Quadratic Catapult!

My students impressed me SO MUCH today!  I am just so excited by the project we're working on and how well they've done so far.

I gave my students a table of available supplies and a budget of $50.  At the end of last week, they previewed this materials list and I showed them a Powerpoint of a variety of photos of catapults constructed from these materials.  I wanted them to do their own research, but barring me checking out mobile labs and supervising web browsing, that wasn't going to happen in school.  Too many of my students don't have internet access at home for me to assign anything for homework that requires the internet.  My pre-selected photos actually worked well because it gave us an opportunity to talk about how certain designs worked. 

Material	Limit	Cost for one	Need	Cost
Plastic Spoon	1	$10
Masking Tape	3 feet	$5/foot
Rubber Band	6	$2
Popsicle Stick	10	$3
Small Cup	2	$3
Cardboard (approximately 8”x10”)	2	$4
Wooden Clothespin	2	$5
Wooden Pencil	4	$4
Staple Remover	1	$25
Paper Clip	4	$2
Binder Clip	4	$2
Total

They started off by spending a minimum of 10 minutes planning their design before I let them "purchase" materials.  Construction was full of redesigns, and all but one group worked together well to solve the challenges they faced.  By the end of the hour we spent on the project today, all groups had a working model that they had tested at least a few times.  (Photos to come)

For those of you wondering, the approximate teacher cost for this project (for 50 students in groups of 3 or 4) was about $15, though you likely have most of the materials in your classroom already.  Substitutions are certainly possible.  No groups used a staple remover.  Few chose pencils, paper clips, cups, and clothespins.  I did want to have a large enough variety of materials that students wouldn't recreate the same design in each group.  I also had several students ask to bring in materials but I didn't allow them to do so.  I could have, and it would have increased variety, but I wanted to keep the playing field level for this project. 

One thing to note: I made a model at home just to test out my idea.  It sent the projectile about 5 feet, perfect for a classroom project.  My awesome students, however, have sent their beans flying 40+ feet (from one end of the room to the other).  It was organized chaos in my room today, but all in the name of learning.  So, if you're at all concerned about safety or the discretion that your students would use during this project, it might be good to test outdoors.  Of course, it's pouring rain for three days here, so we're testing inside and making it work.  I actually had the librarian offer her space, too, so I think we're going to try to be really quiet while we test tomorrow!

Tomorrow, the groups will collect accurate data on the distance their bean travels and the time it takes to land.  We'll find an average for each of those data sets and use it to find the equation of the parabola.  I can't wait! 

If Barbie Were as Tall as Me- A Lesson in Proportional Reasoning

This lesson idea isn't new; it's easy to find many versions of it all over the internet. In fact, I was inspired by a post from fellow teacher Fawn Nguyen.  Here's my spin on it.  My students need to review proportional reasoning this year, so I wanted to focus on application since they got the basics of how to cross multiply and solve last year.

I started by collecting some Barbies and Kens.  Thank goodness for generous teachers in my district and our fabulous e-mail network!  I got 5 Barbies and Kens in no time.  I bought one more at Goodwill for $1 and now I have enough for each table in my classroom to have one.  I'll try to pick up a few more when I can find them (clothed) for $1 or so.  :)

Students will work in their table groups of four on this project.  They'll need to select one student in their group to serve as the human reference.  That student's height will be used and their silhouette will be traced on bulletin board paper.

Next, students will carefully measure and record data on Barbie's body measurements.  I selected six data points I'd like them to collect and superimposed them on a coloring page of a Barbie doll.  They'll write proportions to find out how large these body parts would be if Barbie were enlarged to their height.  Then, they need to work as a group to make a scale drawing on chart paper.  I'm planning to have them place their scale drawings next to the silhouettes to show off how unreasonable Barbie is.  I'm also curious to see if this pans out in a similar way with Ken or if he's more reasonably made.  His abs are unusual, that's for sure!

A screenshot of a portion of the diagram students will use. 

The individual portion of the project asks students to write a letter to Mattel explaining their findings and requesting changes in Barbie's physique so that it will be more true to life.

