problems together after that.