Bragging On My Son….

My first grade son was doing his homework this afternoon, and he was knocking out double-digit addition  problems mentally and not even breaking a sweat. It was AMAZING to watch. I was so enthralled that I asked him to explain his process and I took dictation as he spoke:

“So I took the 40 and the 30 and I knew it was 70. Then I took the 7 and the 8 and I knew it was 15. Then I knew that 70 and 15 equaled 85.”

The “quick tens” were added after he calculated the answer.


“So I just took the 53 and 27 and added the 7 to the 3. I knew it equaled 60. I took the 2 and it was 20 and put it with the 60 and I knew it equaled 80.”

“Because I knew 8 and 8 made 16 and I knew 3 and 4 were 30 and 40 so that’s 70. So I added the 16 to the 70 and I knew it equaled 86.”

“So I knew 3 and 5 made 8 so I just took the 50 and 40 and knew it equaled 90. Then I took the 8 and the 90 and I knew it equaled 98.”

Props (and hugs) to his teacher!

Conceptual Surface Area

Getting further into my drought PBL (and test prep) and I needed a way to get my students to understand surface area, not just be fed a formula and worksheets like the dutiful students that they are (ha!).  Enter Matt Coaty and his surface area activity. (Disclaimer: yes, surface area of rectangular prisms is a 6th grade standard, but I needed them to GET IT before moving onto irregular shapes, which is the 7th grade standard).

I modified his handout somewhat to fit my needs, and instead of taking pictures before and after the wrapping to paste onto the worksheet itself, I had the students do the before, the net, and the after and post the results into a shared Google Slide presentation.

This activity was excruciatingly, painfully lengthy longer than I anticipated.  Like I mentioned in my previous PBL post, the learning curve when it comes to using technology lengthens the projected time of a lesson–in this case 5 fold.  Because everyone was at different places in the activity the further we went along, it’s a good thing they had their research project to work on while waiting for their peers to finish up.

I think this activity was meaningful on many levels, not just for the mathematical content.  My students really got a feel for using technology and what you can do with it.  I still plan to have them do a “gallery walk” so they can comment with their “two stars and a wish”.  So that the various slides get a somewhat equitable amount of comments, I think I’ll have them comment on the three slide sets previous to theirs. All in all, it was a great activity and with some minor adjustments I would do it again.


Conceptual Volume

I’m always a fan of ideas that make learning engaging and fun for my students.  I can’t realistically make EVERY SINGLE LESSON awesome and something the students will talk about years down the road, but I do have some moments when I think we have had an activity worth remembering.

With testing creeping up on us next week, there are a few concepts in my grade 8 classes that I need to expose my students to.  Volume is easy to slip into our weekly plan because it can take just 1-2 days to cover and allow students practice with.  I was initially going to try to flip the classroom and have students watch selected videos on volume of cylinders, cones, and spheres, but once I started watch some videos (here , here and here), I decided on another track.

It really all happened by accident–I woke up in the middle of the night, couldn’t go back to sleep, so I started thinking about the day ahead.  I had in my mind the video with the cute mice and the biscuits (the first one in the list above), and I thought, “How can I get my students to experience this in class today? Do I go buy cookies?  No…they aren’t uniform in shape.  What do I have here that’s circular and uniform in shape?” And it dawned on me: poker chips!

I created this exploratory activity for my students.  I think it was so much more memorable than giving them the formula and telling them to “Go at it!” with a bunch of problems on a worksheet.  YAWN!

My awesome math coach, Karen, came and observed, and as we were tossing ideas around about the cone and sphere demo I wanted to do, she contacted another school in our district and borrowed a geometric volume relationships set (like this one from  She even tracked me down at my son’s school later that day (where I was delivering treats for his birthday) to deliver them!  (LOVE HER!)

My first grade son and I practiced the cone and sphere demo at home that weekend.  He loved it–what kid doesn’t love splashing colored water all over the kitchen?

In the classroom Monday, I gathered students around the demo table at the front (which was really just a commandeered table group–I moved those students out so I could use their space.  They didn’t mind…at least I don’t think they did).  This in and of itself was fun because it was out of the ordinary.  Their eyes were alight with wonder, and for the duration of the demo, they were completely and utterly engaged.  It.  Was.  Awesome.

