Family Math Night Agenda & Reactions!

Tomorrow is the big night. At 7:00 PM, prior to the PTA’s meeting, myself and my colleague Mr. Rodinsky will introduce our curriculum to parents and possibly students. I read the blog post by Illustrative Mathematics and some of the slides from our True Talk with Open Up Math Gurus Global Math Department webinar.


  1. “What does it mean to you to “do math?”
    1. Write down phrases and words from students and parents on chart paper.
  2. Program Overview
    1. Core Curriculum with units divided into big ideas, 45 to 50 minute lessons with 2-4 activities with predictable structure
    1. Assessments: Pre-unit diagnostic, cool-downs, practice problems, mid and end of unit assessments
    1. Problem-based (solve problems to learn vs learn math to solve problems), 5 practices framework, support for all students, Are you ready for more? extensions
    1. Overarching Design structure
    1. Structure of a lesson
    1. Instructional Routines, MLRs
  3. Experience a Lesson: Grade 6 Unit 6 Lesson 9
    1. Learning Goal, Number-Talk warm-up, Synthesis
    1. Activity 2->Synthesis, Activity 3->Synthesis
    1. Lesson Synthesis and Cool-down
  4. Grade 7 Unit 6 Lesson 6 Which One Doesn’t Belong Warm-up
    1. Short preview of the Card Sort from that lesson
    1. Sample student work
  5. Grade 8 Unit 4 Lesson 5 Taking Turns Solving Equations Preview activity
  6. Show Student & Parent resources on and connection to Grade 6 Activity
  7. Reflect on original question: “What does it mean to you to do math?”
    1. What did it feel like to do math tonight? What felt different from your school experience? How might this approach improve learning and understanding in math?

After writing up that overview of my slides, I’m starting to think about trimming down on some of the details that I think interest math teachers more than parents. Any feedback is welcome, I will revisit this blog post after the meeting happens tomorrow. Also, this was one of my professional goals to reach out to families and improve the line of communication about what is happening at our school and inside our classrooms.


Family math night went great! It went for about an hour, than an extra 10 minutes for some answering of questions. Thank you to the PTA for providing time before their meeting for it. I think it’s a great idea to partner with your parent association to make events like this as successful as possible.

The opener was great. I wrote what students and parents were shouting out in orange. Then at the end, when we reflected on the math we did and this original question, I circled ideas that we did. Parents weren’t sure we had done geometry, until I lingered before circling and then they realized that the distributive property was the area model of a rectangle, which indeed is geometry.

I also asked, are there words or phrases we can now add to this list? Those are written in green. They said that they were “cooperative, collaborative, challenged, visual, think time, etc.” I asked if I checked for their understanding; which was the cool down exit ticket.

The curriculum program overview went well. I didn’t talk much about the Math Language Routines because I think that would have been more depth then what was necessary.

We then looked at the learning goal of Grade 6 Unit 6 Lesson 9. I remembered to give the parent and students credit by writing their names next to their method. One parent came up to show how they did the standard algorithm. Before I had them start activity 1, I reinforced how their methods were basically the area model, decomposing a rectangle into pieces.

Then we reviewed the answers. Like I anticipated, parents weren’t used to seeing a prompt that says “select ALL the equivalent expressions.” As I walked around, some people had stopped after getting one answer so I prompted them to look at all choices. I also made a connection to SBAC testing where they will see these types of questions, as well as on the End of Unit assessments. After starting the activity synthesis with an answer they were confident with, I followed up with then what can we eliminate and why?

Then I had everyone start on the next activity. I wanted to model Think Pair Share, so I asked everyone to work quietly and individually for 2 minutes, then I asked them to work with a partner to see what ideas they had come up with. I cut them off about 4 minutes after that. Now I wasn’t going to discuss all the correct answers, so I opened it up to ask what interesting patterns or structure they saw.


One parent said they liked the last 2 rows because it was challenging. I asked them if there was only one correct way to do the last row? He said no. So I agreed that I thought it was kind of a cool potential conversation to have about multiple correct ideas.

On the flip side, a parent spoke up and said that they didn’t see the value in the last 2 rows. They felt it would confuse students who don’t understand the basics. The parent thought that if you know 9+12, why do you need to go backwards and fill out the rest? I tried to explain that if students see non-routine problems like this, they can deepen their understanding and understand the structure of the distributive property if they can go backwards as well as forwards. Please add any suggestions in the comments about this.

I also mentioned that the 3rd to last row had fractions, which was a great time to review content from Unit 4. The row above that was decimals, which was a big chunk of Unit 5. Another opportunity to review.

