Thursday, July 28, 2016

The three act structure for motivating mathematics

I hadn't checked into Dan Meyer's blog dy/dan for a while (basically since my calculus days), but I am very glad I did. He has a whole category of problems that he has labeled 3act --- meaning that there is a three act structure to the activity. (You can find all these problems at To quote Dan,
There are three steps:
  1. Invite students to try a task that is intuitive, but inefficient or inaccurate.
  2. Help them understand some math.
  3. Invite them to re-try the task and see that with math it’s more efficient and accurate.
A really good example that I can use with my sixth graders is the Nissan Girl Scout cookies activity  where you watch a video that advertises the capacity of a Nissan trunk by stuffing it full with boxes of Girl Scout cookies and then estimating the total number of boxes.

Nissan Girl Scout Cookies – Act One from Dan Meyer on Vimeo.

I was wondering how to use this type of idea (make a prediction, focus on math tools that can help, and then test the prediction) using decimal arithmetic. It struck me that one of the best places you can find decimals in the real world is gas stations, and --- sure enough --- the gas station near me shows both gallons and dollars per gallon to the thousandths place.

So here's my question: how do gas stations figure out your cost to the penny? If I wanted to make the most money from my gas station, I would always round up, but perhaps some gas stations are playing fair and rounding to the nearest penny. I'm thinking of a project where I show some pictures of pumps and charges and ask students how to get the final hundredths place.

Thursday, July 21, 2016

Pokémon Go problems for 6th grade math

I've been playing far too much Pokémon Go recently, but assuming the game stays popular, it's fantastic for generating math problems. Here's what I've thought of so far.

Multi-digit long division problems: 

  • To reach the next level you need to earn 10,000 experience points total. If you have already earned 2,350 points, how many Pokéstops do you need to visit (at 50 XP per Pokéstop) to reach the next level?
  • To reach the next level you need to earn 10,000 experience points total. If you have already earned 2,350 points and are a curveball champion (so you can catch already caught Pokémon for 100 XP), how many Pokémon do you need to capture to reach the next level?
Decimal division problem:
  • To hatch an egg, you need to walk a total of 5.0 kilometers. You have walked 0.8 km so far, and can do laps on a waling path that is 1.2 km long. How many laps will you have to do to hatch the egg?
Rates, proportions, and percentages:
  • The picture below shows the progress bar to level up. On my phone it is 450 pixels wide. Based on the picture, what percentage of 10,000 points has been earned so far? How many pixels have been shaded to show the progress?

Decimal arithmetic and unit conversion:
  • What is the difference in weights and heights for the two Raticates shown below? How much would each weigh in pounds (if 1 pound equals 0.45 kg)? How tall would each one be in inches (if 1 inch = 2.54 cm)?

  • Pick a Pokémon that you (or the class) have many of. (For example, Pidgeys or Rattatas.) Find all the weights for the Pokémon you have and find the mean and median. Create a dot plot, a box plot, and a histogram. Try to figure out which Pokémon are labelled XS (or extra small) and XL (or extra large). 
That's what I've come up with so far --- if you have more ideas, let me know!

Tuesday, July 19, 2016

Teaching concepts and not JUST procedures

Last week, our district hosted some PD based on getting 5th grade and 6th grade math teachers together and collaborating. During the workshop, the organizers emphasized again and again the importance of teaching mathematics on a conceptual level as opposed to just teaching procedures.

Here's an example: if I want to see which fraction is bigger, 13/24 or 7/12, I can use the butterfly method (also known as cross multiplication) to multiply 13 by 12 and 24 by 7 and compare the results. But if I do this, I am not really engaged with the fractions at all. I haven't learned anything new about either fraction, and my answer wouldn't help me put either on a number line. If I at least rewrite the second fraction and realize that 7/12 = 14/24, I have a natural way to determine which fraction is bigger that uses the fractions themselves and not somewhat unconnected whole numbers. Here, the butterfly method is a procedure that may obscure the conceptual understanding that comes from using equivalent fractions.