I didn’t have a script, but I basically showed them the relationships between the cone and the cylinder, and then I filled the cylinder with water.  I then asked them to make predictions about what would happen when I placed the cone in the full cylinder.  Most students used the word “displace” when they talked about how the water would flow out of the cylinder as the cone pushed it out (snaps to our science teacher!) and then when I asked them to predict how much water would be displaced, they gave some good guesses using fractions or percents.  Once they saw about 1/3 of the water was displaced, I asked them what would happen if I poured that displaced water into the cone–most students didn’t believe that it would all fit inside, and they were quite surprised when the cone was filled to the brim with the displaced water from the cylinder.  We talked about what that meant, and they were very accurate about connecting that information with the volume of the cone.  From there they came up with the formula for volume of a cone. And continuing on, we followed the same process for volume of a sphere.

The kids liked it, and now they have something conceptual to visualize when they encounter volume problems in the future. Win-win!


PBL–California’s Drought

I’m participating in a three-year program about the STEM disciplines and PBL’s (which I wrote about here).  As part of this program I had to write and implement a PBL. I started out working with a partner, and we she wrote a PBL for our grade 8 math curriculum.  Our district decided to pull in an Integrated Math Program (IMP) unit called The a Overland Trail to take the place of most of the last three  modules of our Eureka Math curriculum, and as our her PBL is meant to replace the last module, I didn’t think I would get to it (or it would be overkill). We are also coming very close to testing (actually, it started last week and we test math in next week). Therefore, I decided to write a PBL for grade 7 that would give the students exposure to the remaining concepts we haven’t covered that I know will be covered on the test (well, I’m 99.9% sure they’ll be covered–I’m going from memory here). Since we live in California, I thought the drought provided a perfect context for our PBL.

We are still in the midst of it, and to be honest, some of the activities have taken a lot longer than I planned for (due to the integration of technology, I think.  Note to self: if the activity is tech-heavy, double the time for the lesson since the students are learning to use the tech at the same time they are learning the concept embedded in the activity).

I created a Padlet as our home base of operations.  Students have found this easier to access instead of posting everything in Google Classroom (although I have the URL for the Padlet posted in Google Classroom). Embedded within the main Padlet are student Padlets that contain links for posting assignments or for jump-starting research.

The students found the work on percents much more relevant because there was context in the Reservoir Data Google Sheet. (This is the assignment that took a lot longer than I anticipated. It morphed along the way due to privacy restrictions on the student accounts, so the final set of directions are actually the fourth iteration).

Students collaborating on their Google Sheet.

This student “two-fisted” his reservoir assignment on a day his partner was absent. I didn’t have the heart to tell him he could open two tabs and pull them apart on one computer.

They started the drought research project today. They had an entry event in the beginning that gave some basic information to prompt some noticing and wondering.  The purpose of the research portion is to revisit those “parking lot” questions and give them the opportunity to hopefully answer some of them. Before even making it through my first group of seventh graders I realized I should have broken it down into two parts: research first, presentation second. Because I introduced the whole shooting match at once, the students wanted to skip straight to the creation phase, and they consequently got lost and didn’t quite know how to start.

The third, and last phase (after some instruction on volume and surface area) will be to develop a rain/excess water storage container that can be used by a single household to help mitigate the effects of the drought. The students will go through the design phase first, and then using scale factor, build a scale model of their storage until. (I’ll post pics in an update when we get there).

To Assign, or Not to Assign? That is the Question. 

I just read this story from the Los Angeles Times and had to chime in with my two cents: 

This news story highlights one of the two reasons I don’t assign much homework anymore. The other is because the homework I DID assign wasn’t getting done. It became more of a struggle in terms of classroom management rather than the learning tool it was supposed to be. I have found that assigning homework that is review and can be independently done (and supports what we are learning in the classroom) is much more likely to be completed and enhances students’ mathematical confidence. And as such, homework really becomes a tool with which you can teach time management and study skills. Because, let’s face it, homework is a large part of a person’s college education, and they need to learn how to do it at some point. 

As far as homework for primary grades? I think homework for them should be playing. Not video games or computer games or watching TV…but PLAYING. Create a maker space in your house and fill it with “stuff”–anything that will spark your child’s imagination. And the conversations you can have around those creations will be priceless!

My Thoughts on Retakes

All year long, I have offered retakes for students who want to 1) improve their grades (THEIR number one priority), and 2) improve their knowledge of a concept (MY number one priority).  I used this idea from Sam Shah for students to request a retake, and I offered the retakes only during lunch on Fridays.  This streamlined the process and made it predictable for the me and the students alike.