I told my audience that this is what makes this curriculum so special, and the top-rated one in the country. The people that designed it are smarter than me. I trust them. My old brain thinks when we finish a Unit, we are done with that topic, and I kind of freak out. my new brain has not freaked out as much this year because now I see that topics are revisited. They especially will be revisited if you make time to have students do practice problems. Later in the Q&A session the parents were wondering about lack of homework. I said that that the homework policy is up to the teacher. Personally, I said, to deliver the best and most thorough lesson possible, I can’t if I’m spending time checking and discussing practice problems. Therefore I do not assign them, but do for a study guide before a unit test.

I then discussed how we did the lesson synthesis as a class, but didn’t spend time on it. Then we passed out the cool-down to show how we check for understanding, and then reviewed the answer quickly.

Then I launched into another routine that I love, Which One Doesn’t Belong:

I should have discussed it more, but I had this hung up and barely discussed that these were sentence frames that help ALL learners. D’oh! Forgot that. I did give 1 minute of quiet think time, and then had people share. I also reminded everyone that there was a reason why each did not belong, and that you are correct as long as you explain why it doesn’t belong.

One parent said the top right didn’t belong because it wasn’t the same equation as the rest. I saw a parent in the front row who had solved all the equations before I even had talked about the prompt. So I asked him if he could provide evidence based on the work he had done earlier. He showed how the top right got a different answer then the rest. So, I infused some vocabulary and said that it was the only one that didn’t have the same solution.

One person said the bottom left had a dot, the rest didn’t. I reiterated that in 6th grade they lose the dot and start writing “next to notation” like 4x. This can be a bumpy transition.

Then I briefly talked about the card sort that followed, and emphasized that there were different correct ways to categorize the cards.

Finally, I talked about the 8th grade activity of taking turns solving equations. They saw that that reinforced more collaboration, and allowed some room for choice, partner practice, and finally individual practice in class.

Then I modeled how to go to the parent section of the Open Up Resources web site to see the explanation of the topic, and a task they can try with their kid.

I also slipped in a slide from Fawn Nguyen that is in my Back to School Night slides 20 minutes before the presentation. It helped me end the presentation with a bang and some useful advice. Here it is if you’ve never seen it:


For the Q&A session, I started by talking about our procedure for selecting the 32 students who will take accelerated math together over their 7th and 8th grade years. That will be another blog post…

Another question was what curriculum would students take for Algebra 1 in the 8th grade accelerated course next year? I did not have an answer for her yet… because it is not clear if Open Up Resources Algebra 1 by IM will be ready by the fall, and it could possibly be MVP math in the fall, the other curriculum that Open Up will be publishing.


Parent Quotes:

“You did a WONDERFUL job Martin – thank you again for planning the Math Night! I’m so glad it was a good turnout. Thank you for having sent reminder emails to your students. The math night was a good refresher for me, and it also nudged me to see math in a slightly different way. I also hope to make use of the Open Up Resources web site, it’s a great tool, and I wish this event happened even earlier in the year!” -PTA President

I will definitely be using some of the materials on Unit 1 from the IM blog post I linked at the top of this blog post earlier in the year to set students and parents up for success earlier in the year.

“Hi there. Thanks for taking the time to do the math presentation, I really enjoyed it. I also am glad to know about the do more work (Ed note: I think she means the “are you ready for more?” challenges.) as I am encouraging Sarah to do it as extra practice.” -parent of 8th grade student, PTA member


Grade 8 Unit 5 Volume: Lesson Synthesis

I am a big fan of Open Up Resources 6-8 Math’s Unit 5 in grade 8. The unit is broken in half with a mid-unit assessment that deals with functions. I also saw a student finally understand slope after it was introduced in Unit 2. This curriculum really does revisit concepts later on!

Students review cubing a value when they look at the volume of a cube when an edge length is known, as well as the circumference of a circle from 7th grade. I also really like how they introduce a non-function where there is more than one output for each input with this warm-up:

In the second half of Unit 5, students carefully learn volume. They make connections to volume of a prism from 7th grade, and a warm-up reviews all of Grade 7 Unit 3, Circles, in about 10 minutes. Once again, they try to address “unfinished learning” and assume students are rusty and forgot. Students and teachers alike appreciate this, I can attest to this with my own opinion and surveys from students last year.

It also launches the second half of the unit with Lesson 11: filling containers where students have a hands-on activity filling up various amounts of water in a graduated cylinder, collecting their height and volume data, and then graphing it. Here they reinforce volume depends on height, and it’s a proportional relationship. Revisiting previous learning, in a new context.

