Minions in Math – My Favorite Thing

Miniature robots zoomed across the floor, lights flashing.    Students bent over computer screens, writing code.      Parents sent emails telling me that their kids couldn’t stop talking about the Ozobots.      My students were reviewing linear relationships, being introduced to systems of equations, and learning some coding skills.   It was the best way I could have hoped to end the semester with my 7th graders.

My students came into this project with a lot of background knowledge.    This is their second year with me.   Last year, I introduced them to some basic coding by having them create video games using SCRATCH.   The Ozobots use Ozoblockly, which is very similar in structure to SCRATCH.   (Both languages are object-oriented visual programming language.  I think this is absolutely the best way to introduce coding.   They allow the user to focus on the big ideas of coding without getting bogged down in the syntax of the language.)    The added challenge this year is having the code control a miniature robot.   This required students to work through a few challenges that had nothing to do with coding, but everything to do with problem solving and making things work.   I documented the journey on my twitter account .   There are videos there showing each step of the projects   (posts dated Dec 8 – 15).  Unfortunately, you will have to go to the twitter account to see the videos if  are interested, because my blog doesn’t support videos.

Building Background Knowledge

InitiallIy, I focused on building knowledge.   Students had to learn how to calibrate the bots, how to write code, and how to load the code onto the bots.


Next, they worked on getting the bots to do what they wanted.   They explored the different capabilities:   getting the bot to move in specific ways, playing with the light features, etc.    During this early phase, I had students work in pairs.   Because there is a certain amount of frustration inherent in the process of figuring out how to make things work, it helps to have someone to share the journey.


The Project

Once I was confident that everyone had a little experience, I assigned a two-part project that would require them to review the work we had done earlier in the year with linear equations and also act as a launch into the work solving systems of linear equations that we will do at the start of the spring semester.

Linear Relationships in Tables and Graphs

For the first part of the project, I assigned each pair of students a different linear relationship.     Each pair was given two ordered pairs, an ordered pair and the y-intercept, or an ordered pair and the slope.    They had to find the linear equation representing their relationship and create a table for the relationship.   Then, they had to create a large scale coordinate plane and write code so that their Ozobot would graph the linear relationship.   The Ozobot had to flash lights on three ordered pairs and perform a different action at the y-intercept (flash different lights or spin on the spot).


Solving a System of Equations Graphically

Next, each pair had to use a second Ozobot to graph a second line intersecting the first line on their coordinate axis.    They had to calculate the point of intersection and time the two Ozobots so that they would not collide at the point of intersection.

While there was plenty of math in the project, the most important piece of math was not what one usually thinks of as math.   It was learning how to make something real actually work.    Students had to learn how to frame a task and then to persevere in the face of challenge (one of the math practice standards).

My Favorite Thing

My biggest measure of success is that the kids dinner time conversations were all about math for the entirety of the project (a number of them ended up getting their own bots for Christmas as a result).




Necessity Is The Mother Of Invention – #ILookLikeAnEngineer

Necessity is the mother of invention.   Unfortunately, the “necessity” can be all too easily forgotten as an essential component in education.    I teach what I teach, in part, out of necessity but it is my necessity not that of my students.   I need to teach the curriculum that I teach because it aligns with the standards set forth by the state but it is not a burning necessity for my students no matter how many times I tell them the essential questions and how they will use it in the future.   Knowing something only becomes a burning necessity in the mind of an eleven year old when they see a need to know it so they can do something they want right now.

So how do we create that need to know?   I think we give kids real problems that they really want to solve.   It’s not something that I can do every day, but I try really hard to find time and space to do it every year.   To do this, I  compact lessons and I accelerate where I can.   This year, I managed to squeeze out almost a month at the end of the year to do an engineering project with my students.

Request For Proposal

Students were presented with a Request For Proposal (RFP) from a fake toy company.    The proposal indicated that this fake toy company was seeking to expand market share to include more girls in their customer base for motorized toys.    The toy company wanted those bidding on the contract to conduct market research and build a toy to meet that need.    The toy company indicated that the toy must meet one of three different criteria:  travel 3 m in 3 s, climb 1 m at a 15 degree slope in 2 s, or climb 1 m at a 30 degree slope.

Creating a Team and Conducting Market Research

Students were assigned teams and formed mini-companies that would bid on the RFP.   They created a team name, logo, and slogan.   Then, they conducted customer surveys with both adults and children in the target age range.    They analyzed the data and determined the type of toy the customer was seeking.

Building Technical Knowledge

ChJmkKSUkAEA9Q-During the same time-frame, students built knowledge of how gear trains work.   They began by building gears on a frame and exploring relationships between the rotations of the gears and the number of teeth on the gears (gear ratios, teeth ratios).   Next, they added a motor and wheels so that they could calculate the rate on a 3 m course and measure the rim force on the wheel.   They repeated this process with gear ratios ranging from 1:3 up to 225:1.   As they did this, they were building important skill in construction as well as an understanding of the different kinds of performance they might expect from different kinds of gear ratios.    From there, they measured rim force on the tooth of a gear connected to the motor.    They did so for different sized gears and then learned how to calculate torque.    With this knowledge, they could explain why certain gear ratios would not move and why certain gear ratios would be well-suited to climbing.   At this point, they had built sufficient knowledge to answer the first stages of that burning question of how to build a toy that would meet each of the criteria.

