Angle of Elevation - Activity

on Wednesday, April 26, 2017
Today we did a great activity that allowed students to get excited about SohCahToa and angles of elevation.

The Set up:
Last week we did an AMAZING 3 act using SohCahToa. Check out the videos here. This helped them remember what they did in Geometry with trig. Then yesterday I re-introduced my students to SohCahToa in a more formal way. We went through how to solve for angles and sides.

The Plan:
Today I started by having them pull out their iPhone, if they had one. (In my school I can count on at least half of the students having an iPhone). I asked students to open the Compass app and swipe right. When they do this, the level opens up. Students with androids were able to look in their app store and find many free levels that did the same thing.

I gave students the instruction: "Figure out how this works." A few minutes later I asked them to hold it in landscape view, parallel to a wall. Then I asked them to, by tilting left and right, figure out what the negative numbers are.

After a little exploration, I instructed students to pick up a half straw that was on their desk -- I told them to place it on top of their phone and use it like a scope. We then practiced looking at random things in the classroom and having a partner read them the angle they were looking up at.

Then, I drew a picture of a flagpole on the board and said "There is a flagpole outside our school. We're going to figure out how tall it is. Now, we're not going to climb up it, and I don't have anything that can reach to the top of it. At your table, sketch this situation on your whiteboard and see if you can figure out how to determine how tall it is." I gave students a few minutes to talk and draw -- they were excited! In their groups realized they could get the angle, and they also realized they could probably get the distance along the ground.

I have a measuring wheel that I bought from Harbor Freight for probably about $15 a few years ago (think -- this is what cross country coaches use to measure their course). I showed them how to work it, and then we headed outside. Students took their measurements in groups of 3 - 4 to help save time in sharing the measuring wheel.

 

 



I created a google form for students to submit their group members names and their calculated measurement. I'll check it out later tonight to see who got the closest and give them a prize!

 

This was a super fun activity and I hope you try it out. If you would like an activity page to accompany it, check out this link.


I do this activity on a block day -- afterwards we practiced drawing pictures for different scenarios of angles of elevation and depression. Then I've used the worksheet below the past few years and enjoy it! The last few problems are good thinking ones!
Angles of Elevation worksheet
Answer key 






Hour Of Code: My Robotic Friend

on Friday, December 5, 2014
My Advanced Math Applications class is an elective for seniors who need or want a 4th year math credit, but don't want to take AP Stats or AP Calc. I have never taught an elective before, and it a breath of fresh air! There is so much freedom in what to teach, and it allows me to really listen to my students and work towards things they enjoy.

Something I heard of last year was Hour of Code, and knew that I wanted to do it with my seniors in AMA! I decided to do the 20-hour course (designed for K-8, but I am making necessary changes as we go to make some things more applicable for my students). All of the lessons have been made, and most of the materials are print-and-go. It's completely rocks. Also, not all the lessons are online, so students learn how to code by working with each other and without technology. If you do not have a 1-to-1 program at your school, you can still do all the "unplugged" activities.


The lesson I did today was day 4 of the 20-hour course, tweaked a little bit. Hour of Code has a graphing activity similar to this, but it sounded way more fun to "Program Your Friend" and build a stack of cups!
 
In a nutshell, students worked in groups of 3. Two students were programmers and one student was the robot. There is a set of cup stack cards that the programmers would choose from and write a program for the robot to follow, and hopefully successfully build the stack! The two programmers had to use the symbol key to write out instructions for the robot to follow. When the programmers were done, they would bring the robot over and make the robot run the program. If something went wrong, the programmers could stop the program, debug their code, and run it again. You can find the entire lesson here.
 


Every student was engaged for the entire lesson! Students loved working together and trying to come up with their own cup stacks for their friends to build. I hope everyone gets a chance to participate in the Hour of Code.

Math Dance Moves!

on Monday, September 29, 2014
Today we continued with our review for variation equations and graphs. The Kahoot was a great motivator for students to learn the equations, graphs, their names, and other attributes. However, why stop there? Since a hyperbola and inverse square curve give us very interesting graphs, whenever I explain which graph I'm talking about to the students, I tend to make the shape of the graph with my hands. So, as part of our prep for the Kahoot competition, I had students practice making the graphs with their hands too! I told them they could use these as sweet dance moves at homecoming...

And I digress.

Anyways - it was fun and fantastic and I hope you use nifty dance moves in math class with your students. It helps form the memory with less effort than trying to cram it in your brain.


