Showing posts with label algebra. Show all posts
Showing posts with label algebra. Show all posts

Literal Equations: Tweets from #mtbos

 Literal equations is one of the topics in Algebra that I struggle finding different activities for. Literal equations is one of those topics that is very procedural and not very conceptual. I put together a list of different activities from #mtbos on Twitter. Look through each of these and see which ones you might like. 



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A Flavorful Application of Mean, Median, Mode

I was looking for a different way for students to apply their knowledge of mean, median, and mode in Algebra 1. I wanted some application where they can use mean, median, and more in a different context. 

I found this article a couple of months ago and found it really interesting.

https://qz.com/918008/the-color-distribution-of-mms-as-determined-by-a-phd-in-statistics/

I had students read this article and groups and come up with what they noticed/wondered about the article. I asked the students if I gave them a pack of M&M's what they would be to extrapolate from the pack. They said they needed to know the total M&M's in the package to determine the location where they were made and the color breakdown inside each one.

Each group of students were given a package of M&M's and had to count how many of each color they had.

Then we put all of our data on the board. Students had to come up with the mean, median, and mode for each color and had to decide which of the data sets to use if they had an outlier or not.



They had to look back at their data and examine which factory their set of M&M's came from. We also talked about what might be different from their graphs to ours and how you might be able to tell the difference between each plant.

This was a great activity for students, they were excited because they got to share and eat their M&M's when they were done.
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Algebra Racecars

There are lots of ways to do this activity, if you want your students to construct the same type of car (which is fine) you can follow these links, then come on back.

http://www-tc.pbskids.org/designsquad/pdf/parentseducators/4wheelcar-english.pdf

or

https://www.questacon.edu.au/outreach/programs/science-circus/videos/balloon-powered-car

One way is I have some of the materials that students may need and some others. These are the items that I bring to school:

  • balloons
  • bottle caps
  • smaller dowel rods (from our shop teacher)
  • cardboard
  • tape
  • rubberbands
I give them 15 minutes to create a car. I normally have them as a group create the straw and balloon together so they have the same propulsion system. They have 15 minutes to create and test their car before we record them with our iPad. I normally have them record 2-3 times just to make sure, during this time other students are collecting how far the balloon goes and the time. 

Our next step is to collect our data. 

I ask students to find the speed their car went and ask them to put a graph on Desmos. We then collect our data together as a class and talk about what each line means who's went furthest who had the top speed.


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Forgetting Proofs

I was reading Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity by Loren R. Graham and I came across a great little quote, but we will get back to that later. The book was like Paul Erdos book The Man Who Loved Only Numbers style of quick writing.  It was a fascinating book with history of some of the most famous Russian mathematicians of the 19th- 20th Century.  This book reminded me of a professor that I had at the University of Nebraska at Omaha.
Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity

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A quick quote gave me inspiration to get students up to the board.

He would begin a proof at the blackboard, pause, and then say, "I cannot recall the proof; perhaps one of my colleagues could remind me."  This was a challenge that the class felt obligated to meet.  One student would jump up, go to the blackboard, attempt the proof, fail, and then sit down with a red face.  Another would get up, perhaps a 17 year old, successfully write the proof on the blackboard while the entire class stared enviously, and then sit down.  Professor Luzin would turn to that student, bow slightly, and say "Thank you, my colleague."  Luzin treated the students as intellectual equals, and his teaching led them to prepare for and anticipate coming lectures.

One of them later ask, "Had Luzin [really] forgotten the proof, or was it a well-constructed game, a method of arousing activity and independence?" They never knew.

This small process of accidentally forgetting the proof or answer to an example is a great way to get students up to the board and motivated to do mathematics.  I especially love the part where the instructor bows to the student and offers a sincere Thank you and recognizes the student as an equal, in mathematics you are always trying to get students to enjoy math and approve of their mathematics.

How could you incorporate this small idea of forgetting proofs in to your teaching?  What benefit do you think would this have in your classroom?  How do you do this now in your room?
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