Well, once I started thinking like this, I started seeing procedures trumping conceptual understanding a lot more. For example, there's a great paper in the NCTM journal Mathematics Teaching in the Middle School called Saving Money Using Proportional Reasoning. It's by Jessica de la Cruz and Sandra Garney and outlines tasks that would make a great project after discussing rates and proportions. Instead of emphasizing cross multiplication, the authors emphasize unit rates and equivalent fractions (which are both hugely important in 6th grade Common Core). Here's a great picture from their article about why cross multiplication can give confusing answers:

What exactly is a dollar-pound?
I was doing some more searching on the potential harmfulness of teaching cross multiplication and found the wonderful site and the free 83 page book that you can download here. It's written by Tina Cardone, and it's full of tricks that math teachers use, the potential harm those tricks may do, and how you can reteach using conceptual understanding. I particularly loved this flowchart on determining if something is a trick:

How often do you hear "Because ____ said so"?
I'm pretty sure I will switch up how I teach dividing fractions just because I read this book (and hopefully will avoid over-reliance on "Keep-Change-Flip"). If you are looking for deeper understanding by your students, this is a good place to start.

Monday, July 18, 2016

Helping with self-regulation

I teach 6th graders, so I often have to work with students who have trouble regulating their emotions (or even recognizing their emotions). What I usually see is students struggling with anger, but I have a lot of "hyped" students as well, who need a chance to calm and refocus. Helping these students is one of the reasons I've been doing some research on mindfulness, but (thanks to my wife) I found a great book that focuses on physical exercises.

The Kid's Guide to Staying Awesome and In Control by Lauren Brukner is probably intended for elementary school kids, but there's a lot here that middle school students can use as well. The first half of the book is written to the kid and classifies emotions as "slow and tired", "fast and wiggly", and "fast and emotional". Then Brukner outlines "Anywhere Body Breaks" (basically, short focused physical activities that can be done in your seat with minimal disruption to the class). An example would be a hand massage, where you use the thumb of one hand to press on the muscles of the opposite hand. The goal here is to give the body proprioceptive input to either calm down the student or help them stay more focused.

There's a lot of stuff besides the "Body Breaks", including more intensive physical activity and tools (e.g., fidget balls) that reflect Brukner's background as an occupational therapist. (The second half of the book, aimed at the parent/teacher, provides more resources as well as pages to copy to help students.) But what I plan to use are the "Body Breaks". I have used student separation in the past, but I often did not do much with it --- the student worked in a corner that was hopefully free of distractions, but I didn't guide the student to help her or him with self-regulation. If I can provide students with a menu of options (the stuff in this book, self-reflections, writing prompts), I have more tools to help the students help themselves.

If you're interested in this type of therapy, Lauren Brukner has a web page at with details on her work and information on this book and its sequel.

Wednesday, July 13, 2016

Really... Playlists are a thing??

Now, I'm no stranger to YouTube: I have a channel (Dr. Mark Schlatter's Math Videos --- real spiffy title, huh?), and I have up about 130 videos that I have created over the last four years. But I didn't understand playlists until this past week.

Note that I'm pretty unadorned when it comes to search. I don't use filters in my Gmail, and I only add folders to Google Drive when I absolutely have to. For the most part, I trust that a Google search will find what I need. But I hadn't realized how playlists make it easier for folks to find connected material.

I created one recently to put together my tutorials on Google Forms, but it wasn't until training to take the Google Certified Educator Level 1 certification that I realized (1) that bundling my videos together might be helpful and (2) I can build playlists of other videos.

Since I taught college for many years, I have a bunch of videos for the calculus sequence (especially the second year), so I built some playlists to bundle those together.

(There's an eigenvalue/eigenvector video in the first playlist that's fairly popular.)
But I also realized that I can build playlists of videos I show in my middle school classroom, not only to help me remember them (much better than looking at what I had embedded in my slides from last year), but so I can send students to the playlist to help them out. Right now, these playlists are a bit sparse, but I expect to grow them over the year.

And I need to add in some of my own videos....
Building playlists is super-easy --- you just find the "+ Add to" under the bottom left hand corner of the video (look under the description) and add the video to an existing playlist (or create a new one).

