# Math

### AIMS Scholars Engineer Part 2

Engineering Week. It’s a lot like Shark Week, but with the kind of interaction where you learn to make the Miura fold instead of losing an arm.

Before going much further, watch the video at the top of my earlier blog post on this topic: AIMS Scholars Engineer Festively! From June 23, 2017. In it, you will see a rocket cart with no “recovery apparatus” attached. Note how far it travels.

During the week of June 19, 2017, a good portion of the present AIMS Scholars attended FPU’s Engineering in the Classroom Festival. It is a required course for those working on a MA in STEM Education and an option for a few other degrees. This year’s focus was on Mechanical Engineering. The participants, all of whom are teachers in the Central or Southern San Joaquin Valley of California, were provided instruction in several areas related to this theme. They passed through a rotation of classes with Mr. Daniel Loewen, Dr. Steve Pauls, and Ms. Aileen Rizo.

Dan’s section focused on the mechanics of slowing a rocket sled, and the mathematics needed to calculate precisely how much slowing could be accomplished with various apparatus. Of course, it’s easy to make a sled stop, just strap a big brick to the back of it that has too much mass for it to go anywhere. This was not the goal though. Instead, these teachers were to model, using mathematics, a few designs that met some very specific mass and volume limits and maximize slowing within those parameters.

Steve’s section focused upon the use of what are known as “Simple Machines” (internet hunt quiz time: what are those five machines, and are there examples of each of them within your muscular-skeletal system?). The teachers performed numerous physics experiments upon each of these machines to understand and communicate that understanding to students the properties at work.

Aileen’s section was the most eclectic. For this session, the teachers were investigating the physics and mechanics of paper-folding, its applications, and methods to model it within a virtual medium like a computer program. They folded paper to create rigid-structures that could withstand compression (a topic from last year’s Engineering Festival) in order to increase reference area for deployment in rocket systems. Then, they examined some very interesting fold patterns that occur in sudden compression. For example, what happens when a piece of paper is wrapped around two cylinders that are separated by a ¾” gap, then the two cylinders are twisted in opposite directions and pushed together to close the gap? Try it for yourself and see.

Now watch this video. In it, you will see AIMS Scholars who have mathematically modeled a particular paper fold and parachute volume that is designed to slow the rocket sled within a predicted distance. The fold came from the lessons learned within Aileen’s class, the use of machines was analyzed in Steve’s, and the modeling and application was accomplished in Dan’s. What do you suppose could come from this experience in the classrooms of these teachers? We are AIMSing (pun intended) for great things.

### Addressing Mathematical Practice Standards Through Multiplication and Division Word Problems

Have you ever given your students an experience with manipulatives and then found when you shifted over to a textbook that the students didn’t make the connection between the two experiences? As a curriculum developer and researcher, I am constantly looking for more ways for students to make connections from the concrete (manipulatives) to the… Continue Reading

### Building Confidence in Math with Multiplication

Why do you teach? I remember when I first came into the profession it was because I enjoyed students and wanted to make a difference. I still love watching movies of teachers that have gone into challenging situations and inspired students to think differently. These teachers empowered the students to be all that they were… Continue Reading

### Tangram Polygons: Composing and Decomposing

In my last post, Tangrams: A World of Geometry, Part Two, I talked about the thirteen convex polygon shapes that can be formed with the seven tangram pieces. In the video, I showed how to make five of them, and then I left a challenge for you to look for the remaining eight convex shapes.… Continue Reading

### Have You Done a Good Math Problem Lately?

In work or social settings it is common to hear the question, “Have you read a good book lately?” The question often starts a lively sharing session about books that elicit pleasure, profundity, or insight. A population that regularly engages in these discussions is an indicator of a literate society. As those appointed by society… Continue Reading

### Writing a Multiplication Word Problem

Word problems are typically not students’ or teachers’ favorite part of the math lesson. When I talk with teachers, they are frustrated with teaching multiplication word problems. I think one of the things we have been missing is teaching students the structure of what is involved in any multiplication word problem. “Look for and make… Continue Reading

### Partitioning Shapes: Is it Geometry or Fractions?

How early should we teach words like half, thirds, and fourths to children? I know that I have often heard that we give young children things they are not developmentally ready for, and I agree. But when it comes to having language identify a concrete experience, I think children can handle it. I was measuring… Continue Reading

### Three Great Multiplication Posts

How to Equip Your Students to Better Understand Multiplication, Part One As I have coached and taught in the classroom, the three most popular ways to describe multiplication is showing ______ groups of ______, using repeated addition and making arrays. Now all of these methods have their place in a student’s understanding of multiplication, but… Continue Reading

### Finding Math in Unexpected Places

I was reading Inchworm and a Half with my 6-year-old daughter, Bethany, last night for the 40th time. She loves reading the section, “Squirmy, wormy, hoppity-hoop! We measure everything, loopity loop.” Even before she could read books she memorized this section and would “read” it. The book is about an inchworm that loves to measure… Continue Reading

### The Problem of Anwar’s Camels

I just started reading Fractions in Realistic Mathematics Education by Leen Streefland, and there, on page 5, Streefland gives as an example an old puzzle problem that I remember giving my students more than 40 years ago. “An old Arab, Anwar his name, decreed before he died that his eldest son inherit one-half, his second… Continue Reading