In Lesson 12 students do a lot of estimation. Of course I love this since I used to do Estimation 180 everyday for my warmup. It also gets students brainstorming about units that volume is measured in.

What I really like the most is students don’t jump straight into finding the volume of a cylinder. They actually work on finding missing dimensions of a cylinder, and later a cone, to really get their feet wet looking at the structure of the V=B*h formula once it’s expanded into V=pi(r^2)(h).

Also, I like the video they use for discovering the cone volume formula. Here’s the video below if you haven’t seen it:

How Many Cones Does it Take to Fill a Cylinder with the Same Base and Height? from Open Up Resources on Vimeo.

(and link to the lesson)

At the top of the board you can see how students estimated if a sphere was less than half, more than half, or equal to half the volume of the cylinder it was inside. I suggest a private heads down vote to get truthful and diverse opinions. Then after the video they know if their first intuition was correct or not.

Before tackling hemispheres and spheres, students looking at how the graph of scaling one dimension (height) and two dimensions (the radius, since it’s squared). This reviews a concept that I know my students I had in seventh grade last year struggled with. Seeing that when you scale a shape by 2, the area is scaled by 2^2, or the square of the scale factor. This is revisited here. Next time I teach this unit, I’ll make sure I give enough time for them to finish their graphs, because I stuck to a lesson a day for those and kids were pretty slow at it since they had to compute some values, then set up axes, then graph it.

Here’s the video for discovering the volume of a sphere formula:

volume of cylinder sphere and cone from Open Up Resources on Vimeo.

Here’s what one class noticed and wondered:

I did see this video on twitter from Cathy, but I still like the video above because it includes all 3 shapes and their relationships. This video omits cylinders.

Note to self for next year: have all students with phones download the Desmos Test Mode app. This allows them to use their phone as a calculator, but locks it and uses a timer so they can’t get their Snap Chat alerts or switch to other apps.

Unit 5 lesson 21 involves a lesson synthesis where groups of students answer 8 essential questions. We didn’t have time to complete this in 1 day, so it extended to 2 days, which I attribute to working on an info gap routine and synthesizing the activity by discussing the two methods of solving for a missing volume and finding missing dimensions.

Day 1 was the warmup, info gap, and assigning pairs of partners to at least 2 posters per question.

Day 2 was finding the radius of a sphere given the volume, an optional activity but definitely worthwhile to reinforce how to deal with a 1/3 or 4/3 in an equation. Then students presented their lesson synthesis questions by standing up as a group. One way I modified this was each table had one question, but they worked as 2 pairs to complete the work so more than 1 person could be writing at one time. I also didn’t want each poster to be the same work, just different examples. This worked out pretty well!

Enter a caption
In each class I tried to focus on this poster, because it was a big question and concept on the upcoming Unit 5 test.

I’m really proud of what many students came up with on their synthesis posters. It was a really good time investment, and a great way to review or learn it for the time before a test. Here’s an anecdote I tweeted out about how one student was solving for volume of sphere on her cool-down:


Desmos Graph 3D Printing Presentation (Slides, handouts, screencast, samples)

I had a great time presenting about this topic at CMC South and North. I was scheduled to present it at Taste of TMC Norcal but my time slot was the same as Howie Hua and Paul Jorgens & Richard Hung so no one came, which made me happy because I got to see Paul and Richard kill it with Desmos and Open Middle activities.

I did want to submit this proposal to NCTM San Diego, but I couldn’t justifying the funding. I did submit this proposal to this years TMC (Twitter Math Camp) being held nearby in Berkeley, CA.

Quick Links:

I am really happy how it went at CMC south. I thanked my audience for coming because I was in the same time slot as Jo Boaler. I got some ideas from the audience and they were really into the presentation. Participants were at round tables and definitely helped each other and I was able to circulate and answer questions. I took Matt Vaudrey’s advice and had music playing as people arrived which created a calming atmosphere. Here’s the feedback I got:

