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! :)

Math Competitions

on Sunday, March 16, 2014
So some people may say that math competitions are really dorky - and having gone to one the past 3 years, I would have to disagree! My school doesn't really have a math club, but our local community college puts on a competition every year specifically for 9th and 10th graders. In putting together teams, I look for students who are reasonably good at math, have perseverance in problem solving, and are good at working with others. It's awesome to ask a kid to join who never thought they were good enough to be in a competition! It boots many spirits :)

Well, we went to a competition yesterday and my students earned 1st and 3rd place in their division! {And the 1st place team was 2nd overall!} Not too shabby :)

I would highly recommend finding a competition to bring students to. The first year I did this, I brought two teams. One of the teams earned 3rd and the other team didn't place. But they had a BLAST! I had a number of girls with me who talked to me about finding a competition they could do as juniors or seniors, or if there was a way to host a competition at our school! All of this after doing a day of math! :)

The Amazing Pi Race!

on Friday, March 14, 2014
Happy Pi Day!

This is my second year celebrating Pi Day with my students and I have had a BLAST every year! At first I didn't think that I could justify taking a day away from teaching, but I think it's important to remind kids that math can and should be fun, and we can do lots of really amazing things with it. Pi Day is a great day to celebrate that.

So, what do I do?

Well, about two weeks ahead of time I start talking it up to kids - letting them know we're going to celebrate it big time! Of course they ask if I will bring pie for them. I tell them: Are you kidding me??! There's 100 of you! But, you can bring in anything you want, and we'll eat it! 


A week ahead of Pi Day I created a sign up sheet for food. I suggest that they sign up to bring in circular or spherical food (for the fun of pi-day, of course) but if they bring in something that's not a circle, we'll still eat it. This year I did it using a google doc. I found out that no one will sign up for anything unless I have everyone take out their computers and look at the page and sign up.

On Pi Day people really go all out with food! Pie, cupcakes, circular tortilla chips, rings of pineapple, and so much more!

Also, being at a Christian school, we have pi-day devotionals and reach from 1 Kings 7:23 where there is an approximation of pi being 3.

While people are eating. we do the devotionals and watch a few random pi-day videos. These are good ones I found this year!
What Pi Sounds Like
Calculating Pi using Real Pies

Then after we have some time to sit, watch, and grab seconds we do the Amazing Pi Race. . . !

The past two years I have used this AMAZING activity created by Pam Burke called The Amazing Pi Race! She is wonderful and oh so generous to have posted her activity (and SOLUTIONS and HANDOUTS!) for all of us to benefit from! I hope you use it, because it seriously is a fantastic activity for students! I have used it in my Advanced Algebra 2 classes, and made an altered (easier) version for my Geometry class. I have a feeling the Advanced Geometry class could have handled it, but not my geometry kiddos.

I love that actually gets gets calculating things and doing math on a day that is considered a "fun day". It also has a fantastic element of competition and collaboration that gets people into the festivities!


Is the Inverse a Function? Horizontal Line Test Activity

on Wednesday, February 26, 2014
Last night my students learned about the Horizontal Line test during their notes video. Every year I've taught the HLT, students get confused about when to apply it and when to use the Vertical Line test instead. So I made this powerpoint in hopes of combatting the confusion! I hope you get a chance to use it. It's a great formative assessment - students give you a thumbs up or thumbs down depending on their answer!


Here's the link to the powerpoint


Compositions of Functions Relay Race

on Monday, February 24, 2014
Today was AWESOME! We just started a chapter on compositions of functions and we did a relay race today to introduce the idea of compositions, domain, range, and notation. Not only do students love the competition, but they totally got the composition concept after spending about 15 - 20 minutes on the whole process. I never once had to explain how the notation works (I find students often do g(f(x)) in the wrong order when first learning).

 I love when things come together like this!

I have the entire lesson in a powerpoint as well as a worksheet that goes with the relay race at my Teachers Pay Teachers store. Check it out!

