Gear Unit

Our second unit was an example of taking one idea and looking at it from different STEM perspectives – in this case, gears. To bring in the student perspective, we had guest learners – kids!! So each group had one third grader.

We started with a web quest to answer the question: What is technology? We discussed, and then each of us had to post a unique example of a technology on the wall – no two could be the same.

Technology Word Wall

We had some gears to play with to see how they worked.


One of the two sets of gears we worked with.

We answered questions such as: How can you get one gear to turn another in the opposite direction? The same direction? How can you turn a gear once and have another gear turn twice? Do gears push or pull each other?

Then we had STEM related questions.  For my focus – math – the questions were:

  • Find a pair of gears such that if you turn one gear twice, the other gear will turn once. How many teeth are there on each of the 2 gears?
  • Find a pair of gear such that if you turn one of the gears 3 times the other gear turns 4 times. How many teeth are on each of the two gears?
  • How can you mathematically represent the data collected in questions 1 and 2?

We looked at different examples of gear driven machines: corkscrew (arm type), bicycle, watch with exposed gears, egg beater, drill, can opener. Then, using K’Nex, each group built a gear-driven machine.

KNex 1

KNex 3


KNex 2

The gear focus was extended to bicycles. Two kid’s bikes were brought in. First we had to make an accurate scale drawing of the bike, indicating our scale. Then we did some math:

For one revolution of the pedals, the number of revolutions that the rear tire makes depends on the number of teeth on the gears. Record and reflection the following for your bicycle:

  • Number of Teeth on the front gear (pedal)
  • Number of Teeth on the back gear (tire)
  • Number of Revolutions the back tire makes for one revolution of the pedal

What is the distance your bike travels in 10 revolutions of the pedal?

How many revolutions would you have to pedal to go on a 1 mile bike ride? (Assume no coasting)

Then we needed to find the following geometric shapes on the bike: a line segment, a triangle,    an acute angle, an obtuse angle, parallel lines, a quadrilateral, a pentagon, and a circle.

I love this unit and plan to use in my Geometry class next year once they’ve been introduced to geometric notation.

Another Linkstorm Post

I know I just did a favorite websites post, but I got a couple good resources in my Multiple Pathways class I wanted to pass them along.

The first is courtesy of Kim Bell, an English teacher at East Union High School in Manteca. Kim was a tech writer before she became a teacher. A former TCSJ student herself, her master’s project was creating a website that would be a resource to find the plethora of free or low cost online tools for teachers: 

The second came out of one of our class assignments. I had to research a topic of personal interest and picked project-based learning in math. I found an article by Janet Pinto on the TeachThought website: What Project-Based Learning Looks Like In Math. These are six sample Project-Based lessons based on the six Common Core High School Geometry topics. I was very excited to find this resource and plan to utilize these in my Geometry classes next school year.

I really enjoyed my Multiple Pathways class. I know our school working to incorporate this idea, and I imagine that we would follow the model of setting up several pathways for students to follow during their time in high school that would incorporate internships at local businesses. The idea is to give students real-world experience and job skills as well as integrating their education to give it meaning and relevance. I hope it succeeds.


I created a new activity for my Geometry students to help them review transformations I’m calling the Transformation Go Round.  I was inspired by Irina Kimyagarov’s lesson, but I adapted it to my classroom’s level, which was a little more basic.

I made six stations labeled A-F.  For each station, I glued a blank graph and the station instructions to a sheet of 12×18 construction paper.  I placed these around the room.

The students divided into six groups. They move around the room, going from station to station.  At the station, they draw the figure on the graph paper (with specific color highlighter, to make it clearer what drawing went with what step), and then list the final coordinates on their sheet.

The first step is to graph the given coordinates and connect the dots to make a polygon. Then they do a rotation, reflection, translation, another rotation, and finally, another translation. Since their starting point is the previous group’s result, they need to check the previous group’s work before they start on each station.

One thing I would have changed is the grouping.  I let the students make their own groups, in order to get more buy-in from them.  But it meant some self-grouped with other low performers and were a bit lost.  Irina Kimyagarov stated that she did heterogeneous grouping and I think that was the key point I missed.  Another thing is that the activity took a bit longer than I had originally predicted, because the students needed to review (using their notebooks!!) the core concepts.