Question Name Choice Value / Answer
The ideas, skills, and strategies shared in this session will be useful in improving student learning
4: strongly agree. 6
3: agree. 1
2: disagree. 0
1: strongly disagree. 0
Mean 3.857142857
What did this session provide that will positively impact the teaching and learning of mathematics?
I loved this! I was so engaged, and my students will LOVE this! Adaptable to any level!.
I loved it! I will take this activity back to my class next week.
Principal has been begging math dept to use 3D printer. I did not like any of the drag and drop images the students could just “use”. This lesson is what I have been looking for . With a bonus of applying to all levels (Alg 1 – Calc) of my classes
How to utilize Desmos for students to create something tangible.
I enjoyed seeing something different, that’s practical but uses technology.
a way to engage students in graphs
Very engaging and useful
Would you attend another session by this speaker?
4: definitely would. 6
3: probably would. 1
2: probably not. 0
1: definitely not. 0
Mean 3.857142857
Did the session match the description in the program book?
Yes. 7
No. 0
Provide the presenter with constructive feedback to help them grow as a presenter.
awesome thank you
Excellent amount of time for practice and playing with the program.
Perfect… always we could use more time!
Having a document that outlines the steps would be helpful to see the big picture of the whole process.
I would have liked a printout of the conversion steps
keep up your great work

At CMC north Asilomar I was once again at the middle school, but this time I got the library! So, there was plenty of room for people. Handing out hershey kisses at each desk was much appreciated by people. Also, for this one I contacted Desmos in time to get some free swag to hand out. Everyone got a Desmos sticker for attending. People that completed and submitted a graph to the google doc got a Desmos pencil. Then I asked everyone how I could fairly give out the Desmos t-shirt and the canvas bag. One person numbered the list, and then went to google random number generator and generated numbers and we gave them away that way. Genius! And here’s the feedback I got from CMC North:

Session Number Speaker overall Meet expections Why for expectations Invite this speaker again Should we invite this speaker again Other
460 Martin Joyce Excellent Completely I loved it!!! The ultimate way for students to love what they do is to let them make a product and take it home. Maybe, depending on the topic Yes
460 Martin Joyce Good For the most part I thought there would be more info on how to transfer design to 3D printer, but I had a lot of fun. Maybe, depending on the topic Yes
460 Martin Joyce Excellent Completely Very cold step-by-step use of Desmos. YouTube video was very helpful. Anyone could work at their own level. Yes, regardless of topic Yes
460 Martin Joyce Excellent Completely Super great activity for many math levels Maybe, depending on the topic Yes
460 Martin Joyce Excellent Completely Just a bit fast at times; perhaps slower for those who have never used Desmos. Yes, regardless of topic Yes Fun! The learning experience was enough prompting. I will try this with my own classes, but without the 3D printing options for now.
460 Martin Joyce Excellent Completely Good use of technology. I liked the way it required the students to know desmos, google docs and the internet. Yes, regardless of topic Yes

I have added the written instructions to the slide show after the link to the screencast. I was really happy to present on this topic. If 3D printing was a faster process, we could even produce some products. I was impressed that a few people in the sessions got as far as finishing their design in Tinkercad. Here are some highlights:




CMC South Palm Springs 2018 Recap

Before I head down to CMC North after work tomorrow with my colleagues Bob and Allan, I need to summarize everything I learned from CMC South a month ago before I arrive at Asilomar tomorrow.

It was my first time at south, and when my speaking proposal for 3D printing Desmos graphs was accepted, I was beyond excited, and a bit intimidated. I had never flown to a concert. I spoke at Asilomar and CPM’s national conference last year, but CMC south was uncharted territories. It lived up to and beyond the hype.

My principal paid for a substitute Friday and I flew out of SFO Thursday night. I planned my day for Friday, and here’s how it went:

Session 1: Grace Kelemanik: Contemplate then Calculate

I own Routines for Reasoning already, and I arrived early to introduce myself and she signed it. Grace is so nice and personable. Her name is pronounced “Kelluhmanick.” I also met someone I know from twitter at my table, Megan, @meganjoy5, and met Deborah. Megan shared the same admiration for Sara Vanderwerf and her name tents and Megan was raving about how stand and talks made her usually quiet students speak more. I have to watch that Global math on it at some point.

Back to the opening session. The goal was to learn how to facilitate productive math conversations. Why do we want students to learn how to discourse? Students construct knowledge socially. She played “Let’s give them something to talk about” by Bonnie Ray.

We were also reminded how important it is for teachers to have a poker face when listening to ideas so we don’t immediately give away that the answer is right, or wrong.

Instructional routines are great for many reasons. They have a predictable design, and students get better at it the more you practice it. Her website is

My biggest takeaway was this: in contemplate then calculate, the first pair of students that share have a sentence starter: “We noticed…” When you listen to them, you gesture to the dot talk image, do not write. Then, ask the rest of the class to restate their thinking with this sentence starter: “They noticed… so they…” THEN you annotate. I love this move so much because it keeps students accountable for knowing what others say, and you only write it when someone else repeats it.