See that "+ Add to" at the bottom left?

Here's the dialog box I get --- yours will be differ depending on what
playlists you have created.
For most folks, I'm guessing this is not news. For me, this is a big example of how I am still learning.

Tuesday, July 12, 2016

Image-based quizzes in Formative

Looking at Richard Byrne's blog post, How to Create Image-Based Quizzes in Formative, I decided to take a look at the feature and test it out. I've used Formative a few times in my math class, but always had a few issues:
  1. Having students log in with their Google accounts was difficult --- it worked, but students were not good at logging out from both Formative and Google Classroom at the end of class, and that caused serious problems for the next class.
  2. The sketching UI is nowhere as nice as The line work isn't as smooth, so my students have problems writing out text and erasing is much more difficult. This appears to be a problem on iPads only.
  3. My local network is a little too slow to show student responses well on my Smartboard.
Given all that, I love the concept of Formative, it's just that the execution is problematic at times.

You can follow the instructions on how to create this type of quiz on Byrne's blog (he has a video). I wrote up a quiz where my students would critique two solutions to a rate problem. You can view and take the quiz yourself by going to

What works great about this type of quiz is that the questions can be located right next to the information in question. So above, I am asking students to correct the error in the final answer right next to the error itself.

You can see the same feature in this image. Question 3 appears right where the unit rate is computed.  You can also see question 4 down below, ready to be clicked on (it's a question on decimal division). This isn't a huge change from what you can do in a Google Form, but it's slightly more interactive and I can see my students having some fun trying to find the questions as they work through an image.

Monday, July 11, 2016

Mindfulness resources

I have done a few mindfulness exercises in my class (usually with a chime and a prompt to students to listen carefully and then raise their hands when they can no longer hear the tone), but I decided to do more investigation this summer. I have benefited from meditation myself, and I want to teach more students some strategies for self-regulation.

A helpful book is Mindfulness for Teachers by Patricia A. Jennings. It is much more focused on teachers and their reactions than students, but since Jennings is trying to get teachers to model mindful thinking, the emphasis makes sense. There's a lot on understanding emotions and the basics of mindfulness, but it didn't get too "new age" for me and there are exercises at the end of each chapter for teachers. There's also a ton of resources at the back, including research on the effects of mindfulness in the classroom. This is definitely going into my classroom library.

When it comes to mindfulness activities for students, there's a lot of curriculum you can pay for. I was looking for something smaller in scope and hopefully free. (Since I don't have my students all day long, I really can't commit a large chunk of time.) My absolute favorite resource for this is the activity page at Mindful Teachers. There are about 25 activities excerpted from mindfulness curricula and books, and I think I can use at least half of them in my classroom. The activities are broken down by types ("Relaxation", "Five Senses", etc...) and all of them are fairly short.  I hope to use these as my go-to exercises in the fall.

Friday, July 8, 2016

Grading in Google Forms: What does feedback look like?

If you want to use Google Forms to grade student work using their tools (and not, for example, Flubaroo's), there's a lot of ways to give students feedback on how they did. I'm going to cover some of the quiz-wide options you have. (There are also options you can give for each question which I'm not covering here.) BTW, I haven't made a video for how to make a Google Form quiz, but you can go to Richard Byrne's blog post Free Technology for Teachers: How to Enable Automatic Grading in Google Forms for a quick video overview.

When you decide to make a Google Form a quiz, in the quiz settings you will see the following options checked by default.
Let's look at what each of these options do in detail. I created a sample quiz and answered it the same way while choosing different options out of the three above. Here's what I get with all three chosen:
Note a couple of things: we get a score for each question and a total score (because we checked "Point values"), we get red and green highlighting of incorrect and correct answers (because we checked "Missed questions"), and we get the correct answer to the checkbox question we missed (because we checked "Correct answers").

Here's what we get if we just check "Missed questions":
Notice the red and green highlighting.

Here's what we get if we just check "Correct answers":
Notice everything is in grey.