Making a Prototype

Each team began construction of a basic prototype to meet their desired criteria.   This amounted to attaching the motor and the desired gear train along with the wheels on the frame structure.   Students then tested their motorized frame to see if it met the criteria.   Once they had a basic working prototype, they started constructing a body to give the toy the desired aesthetics.    As they constructed the body, they continued to test the toy to make sure the additional weight did not place them out of compliance with the criteria in the RFP.    They repeated tests multiple times and used median values in order to eliminate outlier trials resulting from poor testing technique.

Sealing the Deal – Writing a Written Proposal and Giving an Oral Presentation


When the toy was completed, each team wrote a written report in response to the RFP and prepared an oral presentation.   The final stage of the project required each team to present their toy to a panel of judges representing the fake toy company.   I recruited 3 engineers and a soon-to-be lawyer to represent both the technical and business interests of the company for the panel of judges.   (I am lucky enough to have Sandia National Laboratories nearby and willing to provide this kind of support to encourage excellence in math and science.)   The judges selected a winning team based on the presentation and a demonstration of the toy.   (The winning team members each got a gift card to Cold Stone Creamery).

While this last stage is not “math”, it is very much a part of what engineers do and I wanted my students to appreciate the importance of being able to communicate effectively as an engineer.  Reading, writing, and speaking are just as much essential skills for an engineer as are math and science mastery

Why It Mattered

  • Students got to experience the engineering process, which is so much more powerful than hearing about it.
  • Girls had to learn how to make something and how to make it work.   It’s not that they are any less adept, but many of them are much less experienced.   This results in a certain amount of hesitancy, initially,   Having to make it work pushes them past this hesitancy and they discover just how good they are at it.    Giving girls this experience and confidence is important in leveling the playing field when it comes to engineering.
  • Students used the math that they have learned this year to do something real that mattered to them (finding unit rates, conducting surveys, making data representations, analyzing data to make decisions, finding medians, using equations to calculate torque, measuring radii).
  • Students had to find ways to work together – teams could not shift part way through the month long project.
  • Students who lacked confidence as speakers learned that public speaking is a learned skill and that you get better at it with practice.   (I made each team do a dry run of their presentation in front of their classmates and get feedback the day before the final presentations.  They took the feedback and were so much better the second day.)

Gallery of Toys


A Smile A Day – Life in Sixth Grade

“Can we copyright this?”

All of the teams in the motorized toy challenge had discovered that nothing is free.   Each element they added to the body of their toy had an impact on its performance.   One of the teams took this knowledge to a whole new level.   They decided to build a toy with only three wheels.   When it worked, naturally, every other group in the room seized upon the idea.   One of them took off not one, but two wheels.   Surprisingly, it worked and it went pretty fast.

Then, the quest for “ownership” of the idea began.


I suspect that I have some future entrepreneurs in this class.  In the meantime, they make me smile.



The Machine Awakes – Making Connections to Bring Learning to Life

I have always been a math/science person.   In school, my electives generally reflected that.   I used them to squeeze in more math and science classes wherever I could.   The arts were a gaping hole in my education.   I have never taken an art class.   I  play the piano poorly.    It’s not that I don’t appreciate the arts.   I just never felt like I had any particular talent in that area so I didn’t really pursue them.   I had a fixed mindset with regard to the arts long before I knew what a fixed mindset was.    I’m trying to expand my thinking, and have been looking for ways to connect math to the arts.

A few months ago, I approached our band director about the possibility of creating a cross-curricular event focusing on machines.      The music department was “all in”.   The art teacher and a science teacher also agreed to be part of the event.

We held the event last night.    Here is a quick snapshot of the night.


As visitors arrived, they were able to peruse an exhibit of student work relating to machines in the lobby.   Tables displayed instruments created by band students.

Simple machines created by art students were also on display.


The exhibit also displayed roller coasters created by science students.


As visitors perused the exhibit, they were serenaded by various small ensembles from the band.

Video Game Expo

After seeing the exhibits in the lobby, visitors proceeded to the computer labs where they played student-created video games.   These were games that I had my students create in February as part of joint Math-Social Studies project.   For the project, students could work individually or with a partner to create a video game about one of the ancient civilizations about which they had learned in Social Studies.   The game had to include at least three levels:  one level focusing on the civilization’s geography, one level focusing on the civilization’s religion, and one level focusing on the civilization’s history.


Motorized Toys

Visitors could then see demonstrations of student-created motorized toys.   These are toys that I have my students designing, building and testing as part of an engineering project.    This has been a way to introduce students to the engineering process, going from receipt of a Request for Proposal to a final written proposal and oral presentation before a panel of judges.     The project has allowed students to use math in very real ways as they have explored different gear ratios and calculated unit rates to determine if the toy was meeting the speed requirement specified in the RFP.



Finally, visitors attended the final band performance of the year.    Their focus piece for the evening was Machines Take Flight.


So would I do this again?   In a heartbeat.   The process was a great experience for students as they tied related ideas together in so many different ways.   It was also a great way to bring our community into our school.

From a strictly math perspective, I think this was incredibly valuable for my students.    They had to take an unframed problem and create a framework for solving it.   They had to apply the things they knew about ratios and rates in a real context.   Some of them had a hard time seeing how to do the ratios or the rates in such an open context.   Forcing them to do so, to figure out what to do and how to do it outside of a math problem was so good for them.   Giving girls the chance to build something real and figure out how to make it work was so powerful.   They went from hesitant to confident.   They will not be as hesitant the next time.