All the routines end with a reflection prompt. You can choose your starter, such as “to find a shortcut, look for…” or “Noticing _________ helped count _______.”

My reflection was, “Knowing area of squares comes in handy when counting quickly because you can quickly get an array of dots that form a square quickly.”

It’s important to be explicit about the goal: how you learned to think like a mathematician in the future.

Session 2: Daniel Rocha, then Robert Kaplinsky

Daniel Rocha was given an awfully tiny room and I was rejected due to fire code and not being allowed to stand. He gave me the link to his slides at

I had never seen Robert Kaplinsky present, but I had met him at NCTM SF a few years back. I have also liked his Ignites when I watched them online, so I was excited. He was in a huge room with a lot of attendance.

His session had us ranking lays, nacho cheese doritos, cool ranch, cheetos, sun chips, and fritos from 1-6 to see how they could distribute them in a variety back to maximize profits.

We also looked at a task of a large drug bust of money. We estimated how much money the huge brick of 100 dollar bills would be.

Session 3Think Like a Mathematician by Vicki Vierra and Jim Short

I was really excited about this session. The description clearly said that we would be working on mathematical language routines. That was one of main focuses, since they are integrated with the Open Up Math curriculum. Vicki and Jim did a great job. We worked on this task:


They flashed it on the screen briefly, just so we could discuss what we noticed. It was great because it didn’t make you quickly solve. I think this was Contemplate then Calculate, #cthenc, again, but I was glad it wasn’t a dot image.

Once again, the first person to share, the presenter, had sentence starters: “We noticed… so we… We knew.. so we…, or our shortcut works because..”

Again, you only gesture when the first person shares. Second person who restate, the audience, says “they noticed… so they… They knew… so they… or This shortcut works because…”

My reflection was, “to find a calculation shortcut, look for relationships between numbers and see if they are divisible by a common factor.

In our group discussion, it came up that shortcut had a negative connotation. So we brainstormed replacements: elegant or efficient” method.

The 3-read strategy or routine helps students identify quantities and relationships. We want students to ask themselves, “What can I count or measure? How are those things related?”


  1. What is the problem about? (3 types of laughs)
  2. What is the question? (how funny is a cackle in point value?)
  3. What information is important

Making a t-chart helps, brainstorming quantities and relationships. We were also asked to do a sketch. I had read parts of the book Routines for Reasoning where students didn’t make sketches to scale, so when I worked on mine, I used my grid paper to properly scale the problem, like this:

Session 4: Geometry Practices by Jed Butler and Jenn Vadnais

The audience here was great because I got to sit with Casey, Chrissy, and Michael Fenton was there too. They had a huge Desmos activity builder that they ran the presentation through and it went really well. Tons of cool little activities that showed the progression of geometry from area of rectangles to much more complex shapes. We did a paper and pencil Steve Wyborney activity. We also used the Desmos sketch tool to find area. We were creating formulas by decomposing and rearranging.

Day 2 Session 1:

My session! I was first one of the day, and it was great. I think I’ll have a separate blog post about that. I was surprised by the great attendance, at least 60 people and I got great feedback from people in person.

Day 2 Session 2: Student Agency by Daisy and Katerina from

Here we did some role playing about lesson study. We watched a group work on an open ended problem where figure 1 is 1 tile and figure 2 is 8, and watch what they could come up with.

We were attending to status, sharing a student’s idea for the class to consider, and they are trying to abolish the phrase “I’m not a math person.” I recognized Katerina’s name and I was right, she is the same person who wrote the Functions unit with the border problem that’s on YouCubed!

Day 2 Session 3: Empower Students with Disabilities as Math Thinkers by Rachel Lambert

I follow Rachel on twitter (@mathematize4all) and know she is well respected when it comes to students with disabilities (SwD). She asked us what problems we see in math teaching and learning for these special populations? Cognitive deficits, achievement gap, SwD not offered access to standards-based instruction and not participating deeply.

I can honestly say I’m so glad our non-mainstream classes are using the same Open Up curriculum with more support and a slower pace. That’s awesome news to report.

What are her main takeaways? We need to change the way we think about disability. We need to offer intervention in our classroom, build relationships, see student strengths, invest in problem-solving routines, and provide scaffolds.

Then she talked about UD, Universal Design. It is when we design anything we want to expand the group of people who use it. We need to students to participation in math discussions because this predicts achievements. They need to engage in the strategies of their peers. Without supports, SwD participate less actively. The SMPs, or Standards for Mathematical Best Practices are best practices for ALL students, SPED, EL, everybody.