Graph Wars! Formative Assessment for Graphing

on Sunday, September 28, 2014
 I love finding ways to engage my students in what we're learning about. Graph Wars has consistently been a student favorite! 

I set students up in pairs, and their goal is to graph the equation correctly, but also first! When you're done you yell "DONE!" so your partner knows. Then once both students are done graphing, they look so see who got it right. 







Check out the whole activity here at TPT!

Kahoot!

While I am not one for games in the classroom, since most tend to have one person doing all the work while everyone else watches, I can be persuaded to try one if it looks like it has potential. I was introduced to Kahoot as a classroom game this summer. I made one that helped my students review variation equations, their corresponding graphs, their names, and other features such as domain, range, and asymptotes.

What I love about Kahoot is that students get extremely competitive as they play, and they want to win! The picture below shows what gets displayed on the board and what a student sees if they play on their phone. A student can also play on their computer.



Here is a picture of what my room looked like when we were playing this game! The students were very intense about the whole process, and engaged the entire time. If you want to use my kahoot, go here!




Pros:

- You can see a ranking of top students.
- Everyone plays
- Once a student has voted they get feedback if their answer was correct or not. (Great formative assessment right here!)
- Kahoot has a bunch of math symbols you can insert! Woohoo!
- You can download an excel doc of the class and how each student did! Kahoot for the win!


Cons:
- Speed based game. Math isn't about doing things the fastest as long as you can still do it correctly.
- Students get to choose their own "name" for the game. If they choose an inappropriate name you can't necessarily tell who it is. (However, you can kick them out by clicking on the name!)
-


Happy Kahooting :)

First Week in Math Class: Don't use numbers

on Saturday, August 16, 2014
August makes me antsy. I feel like all teachers get nervous-excited for the start of school, and August makes me think of that! It is close, but not close. The start of school is far enough away to not feel burdened, but close enough to know it's time to get work done! I remember Meg Ryan's character from You've Got Mail talking about bouquets of freshly sharpened pencils - and I quite like that idea.

Going into my fourth year of teaching, I no longer feel like my summer prep is only focused on creating lesson plans and worksheets. I am thinking more about how I want the whole year to play out, and how to set my class up for success in the first week. 

During student teaching, my cooperating teacher told me about the "don't smile until Christmas" rule that many teachers abide by. If you've never heard of it before, the idea is to keep firm rules and guidelines in your class during the first months so that students are aware of the expectations, and then by second semester they should be able to follow them without thinking.
Textbook used for AMA
In a graduate course I took this summer (Educ 531), we explored the idea of community, culture, and collaboration within a school or classroom context. As a result, I questioned the no-smiling rule and wanted to find a different way to start the year with my students. One that would encourage students to follow the rules or guidelines for the class because they felt as if they were part of something, not out of fear. 


So I came up with this for my Advanced Math Applications class. This class is special because it is for only seniors who want to take a 4th year of math (we only require 3 for graduation requirements) but do not want to take an A.P. math course. They are likely interested in math, but do not see themselves as an A.P. student. 
On the first day, I will have some sort of homemade goodie for them that they can grab on their way in. Have you ever noticed how food brings people together? If you think about great conversations or fun experiences you've had, I bet you that food was involved. Not only that, but I want to catch my students off guard. I want them to wonder what I'm up to. I want them to think it's a little weird, but not necessarily bad... 


When class starts, we won't sit at our desks. We'll gather our chairs into a circle so that we can see everyone. I have an introductory powerpoint that tells students about me, my background, what I like to do for fun, and what I did during the summer. I've heard from students that they like knowing that at the beginning of the year because they often don't get to hear about that kind of stuff - especially in a math class. Once I'm done introducing myself, I will have all of my students go around and introduce themselves. Not with the same fluffy stuff they usually answer (what's your name, favorite food, favorite activity), but some more interesting questions - Why did you sign up for the course? What are your plans after graduation? What are your aspirations? (This year... life... ?) This will likely take us the entire first day and potentially into the second. 
Whenever we finish, we'll start on the Why Study Math activity that I've used the past few years. I'm pretty passionate about avoiding the syllabus for at least the first week, and this activity gets students working in groups, using their laptops, and sharing in front of the whole class. Additionally, I just facilitate the process. The students are talking most of these three days which is useful for building up trust between students so that they will hopefully talk to each other once they start working on actual math problems. After about 3 class periods, this activity comes to a close and I'll review the syllabus. 