My requirements for a retake were that students do some sort of practice to build their confidence with a concept.  I offered several options for this over the course of the year, starting with suggestions for what they could do (including Khan Academy practice, work with a parent or older sibling, or lunch time help with me–guess which they “said” they did? There was no way for me to verify these for certain), and ending at the current iteration of the process: Google Classroom assignments with embedded Zaption videos that require them to watch and answer questions along the way.  (I checked on the “analytics” of each video to make sure the student actually did the work before allowing the retakes).

While the idea of retakes is great in theory, in practice it didn’t work out so well.  Only a handful of students took advantage of the retakes, and they were usually the students who were already earning an A or B in the class.  I also placed a lot of responsibility (in terms of completing the steps required for the retakes) in the hands of children whose brains are still developing (and their frontal lobes have a lot of “holes” still).  They simply don’t know HOW to take responsibility for this yet, nor do they have the discipline.

Enter, error analysis.

With the last round of assessments, I chose to have the students do error analysis on their mistakes instead of all the work for a retake, due to the quarter ending yesterday. There simply wasn’t enough time for the retake process.

Here are the steps I expected:

1) On binder paper, redo the problems you got incorrect.

2) Next to each problem, explain your original mistake.

3) Staple this to your original test and return to me.

The second step was the most important, and I didn’t accept the error analysis without it or if the sentences a student wrote were too general (“I did the math wrong” instead of “I subtracted 2x from each side of the equation instead of adding 2x to each side”).

When I grade, I use highlighters to color code their mistakes (a la Fawn Nguyen) to start the metacognitive process and hopefully get them thinking about how to fix those mistakes.  (See the photo caption for an explanation of which color means what).


Yellow = process is good, minor calculation error. Pink = process is incorrect (I mark WHERE their first mistake occurred). Blue = not enough work to decide if you know the concept or not.

My favorite brand of highlighters EVER!


My entire grading “pen” repertoire. I often look like Freddy Krueger with markers sticking out from between the fingers of my left hand, ready to grab when I need a specific color.

I didn’t require the error analysis, but made it available for students who weren’t happy with their grades.  I received quite a few on the due date, and most of them had very insightful thoughts regarding their mistakes (I wish I had thought to take pics of some them). Some didn’t write the sentences or gave general statements, in which case I returned their papers for them to fix.

For Quarter 4, I think this is what I will do for students who wish to improve their learning and their grades instead of retakes.  It is much less prep on my part, and it’s a much more valuable learning experience for the students.  After all, teaching them metacognition is one of my goals, and this is the perfect format for that.

Wiped Out

Full disclosure: I’m not perfect. There…I said it. 

I usually post about cool things happening in my class, but in no way is my classroom awesome and cool all the time.  And there hasn’t been much of that lately anyway because…

I. Am. Wiped. Out.   

It took me a lot longer this year to figure out WHY that is than in years past. 

I expend too much energy thinking for my students. Problem solving for my students. Feeling the pain of their failure. And in doing that I’ve been robbing them of a valuable learning experience. I just got too caught up in the pacing of the curriculum and the parent pressure of, “What else can you do for my kid that you’re not already knocking yourself out to do?” Shame on me. 

Yesterday this all dawned on me, so instead of responding to their cries of, “This was hard so I didn’t do it!” with my usual exasperated, “Oh my gosh you guys! How are you going to learn anything if you don’t try?”, I chose to look at them and say, “Okay. Thank you.” And we moved on anyway. 

I decry the enablers, and here I’ve been one of them all along! No more, I say! NO MORE! 

I feel free now. It’s an amazing feeling. 


Checking for Understanding

I need to come up with a much more structured way of teaching new concepts and checking for understanding before assessing. As I’m sitting grading the latest grade 8 quizzes on solving equations, it’s becoming clearer and clearer to me that I didn’t do a very good job of it this round. 

Idea #1: direct instruct in small chunks, then do lots  and lots of checking for understanding whole class using whiteboards (or the students’ favorite: writing with whiteboard markers on their desks) and other formative assessment tools. This could take DAYS given the complexity and rigor of some concepts. And obviously some concepts don’t lend themselves well to this format. This could get boring though…

Idea #2: use a Daily 5-ish workshop format with small bursts of instruction, followed by Cafe menu choices and small group work with the teacher. This would take some massaging, but I’ve tried it already and I think it could work with some tweaking. This allows for more creativity, and one of the menu choices could be working with whiteboards (because they love whiteboards as long as that isn’t the only formative assessment tool we use). 