Rachel researched a 5th grade classroom where they had a consistent routine of number strings and CGI story problems. They worked on fractions, partitive and measurement.

They noticed that SwD are more willing to share if they are collaboratively sharing in front of the class with their partner, not standing by themselves.

Day 2 Session 4Mathematical Practices for Struggling Learners by Amy Lucenta

Amy co-authored Routines for Reasoning with Grace. She was also gracious enough to take a picture with me and sign her book.

When students work within contexts, they are using MP 1, 2, 4. When they communicate their ideas: MP 1, 3, 6. When they connect ideas and representations: MP 2, 4, 5, 7. And when students abstract and generalize, they are using MP 2, 7, 8.

We can ensure all students are doing these by using specific routines that support students in how to communicate effectively.

That is interconnected and makes sense.

How can we support our special populations? Give them avenues for thinking.

Like helping their quantitative reasoning. A quantity is something you can count or measure. It has 3 things: a value, sign, and unit. A simple tip like giving a sentence starter like “The number of…” helps students track important information in problems.

We then did a dot talk. We looked for repetition. I came up with the equation 4(N-1)+4 by visually looking at the pattern. My reflection was: when looking for repetition, I learned to pay attention to how groups of dots being added is related to the figure number.


Friday night pizza was a lot of fun, and it was great taking selfies with all the people I talk to on Twitter. It was also shocking that people recognized me from Twitter and as the guy who is the “Open Up Math guru.” CMC South was awesome and I hope to go every year. The fact that they cover your travel costs is a huge motivating factor. Now that I’ve blogged about my experience, I can come back to these notes and actually use them and now create more space in my brain for this weekend: Asilomar!

#MTBoS Math Colleague Photo Gallery

Whenever I go to math circles, trainings, conferences, or any events I like to take selfies with people I’ve talked to on Twitter, read their book/blog, or been a participant in their session. Here are my like minded people:

Mike Serra, author of Discovering Geometry, at Desmos HQ
Cory McElwain, Desmos engineer
Dan Meyer, author of many 3 act tasks, presentations, & Desmos CAO checking out an #openupmath lesson I taught!
Tyler, Aristotle, & Scott at lunch during #tmcnorcal
Mayor Kawata checking out my math class on his visit from Japan
Lisa, IM curriculum writer, coach, & Desmos employee


The two nicest Canadians I know on Twitter: Kyle & Jon
Andrew Stadel, creator of Estimation 180 
I chaperoned our Sojourn to the Past field trip, and met civil rights hero Jimmy Webb
Not a math teacher, but our music teacher Mancho. There’s music in math!
Marc Petrie had a great presentation at CPM SF 18, and was mentioned in Boaler’s Mathematical Mindsets book
My fellow CPM assessment question writers
Founders of CPM: Judy Kysh and Tom Sallee
Civil rights legend Minnijean Brown: one of the original Little Rock Nine
Not a math guy, but one of my heroes: Jon Taffer. I posted his meme in my classroom: “I don’t embrace excuses, I embrace solutions.”
Chrissy Newell, IM certified trainer, after her great session at CMC Asilomar 2017
My first born daughter, Everly, helping me grade
Leeanne & Kathy at the Illustrative Mathematics training in San Francisco summer 2018
Marisa Aoki, savior attendee of my first ever Asilomar presentation and also at the IM training
A few of my math department members: Carrie Wong, Jessica Yee, myself, Jonathan Lee, and Bob Rodinsky.
selfie with Casey, the #MTBoS chief evangelist
Selfie with Desmos founder Eli Luberoff, at CPM Academy of Best Practices in Seattle
Howie Hua at #TMCNorcal
Desmos engineer, Anand, checking out some #openupmath

My plan is to continue to add to this list. I obviously don’t have pictures with everyone I know, but plan to!

Open Up Resources 6-8 Math Grade 8 Unit 2 Lesson 13… Math routines & cool-down comment codes!

Today was the culminating lesson of Open Up Resources 6-8 Math grade 8 unit 2, lesson 13. I wanted it to go better than the last lesson of Unit 1 went with students not really getting too far past the warm-up activity of exploring angles of pattern blocks.

This lesson started with a notice and wonder of 2 photos of 3 pens, one outdoors with equal shadows and the other indoors with a lamp as light source. Students were very intrigued.