My syllabus for the Advanced Math Applications class spells out some of what I want to do. Being an elective, I have a little freedom. I decided that with this class I am going to be a little adventurous and try to implement some of the things I learned and believe in. 

The goals listed are:
1.     Convey the power of mathematics by showing a wide variety of problems that can be modeled and solved using math. 
2.  Apply mathematical knowledge to daily life experiences.
3.  Understand how certain parts of our world work.
4.  Learn how to think mathematically.
5.  Work collaboratively, helping each other learn and succeed.
6. Connect to the community through speakers, trips, and working with an elementary class.
7. Perseverance through difficulties.
8. See God’s hand in the world, including mathematics.

On my syllabus I do not mention anything about rules of the class, do's/do not's, punishments, or behavior requirements. We will end the syllabus by reading Romans 12 from the New Living Translation. As a class, we'll use this passage of scripture to come up with guidelines on how to act - like a contract of sorts. Linking expectations to scripture instead of to what I want, and realizing it is about community will hopefully set my classroom up for success. 

Long story short, don't use numbers during the first week of math class. Shake it up. Live on the edge. Throw your students off a little bit. Make them wonder what you're up to. If nothing else, it will help them understand a little bit that you care about them more than getting through the material.

How I Made Learning Logarithms EASY!

on Thursday, March 20, 2014
Teaching logs the past few years in my Algebra 2 class has always been stressful. I feel like the students never really understand the notation or how the pattern works... I have had other teachers tell me to teach them "little to the big", tried to connect it to the inverse of 10^x, tried to hammer translating from logarithmic to exponential equations, and it all ends in huffs and puffs of confusion and frustration... from me and my students.

Logs are dumb. Logs are weird. The notation doesn't make sense. I just don't get it.

I hate hearing these things! So I set out for a better way. A better way to teach and a better way to understand. And that's when I happened upon this gem of a video by Vi Hart.



I was inspired! Inspired to make a lesson that my students would not huff and puff at! So I took the big ideas from the video and made my own teaching script. The idea is to link students' understanding of regular number lines to a number line found by multiplying.

Start with reminding students that they know how a number line works. To get from one number to the next you take a step of size 1. If you want to do 1 + 3, you start at one and go three +1's. If you want to do 1 - 3, you start at one and go three -1's.


Not rocket science. 

Then you introduce the idea of a new kind of number line. Instead of a number line that works in an adding kind of way, we're going to look at a "times-y" or multiplying way.

So if we start at zero and label up to step 5, and have steps of size "x2", how does the ruler work? Well, start at 1, and times by 2 to get 2. Then times that by 2 to get 4, and that by 2 to get 8, and so on.


I asked them, how do the 5 and the 32 connect? And right away students see that 2^5 = 32. I asked, what does the 2 mean in our number line? They see it's the size of the step. What does the 5 stand for? It's how many steps you take! So in a "times - 2" number line, we can take 5 steps and get to 32!


This is a good point to have students try to explain why we always start with "1" above the "zero" step. (It's because any number to the zero power will equal 1!)

The next scenario to explore is this: Sometimes we know the size of steps we want to take and the number you want to get to, but not how many steps it will take us to get there. I draw the following on the board... If you are taking steps of "times 3" or x3, and you want to get to 81, how many steps should you take?
I tell students it's likely useful if we write this in a way that solves for x.... 3^x = 81 is what they usually come up with... but it still doesn't solve for x. So we introduce this new notation:
STC (System That Counts). So in a system that founds in a times 3 sort of way, you can get to 81 by... taking 4 steps! And it totally clicks! So I ask a few more, to make sure they understand -


And then come the awkward part of telling them you lied about this notation and that it's not really how it's written. But explaining how you only change a little bit of the notation to include the log doesn't seem to phase them.
After we go through the log to exponential equation translation ....
..... I take them through a bunch of examples.

You can explain the log(1/1000) by thinking of backwards steps or "divided by" steps. For log problems that have really odd fractional powers, I do not go into how this STC works, but Vi Hart does a great job of it and I might show my students that part of the video soon!

I know what you're thinking: "This really works? They get it?" YES! They do! After my first hour of teaching this, one of my struggling students said (no joke): "That's it? I think that's the easiest thing we learned all year!" The past couple of days this student has been helping other students understand logarithms!

I hope you can make learning logs easy for your students too! :)