Sprinkler System Design

After determining how to write the equations of circles through the Shell Center activity: Equations of Circles 1, my students needed to practice using equations of circles. I decided to find my high school on Google Maps and make a screenshot. I then imported the screenshot into Desmos and adjusted the size of the image so that 1 unit = 1 foot in my image. I shared the link using google classroom, but it could be shared in any way that you choose.


I had students submit the link to their final design using a google form, the response spreadsheet made it simple to manage and grade.


The assignment was to design a sprinkler system that covered all of the grass, at a minimum cost. I researched commercial sprinkler systems and found that the maximum radius of a sprinkler is 15 feet. Here are some students designs (click on the image to go to Desmos):


Next year I want to provide students with a list of pricing per foot for trenching, sprinkler pipe, heads for various radii, control box and also require that they calculate the cost for their design. I also want to require that they draw in the underground piping which would allow students an opportunity to review linear equations and piece wise functions as well. Additionally, calculating costs would force students to apply distance to find lengths between the sprinkler heads too.

[update 7/10: Desmos made a formula to calculate pipe length! I could have students explain what this formula does. click on the image to go to Desmos.]

Day 155 & 156: The Triplets of Cellville

I chose this Mathalicious lesson because we have not used circles enough in my geometry classes. We stared the school year with constructions, but haven’t used them much this semester and I wanted them to recall and extend prior learning. I also wanted students to gain more experience modeling real world scenario’s with mathematics & I thought this task would be engaging do to it’s relevance to students lives.  I started off showing the introductory video clip which is a news story of a woman explaining how photos taken with a cell phone include GPS data and how your cell phone records your location. I was surprised that ALL of my geometry students were furious at this video. They thought this lady was dumb for being surprised because “…everybody knows that you can turn on and off the location settings on your phone!” one student argued that if this woman in this video was her mother, she would be furious at her for being so clueless. It was great because it got very intense, and I had no idea how savvy students are with their cell phones. After this discussion died down students inevitably asked: “Wait, what are we doing today? Are we learning how to stalk people with their phones?” and “Mrs B, you are so weird.” Also “This is going to be awesome!” They were hooked.

I don’t want to describe the entire lesson in too much detail because I want you to support Mathalicious and their quality activities, but students constructed circles on a map to determine possible locations of a person in relation to a few cell towers. The lesson also discussed coverage vs locate-ability and students had to use estimation & area formulas in order to draw conclusions and also to determine and justify where they would add a cell tower in a city if they were in charge of making the decision. The only thing I would change for next school year is that I would modify the lesson to use our town and cell tower locations locally to make this more relevant and less hypothetical. Students were engaged and it was a good way to use student interest and incorporate modeling at the end of a school year when motivation is typically pretty low.

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Geometry: Planning the last 6 weeks

The last six weeks of geometry will focus on similarity, dilatation, indirect measurement, similarity transformation proofs, and circles:

We will start with a review of real world ratio and proportion practice, interactive notes page & review, possible including activities such as New York Minute (NCTM Illuminations).

We will then head into applying the properties of proportion to geometric figures in discovering and defining similarity as described in the investigation activities in Discovering Geometry.We will complete an interactive notes page and practice. We will use similarity to measure tall objects using a mirror and measuring tape with indirect measurement. It is also an excuse to get outside, since it is getting warmer out and we are all developing cabin fever.

I am hoping we will have time to incorporate the Math Assessment Project‘s lesson: Solving Geometry Problems: Floodlights (MARS).

I am very excited to try to channel my inner Fawn by spending 2 days on Letting Them Own the Problem applying similar triangle properties.

We will explore & discover properties of dilatation’s with the Flip Family (page 13 of this pdf), followed by an interactive notes page and practice. I am just going to have to create a Dilatation Station Rotation because that has a fun name (and students will need some practice).

The scariest part for me will be attempting to teach similarity proofs through transformations as describes by Kate Nowak here. Hopefully, at the least we will all learn something.

Next we will discover & apply the relationship between similarity and proportions with area and volume through discovery activities, interactive notes and this little gem.

Then we are on to a short excursion into circles. We will begin with developing an understanding of radian measure, followed by a 3 act lesson by Mr Stadel. I plan to dedicate a few days on the Math Assessment Project’s Sector of Circles lesson. We will also do the 3 act lesson be Dan Meyer: Lucky Cow.

I plan to end the school year with a Modeling project adapted for my students to be more self directed: rolling cups.