Here are the images from reference, linked from the lesson plan freely available above:

After 2 minutes of quiet think time and passing out the lesson 12 cool down, I gave classes a minute to share with their partner before writing their thoughts on a T chart (MLR 2: Collect & Display). Here were highlights from 2 classes:

I’m glad that someone from another class also noticed that the bottom photo created slope triangles. Also, a few noticed the direction the sun was shining based on the direction of the shadows.

In the slide show the next photo draws lines from the light sources to show the angles created by the shadows indoors are not equal but the light rays from the sun outside create parallel light rays that make the angles with the ground equal.

Before jumping into the lamp post activity, I re engaged students with the lesson 12 cooldown that challenged students to check if a point was on the graph of a non proportional equation. When students took the cool-down, I prompted students who were stuck or blanking out to try to find the slope of the line. Before looking at each classes results, I worked the steps myself to guide my thinking of how students may approach the task and to plant a seed on how I wanted students to re-engage with the task the following day.

This is where I created some comment codes, that I’ve talked about in our weekly Open Up Resources 6-8 Math chat at 5:30 PST every Monday, and many people have inquired how I do it. Here is a perfect example to show.

Students received an “S” if they were unable to identify the slope of the line. If they did figure it out, no “S” code. If they weren’t able to set-up an expression or equation equal to the slope, they got an “E.” If they didn’t check if the point was on the line or incorrectly used their expression or equation (switching order of ratio, switching x and y coordinates) they got a “P.” So the less codes you got, the more you understood the task. My general marking codes are similar to the ones I learned in MARS tasks: check mark for correct, x for incorrect, and ^ (caret) for correct but incomplete thinking, that wouldn’t get full credit on an assessment.

To re-engage students the next day, I asked students if this was a proportional relationship. They said no, it doesn’t pass through the origin. Some kids divided the y coordinate by the x coordinate to see if they would equal to the slope, 1/2. They were referring to the classwork activity a day before where the line was y=3/4x.

So, I asked the class what the slope was. Many said, 2/4 or 1/2. I then asked raise your hand and prove it. So many talked about drawing a triangle between two points, and labeling the vertical and horizontal lengths, and writing vertical/horizontal.

I asked students to call out lattice points, points that were on the line and exactly on the corner. As they called them out, I marked and labeled them. I then labeled how the student volunteer found the slope, and pushed students to see how the slope was related to the pair of coordinates. Kids saw the vertical was the difference between the y values, and the horizontal was the difference of the x values.

Then I said, let’s mark the point at the edge of the graph, not a lattice point, that we aren’t sure of the coordinate and call it (x,y). This represents a point anywhere on the line. If we can make a slope triangle using this, we can find out if any point is on the line. Then I asked how to label the slope triangle between (x,y) and (8,7). [I was careful to not pick a point whose x and y coordinates were the same, as this would not help differentiate the x and the y coordinates]. They said y-7, then x-8. I asked students what we should do with those expressions, and they said divide the vertical by the horizontal. I replied, and that should equal to…? (1/2). I reminded them this is true because the slope is equal between any two triangles on the line because they are… similar! [I’ve noticed a lot of mix up between the words corresponding, congruent, and similar. It’s a lot of language demands for students]

Then I asked how do we see if (20,13) is on the line? I honored that some kids made a mistake here and I understood that for slope vertical is the difference in the y coordinates first, but in an ordered pair, y is not first, x is first. A few kids switched this around. I asked what should we write instead of y-7? (13-7!) Instead of x-8? (20-8). That equals 6/12, and wala, it is equivalent to the slope, 1/2. I also had students write a sentence, declaring that answer: “(20,13) is on the line because when you substitute 13 for y and 20 for x in the equation, it equals 1/2, the slope.”

I have to show what this student did. Although there’s no equation, the SMP’s are evident all over this with the perseverance, and the repeated reasoning of a pattern.

Then we jumped back into the lesson. Students had 2 minutes to notice any relationships between the heights of the people and lamppost and their shadows:

My students asked if I was the guy in the middle. I did admit that this gentleman is the same height as me (72 inches or 6 feet), although he has 2 sons, and I have 2 daughters much younger.

Most kids found the approximate constant of proportionality (1.5), but in my first class, one student had a REALLY clever way of finding the lamp post height. I mentioned him, Carson, in later classes to show students there was an alternative method. He got his protractor and measured the man’s shadow and got 2 centimeters. He then measured the lamp post shadow and got 5 centimeters. He reasoned that 2 times 2.5 is 5 centimeters. So, he said that the lamp post must be the same size of 2 and a half men! He said 72 plus 72 is 144, and half of 72 is 36, so 144+36 is 180, which is pretty darn close to the answer students got of 171 inches when multiplying the lamp posts’ shadow by 1.5.