Since it's Monday, I'm posting to made 4 math.

EDIT: There's a follow-up to this post here that contains files you can download.  

The joy of a rich question

I was considering the first unit for my Intermediate Algebra class and how I could enliven it.  My first unit isn't even really part of Intermediate Algebra but rather part of my state's 8th grade curriculum.  Because I teach high school courses in middle school, I'm responsible for delivering two courses worth of curricula in one school year.  Thankfully, we operate on a schedule that allows a year-long every day block of 88 minutes for math and reading, so I can get it done. 

I'm challenging myself this year to find a really rich question to ask near the beginning of every unit with the intention of answering it throughout the unit.  Today, I started my measurement unit with my students.  Our state standards require students to find the area of composite figures composed of polygons and circles and to find the volume of cylinders.  I posed the following question to my students: "How much would it cost to paint the ceiling throughout the school?"  Our school is highly irregular in design thanks to its age and at least three renovations/additions of which I'm aware.  The map is far from rectangular; my room is a trapezoid and our cafeteria has a wall that bows out in an arc.

I set the students to work in a Think, Pair, Share in which they had to list factors we would have to consider when evaluating the cost.  I meant to take photos of their posters.  They'll get added to this post when I get back to my classroom.  Here are a few of the "obvious" answers and some highlights that show they were really thinking about this in depth:

• The area of each ceiling tile and number of ceiling tiles
• The amount of paint per can, its cost, and how much surface it would cover
• The amount of masking tape, plastic sheeting, brushes, rollers, stir sticks, paint trays, ladders, and gloves needed. (I get the feeling these kids have painted before!)
• The salary of the crew, how long it would take to paint, and when the painting would happen
• How the lights would be treated, if at all.  (This was a point of great contention.  Some students thought it was a fabulous idea to paint the lights and give everything a blue cast.  Others thought they would like regular white light in the classroom.)
• What kind of paint would be necessary. (They realized that the gym has a different type of ceiling than the classrooms and that they would need to research the proper materials.)
• The need to consider HVAC and proper ventilation. (They pointed out that we would waste A/C if we left the windows open to let the fumes escape.)

I was very impressed with their quick brainstorm.  Now I would like to hone this into a class project that culminates with a presentation to our principal.  She used to be a math teacher, so I think she would appreciate it.

My next plan is to have them consider the list they made and decide what math skills they know that will help them with each aspect.  I see applications of area, perimeter, volume, proportional reasoning, and likely percents (when items are on sale or using the percent of ceiling covered in lights in my room to predict the amount covered in the whole school).  Just my luck, all of these are within my curriculum.  :)

Students will then work on determining the area to be covered.  I know we can do this with the maps of the school that we have, but I think I might be able to use my classroom GPS units at some point to get measurements on the outside corners of the building to help the students calculate the total area of the ceiling of the school.  I honestly don't know much about how the GPS units work and need to learn what to do with them.  That's a goal I have for this year.  I did buy a book of lesson plan ideas so I could try to incorporate them this year. 


Next, I will divide the class into teams, each of which is to research one area of interest (paint type, salary for workers, other materials, color selection) and provide two or three options for the proposal along with their recommendations for which one is the best choice.

At that point, we can put together a PowerPoint as a class and (I hope) "brief" our principal on the idea in our teams.   

I really doubt we'll be painting anything, but it's food for thought! 

Welcome!

Thanks for visiting my new blog.  I currently teach Pre-Algebra and Intermediate Algebra at a middle school and as I was beginning to be inspired for the new school year, I found I had lots to share.  While Pinterest is fun, I needed a place to share my own creations. 

I chose "i is a number" for the title of my blog because it gets at my love of math and sounds like poor grammar- one of my major pet peeves.  Teaching students about i last year for the first time was such an experience!  "Really, kids, it's a number.  I promise!"

I don't know how regularly I'll get to update as the school year progresses, but I'm looking forward to networking with other secondary math teachers, especially any with PBL or STEM experiences to share.  I hope you find something here you can use and that you let me know if you do.  Thanks again for visiting! 

Miss B