Warm Up or Entrance Ticket - Exponent Properties

on Tuesday, February 4, 2014

I teach in a flipped classroom, so each day when my students arrive, it is imperative that I figure out what they understood {or misunderstood} from the lesson they watched for homework.

An activity that I've come to love and use as a warm-up or entrance ticket is called Teach and Be Taught.

How it works:

Tell students to partner up (usually with the person they're already sitting next to)
Put 2 questions, and their answers, on the board.
Tell them that if one of the partners feels very confident about this type of problem, they need to be the first "teacher" and teach it to their partner. Their explanation needs to be good enough so that by the time they’re done, their partner can do the second problem and “teach” them back.
The answers are there so they know if they are indeed doing it correctly.

Can I hear a HOORAY for students teaching students??!

Anyways, here is the powerpoint that I used for this (doing exponent properties).

Review Game - Factoring Battle Royale!

on Monday, February 3, 2014
The past few days we have been working on factoring strategies - perfect square trinomials, greatest common factor, difference of squares, and scenarios where a=1 and a >1. They've had a lot of seat work the past 4 days. Probably too much. So today we had the most epic battle for review! (Or at least, that's how I posed it to the class!)

Also, I cannot remember the last time I had so much fun and laughed so much in a class :)


How the Battle works:
After a few warm up problems, I told students to get ready for the ultimate face-off! At their table of 4, they could choose one of two options.

(1) They could have one side of the table vs. the other side of the table. (If they chose this way, I reminded them after each face-off to pass of the power of the whiteboard and marker if one person was doing the majority of the writing)

(2) They could put the whiteboards up between partners (mine are double sided) and have it be every man for himself!

We have done a few "face-off" style activities before, and my students are used to yelling "DONE!" when they are done! It's fun for them to see how quickly they can get an answer, and it's a way for their competition to know they've been beat. However, I did not tell them how to score, or if that they needed to keep score. This is where high school students are the best - they'll come up with creative ways to score if they want to, or they won't keep score at all if it really doesn't matter to them!

LOVE seeing the two colors of markers in this problem!
(If you're wondering... it was PJ day at school!)
For each question I put up I was able to walk around the room and check to see how students were doing. I didn't give a whole lot of feedback if someone was doing it incorrectly. However, as soon as I heard a fair number of "DONEs!" I told students to check with their table to see if they got it right. This allowed two things to happen. First, students who weren't quite done could keep working without seeing the answer on the board. Second, students who got it wrong were able to see correct work, have time to fix their mistake, and get an explanation from a classmate.

One major con about this activity is that is does focus on speed. Students see the purpose of this activity as to get it done first so they win. So, I decided to address this to the whole class. After we did 2 or so problems, I acknowledged that I knew people in this room were getting flustered and couldn't think as fast as everyone else. I then reminded them why we were doing this - to review! And the point of the review is to help them be prepared for their factoring quiz! I asked them: "When you take your factoring quiz, will you get points if you get done first or if you get it done right?" That was a good lightbulb moment for a lot of kids - especially those who were feeling overwhelmed with the speed at which others were completing some of the questions. I think making this kind of a statement is necessary so that students who work at a slower pace don't feel excluded.


I hope you use/tweak this activity to fit your needs!

Link: PPTx




Review Activity - Showdown

on Monday, January 27, 2014

Showdown is a great review activity that can be adapted to any topic or material. I love it because it allows students to have time to work individually, but also to get help from their group. It starts with each group selecting a team captain who sets the pace of work. Each student needs a handful of answer slips (there are 16 problems in total) and a team answer sheet.

Process:

1) The captain helps the team pick which problem they want to begin working on. All team members work individually and silently on the problem, write answers on answer slips, and turn them upside-down when done (or totally stuck).

2) When the captain sees all slips are upside-down, he/she calls “Showdown”. Group members show and compare their answers, explain their work, and come up with a group answer. The captain writes the group answer on the team answer sheet. This is a perfect time to help explain to those who got hopelessly stuck, or to have a small bit of error analysis. 