Idea #3: maybe it’s an engagement issue? In that case, a PBL structure with small bursts of mini-lesson instruction as needed is the answer. Again, this allows for much more creativity, and then the instruction is really guided by student interest. 

Idea #4: I got nothin’. Ideas, anyone?

Oy vey…I need a drink. 


Reading Apprenticeship and Math Part 2: Talking to the Text

As mentioned here, I’m participating in a fantastic professional development series on Reading Apprenticeship in my school district.  As a math teacher, I was driven to explore ways to pull in reading strategies to my classroom since the curriculum we use is heavy on reading.  

Many of our students are 1-2 grade levels below where they should be in reading.  What I’ve learned through this training is that so many of our intensive reading programs designed to help students become “better” readers focus more on fluency and decoding and less on comprehension.  This leads students to believe that to be a “great reader” they need to read quickly and fluidly.  Comprehension takes a back seat.  


Example of a word problem in the Grade 7 workbook. Oy vey!


Example of a crazy-difficult problem that my Math 8 students historically have trouble understanding.

Just LOOK at those problems!  I’m here to tell you that even I had to re-read these several times to understand what the heck was being asked…and I’m *ahem* several years older than my students.  

Hence, the need for some good strategies.  

Enter, Reading Apprenticeship.

And here’s where we went with it:

I took a typical problem and did a think-aloud.  I spoke what my brain was thinking as I worked through reading a problem. I didn’t even attempt to solve or build an equation or anything mathematical.  I.  Just.  Read.  And talked.  And re-read.  And talked some more.  And talked to the text (took notes…CRAZY notes) all over the problem.  Then I stopped.  

I asked students to discuss in their small groups what they heard me say and saw me do.  

And we made lists.  


Strategies lists from 4 of 5 of my classes. You see some talking to the text above the lists.

I took the lists and combined them:

And we have a living list!  We will continue to add as we go, but what a great start!  

And here is what my 8th grade students were able to do with it (the first three problems were teacher models, the last two were done in groups):


My favorite because of the question he asks to the left of #4–how cool is that?


I love the modifications this student made, and the fact they added “conjunction” to their notes on #4.


We didn’t focus on correct equations, but rather on the talking-to-the-text process.

In all fairness, I can’t take total credit for their amazing-ness with this strategy.  They have been immersed in Reading Apprenticeship with two spectacular language arts teachers in our wing (7th and 8th grade) over the past two years.  I’m merely expanding the students’ Reading Apprenticeship universe.  

I’ll keep on with this, slowly and steadily getting the students to do it more independently.  My next wish is to develop their metacognition so they can think about their processes and understand when  and where they make mathematical mistakes.  For now, I’m very happy with where we’ve come.  

Rubric Grading

I’ve decided I REALLY like my grading system. I think parents and students like it also. It takes some getting used to because it’s different than what they’re used to, but I believe it gives the best picture of WHAT a student KNOWS. And the students and their parents like that it gives students room to continue learning and growing with specific learning targets. As such, retakes are an essential part of this process.

I use a slight variation of Sarah Hagan’s “A, B, Not Yet” rubric scoring system (read about it here and here).  I started out using B also, but changed it to C mid year, because C to me means “average”. I like color-coding, so students’ folders have a list of learning targets pasted to the front. That’s where I mark their scores.  

Student folder after the first quiz of the unit.

Same student’s folder after the second quiz of the unit.

These learning targets are the assignment names I enter into our online grading program. “NY” translates to 55%, “C” translates to 75%, and “A” translates to 100%. I also record homework, but as credit/no credit so that the real weight of a student’s grades lies on the learning targets. These learning targets are flexible and can improve all the way up until the end of the quarter, provided the student practices the concepts and either requests a retake, or (if I include those concepts) shows improvement on the next quiz. 

I prefer this grading system to what I’ve done in the past (recording assignments and tests as points correct out of a total) because I can look at their grades and get an accurate  picture of how a student is learning in my class without necessarily keeping a portfolio. I’ve also come to believe that points correct out of a total and recording homework grades with more weight is more a measure of a student’s work ethic, organizational skills, and behavior than of their actual learning.  (I can thank  Rick Wormeli and his book “Fair Isn’t Always Equal” for that–and the many discussions I’ve participated in on Twitter). 

I’ll probably continue tweaking this process, but for now I’m fairly pleased with the results.