The next activity is pure genius. After that activity synthesis, it fades out the photo and draws black lines on the angles created by the people and their shadows. Students are given 2 minutes to come up with their first rough draft explanation of why there is an approximate proportional relationship between shadows and heights.

This was my first time I was going to use the MLR 1 (Math Language Routine), Stronger and Clearer Each Time with successive pair shares. I first experienced this routine at Asilomar last year in Chrissy Newell’s session that was right after my session. I didn’t follow the instructions exactly how I was supposed to, after referring to the Course Guide outlining the procedure, I realize that students were supposed to think about what they were going to say to their partner without looking at what they first wrote. I will read through that again before I try this great routine again.

When I executed the routine, having cards taped to each desk for random seating really helped. Students matched up with students at the table across from them with the same suit to share their thoughts, listen to their partners, and critique each others reasoning and add to what they wrote (some had wrote nothing in their independent time). I could see students who usually didn’t produce as much work output, working harder to incorporate notes from their partner’s ideas. I then had them think and write a bit, then pair up with a different table. This really helped in the activity synthesis because students were more willing to share one idea they had.

The main point to drive home was that the shadows and objects created triangles that were SIMILAR. Yes, they were all right triangles, but that only proves that which angles were the same? The 90 degree one. So, students, how many pairs of angles must be the same to be similar? (2!) So, how about a second pair? They saw that they were corresponding because the light rays appear to be all be parallel. This means that the side lengths are proportional to each other, and are scaled copies.

Then students went outside with clear roles: 1 student would stand, whoever knew their height by heart. Two students would measure with a meter/yard stick, and the 4th group member recorded the data. Then they measured the shadow of a tree or a tall object and then went in to do their calculations. We ran out of time, and one of my classes had inattentive behavior that slowed the flow of the class period which made me omit the outside portion and just have a longer conversation about why the relationship was proportional.

I am really happy with how this lesson went. With this curriculum, Brooke Powers reminded me that my students are making memories of learning experiences in math class that I believe they will remember and recall later on.

As Illustrative Mathematics says, the units and lessons follow this model:

Screen Shot 2018-10-19 at 8.21.21 AM

I really am happy with how students consolidated and applied their learning in this culminating unit 2 lesson. I am also excited to try successive pair shares (MLR 1) again with a different concept.

OUR Grade 6 unit 2 lesson 1 Intro to Ratios

I felt that this lesson was a great introduction for students to grapple with the language of ratios and to see them come to life.

The warm-up is such a great start to the lesson. I don’t have it pictured here, but basically there are different colored shapes with different areas and arrangements of squares. This is where having the consumable workbooks from Open Up Resources really comes in handy because they are printed in vibrant color! It gets students thinking about what color categories they could be sorted into, as well as how many groups that is. Then they sort by area, and then come up with their own sorting. One student named all the types as small rectangle, square, big rectangle, small L, big L, and I forget what they called the other two shapes. Others said rectangles and non-rectangles.

The lesson plan offers a teacher collection of dinosaurs of different colors and characteristics, but I decided to use a prominent collection I’ve had up for many years: my bobblehead collection:

I brought them down in front of my display TV so kids could see them better. Here they are asked to come up with a way to categorize them. I’m glad they said the primary way I thought they would: by sport. There’s baseball, football, and basketball. They also said animals and people. A really creative one was if they had a helmet on or not. I asked if a hat is a helmet, so we revised it to headwear/headgear or not. Another suggestion was if they were in the act of playing the sport or not. This lead into us co-constructing ratio sentences based on my collection. The lesson plan is explicit to come up with one from each type of sentence. Here’s what we came up with:

After this, students sorted their own collections. I had at least one collection per table, but one group no one had brought any in so luckily I had some of Christopher Danielson’s wooden tiles to sort.

Here some students sorted B’s massive collection of erasers:

I think the 3 categories were food, animals, and non-living objects
Sorting process
Sorted! And you can see the warm-up question in the background.
Here’s their categories and data.
@trianglemancsd to the rescue!
I love how they named the pentagons crowns.
Then they were like, hey they fit together!

Afterwards, they were given an exit ticket (cool-down) with pictures of cats, mice, and dogs. I was really impressed how well students were able to apply the knowledge of the ratio sentences and the reference on the poster was a huge help for all learners. This lesson was an exciting launch into Unit 2 on Ratios!