3) The captain turns the problem card over and compares the given answer to the team’s answer. If the answers are different, discuss. At this point, you can ask the teacher for help if you can’t figure out how to get the answer.
4) Move on to the next problem and repeat.
Thanks once again to the Exponential Curve blog!

Showdown PDF

Ohio Jones and Graphing Systems of Inequalities

on Wednesday, January 22, 2014
So I have been trying to figure out how to make practice problems no so boring. However, that can take a lot of time! So today, I give ALL the credit for this fantastic idea to The Exponential Curve blog! This teacher created an awesome Indiana Jones Themed worksheet for graphing systems of inequalities. You shade the correct path for Indiana Jones' cousin Ohio Jones to escape from The Lost Temple de Los Dulces! Not to mention - it's a self checking activity... if the path doesn't make sense, students know they shaded or graphed incorrectly. A preview of my answer key is below, but you can find all original worksheets at The Exponential Curve!

I am so thankful for other math teachers who are willing to put their resources out there for others to benefit from! Hopefully some of the things I post will help others too!

Complete the Square Stations

on Tuesday, January 21, 2014
This was my third year teaching students to complete the square. The first year I did not do a great job introducing the topic, and it turned out very difficult for students. Last year I had students work on one side of the equation - which resulted in messy math, clearing the fractions, and frustrations for all. This year when I saw this post on The Life of Mrs. Reilly, I noticed the order in which she had her students do steps to complete the square. I must say - it's SO much easier than what I was trying to do.

You know those days were you feel dumb? Yeah, this was one of them.

Anyways....

So the big idea behind her activity was to help students keep the steps in order. I modified her activity just a little bit - here is what I did. In envelopes on the student table I cut up each of the station sheets into slip. The Type A personality in me color coded the paper each station was printed on with the color I wrote the station number onto the envelope. I figured it would help me, and the students, keep things straight! So on each table there were 5 envelopes. Additionally, each student got a page that had an organizational table for each of the examples.

During my first few classes of the day, I had the envelopes on a table and a student picked one to reorder with a partner. When they were done with one, they did another one. It was nice having them work together. However, I got the feeling that many of my students understood the completing the square process and steps, and weren't benefitting from this activity. Therefore, during my last few classes, I changed things up. I told students I wanted them to hold up a "1", "2" or a "3" with their fingers. A "3" means I could do this in my sleep it's so easy. A "2" means I could use some more practice, but I have an okay idea of what's going on. A "1" means Yeah... I'm lost. If students held up a 1, I had them pick up an envelope and try to organize it (without the organizer chart page) on their desk. The rest of the students started on practice problems. This worked out really great because I could focus my attention on my Number 1 kids while the Number 3 kids helped the Number 2 kids on the practice questions.

An interesting thing happened in one of those classes. I had two boys who voted themselves as a "2", but thought they'd still benefit from the activity. They each tried organizing one on their own, and when they had finished, opted to try yet another! I love when students know what they need, and go for it! After these two boys had done a few of the organizing problems, they started on their practice problems for the day. When they finished, one of the boys asked me to come up with more examples that have the number in front of a (where a is not 1). So I wrote a few down on a scrap piece of paper, took a picture of it with the iPad, gave the student the paper, wrote solutions on the picture, and sent the freshly written answer key to the student through Edmodo! (If you aren't using Edmodo at your school already, check it out!)

At the end of the following day, that student had an extra 10 minutes at the end of class. When asked what he should do I said he could always grab the test review if he wanted it early, but he didn't have any extra homework for this class. Comically he said, "Let me try my remedial learning problems...." as he pulled out the page I had given him the day earlier. By the time he left he told me he had them all right and felt much better about them!

Below are the documents I tweak from Mrs. Reilly's blog post. Please use and enjoy!


Student Sheet: pdf

Station Sheets: pdf