And here's what we get if we just check "Point values":
Notice the score at the top and next to each question.
When I use Google Forms for formative assessment in my classroom, my students like to look at answers from other students. To encourage as much learning as possible (and not just copying), I will probably check "Missed questions" and "Point values", but not "Correct answers" (so a tough question will need everyone to think about it). If I use this for summative assessment and a grade, I will probably not check any of the boxes. Your mileage may vary, and I'd love to hear about different ways of using these options.

Wednesday, July 6, 2016

Programming resources: part 2

In my last blog post, I wrote about the programming tools I use (primarily Scratch) to work with middle school students in our video game programming club. For many students, the block-based approach in Scratch along with the emphasis on game programming is a good challenge. However, I did have a few students who would have benefited from something more intensive.

Since I didn't want to use (that's already being used by our robotics class), I followed a student suggestion and tried out codecademy. Unlike Scratch and, codecademy is intended for adult learners and offers courses in a number of programming languages.

Some of the choices in codeacademy
I worked through two languages: Python (because I knew the syntax was very straightforward) and JavaScript (for a number of reasons which you can find below). In both cases, the teaching method was the same. You had separate lessons introducing each topic, with each lesson broken up into tasks that you had to complete before moving to the next task. (For example, an introductory task might be to write code to print out "hello world!") If your code isn't right, you can't move on, but if it is, you make progress, eventually earned badges and points. By the way, all of this is free and just requires signing up with an email address.

A sample task from the JavaScript unit
Could middle schoolers handle this? Well, at least a few of my students from this year could probably make progress in this environment. There is some math required (especially in the Python unit), but it is mostly exponents, decimal arithmetic, and understanding mod and remainders. Both of the units I took covered Boolean operators (which I think talented students could handle) and the basics of object-oriented programming (which may be too much).

If I give this option for students this coming year, I will use JavaScript for a couple of reasons:
  1. There's something really cool about coding dialog boxes that appear in your browser --- I think my students will love that!
  2. If my students are advanced enough, JavaScript can lead up to the App Lab at
  3. If I become fluent enough in JavaScript, I might be able to better understand Google Apps Script and learn to use scripts to supplement what I do with Google Apps in my classroom.

Tuesday, July 5, 2016

Programming resources: part 1

Last year, I decided to sponsor a club for the first time and created a video game programming club. After a fair bit of research, I decided to use Scratch for the purpose. While it didn't work on my iPads (a HTML5 version is apparently forthcoming), I was able to use a computer lab in my wing to get students started.

When I started the club, I focused on the basic tutorials in Scratch and my students remixed projects like:
Some of the Scratch starter projects
As I continued, however, I decided I wanted a greater variety of games and more help for my students. (I had about 20 showing up each month, and they needed more help putting commands together.) I built a simple webpage for the club and directed students to the Google CS First material on game design. What I liked about the site was that it broke game design into nice small chunks for the students (watch a video, carry out the steps in Scratch, repeat) and offered a nice selection of games types. In the spring, my students worked on the racing game, the platform game, and the escape game, and some students put up their final projects in a class studio.

The Ridgewood Middle School Studio
For a first year attempt, I thought the whole thing worked well. The biggest problem was tracking student work. As far as I know, the Scratch team is still working on teacher accounts (which would give the teacher the ability to enroll a class). So instead, my students log in with their own usernames and passwords, and I attempt to connect us all up by following each other and having students be curators of the studio. It's not a simple system, and it's made harder when students forget passwords. I'd like something like the set up at Code Studio (which I don't use since the robotics course at my school uses the curriculum). 

For this coming year, I'm hoping to have a better system set up for tracking student work and more challenging work for the students who have already done a year in Scratch. More on that (hopefully) in my next post.

Friday, July 1, 2016

Kahoot! profiles

A quick post today. Kahoot! has created a nice feature: profiles of Kahoot! creators. I was asked to participate in the beta stage of profiles and was finally able to get mine up. I like the idea of following different creators as they post their quizzes, but I don't think the site is up to that yet. However, if you want to check out my quizzes, go to