Quadratics Chain - Math Activity

on Friday, December 6, 2013
My competing love and disdain of worksheets has led me once again to seek out an activity that has built-in practice while giving students a break from traditional bookwork. I happened upon this post from Kim Hughey about her Star chain activity. The idea is that you start of with 11 or 12 questions that have unique solutions. You put the answers on a different square than the question appears. Students cut the sheet and line up the the questions with the correct solution as they go.

Here's what my page looked like. I used it for our lesson on graphing quadratics (and Newton's Formula). Some of my students come from middle schools that prepared them very well with how to use their calculator while others have no idea how to work it. This was a great activity because it allowed the students who knew what they were doing to zip right through without listening to me explain how to do a bunch of problems. Since it is a self-checking activity, they could tell right away if they were on the right track because the answer would either be there or not (kind of like a multiple choice test scenario...). The students who were less confident were able to take their time and ask questions as I roamed about the room.
Here is a link to the downloadable document: pdf / dock
Here is the answer key for my "star chain".

If you notice, I did a few things different than Kim's original star chain. I had a definite start point that my students began with. This allowed me to have a definite end point (which is the square in the far right). I wanted to have at least one open ended question for my students to be able to answer. Also, you'll see that in the top right corner of each square there is a letter. I found a word that is 12 letters long without repeating a letter and put one in each box. The word I found was AMBIDEXTROUS. I did this so as I was walking around, I would be able to look at the letters and know if a kid was on the right track or not.

But.... I know high school students would try and figure out what the word was as they went, and then figure out how to line everything up without actually doing the problem. So how did I get around this? I spelled it backwards. The first question they do is the S. The second question is the U, and so on. I wasn't sure if it was going to work.... but they were all totally stumped.

I got a lot of, "What's suortxedibma?"

Yeah.... imagine hearing 100 kids try and sound that one out! 

Everyone's an Expert - Math Review Activity

on Thursday, December 5, 2013

The last few years when I would spend class time reviewing for a test, I found myself exhausted from explaining the same problems every hour. This year I got to thinking, "What if my students did more of the talking?" I firmly believe that whoever is doing the talking is doing the learning, so shouldn't I want my students to talk more than I am?!

That's where this activity comes into play. I call it, "Everyone's an Expert."

Here's how to set it up:

As prep work, you will need to create a question for every pair of students you have in your class. My largest class is 28, so I made 14 questions.

I printed each question onto different colored sheets of paper so it would be easy for students to keep track of what papers belonged to each person.

The day before we did this activity I handed each student a slip with a question on it (making sure I handed out 2 of every question). Before they left they needed to check their answer was correct with me and turn in their question - mostly so they wouldn't lose it! This is the question they are an expert for.

On the day of this activity I set up my desks in a circle. When students came in I handed them the question slip they completed the previous day. They were instructed to sit directly across from the person who did the same question. Once seated, I had students get extra question slips for the rotation. I told the students sitting in the inside circle to get 26 slips of the question that matched the one they did. Once they are back at their table they should split the slips with their partner. That way each person who did question #1 has 13 slips of question #1, each person who did question #2 has 13 slips of question #2, and so on.

To begin, you rotate! I had my inside circle do the rotating. The key is to tell students to bring everything with them - including those question slips. When they do this rotation, they will be sitting across from someone who is an expert on a different question. So they swap question sheets and work individually on their new problem.

In the first minute or two when students are working, it will seem eerily quiet. Don't be nervous. However, you'll start to hear whispers turn into great conversations about the problems they are working on.

The first time you do this you'll want to monitor conversations and know when to call for a rotation. My downfall this year was that the time it took to answer a question varied greatly - one was to explain the ceiling function and another was to run a linear regression and explain all of the values in the context of the problem. As a result, some conversations got off track because they had too much time, and for others they didn't always have enough time to finish.

Well, that's how to make everyone an expert!

The beauty about this activity is when a student gets stuck, they can look up and immediately see someone who already knows how to do the question! Also, when a student finishes, they have a person who can tell them if they got it right or not.

Even the kid who doesn't talk a lot in class and might be intimidated by talking to the football player is put on an even playing ground with this activity. Because it is a one-on-one scenario, and the student already has the answer to their own question, it is a low-risk and high-success review activity.

I will definitely be doing this one again!

Going In Blind - Math Activity

on Monday, November 25, 2013
Is anyone else obsessed with whiteboards? I love them. I have a classroom set of 15 so that every pair of students has one. Well, I wanted to do a twist on our Graph Wars activity for my lesson on matrix translations, so I came up with this. I call it Going in Blind because only 1 person out of the pair actually sees what's going on!

The Set Up
Students are in pairs. One person in the pair faces the “front” or the screen where you display a certain problem and the other faces the back of the room. The two people are face to face. The person facing the back of the room has the whiteboard. On the screen you display a question the partners must accomplish together. The person looking at the screen can not offer up any information unless they are asked a direct question about it. The person holding the whiteboard should ask questions to figure out what the problem is and to get the necessary information of how to answer it. All their work should be done on the whiteboard. However, they c

an’t ask “what’s the answer?” or “what should I do?”

Here's an example picture of what I put up on the screen with the question: Write the matrix equation for the translation.
Image Credit: Regents Prep

The student asking questions should start off asking, "What's the question?" Then they are able to figure out there is an image, so they can ask "How many points is it?" or "What are the coordinates of the preimage?" They keep asking questions until they think they have it right, and usually the question answer-er will help them figure out what they did wrong if they happened to go astray. At the end of each question you switch spots so the other person has a chance to ask questions.

What I love is that the student asking the question is forced to envision what the picture could possible look like and know what kinds of questions will help them get the answer they need. The other thing is that it gets students talking about math. They are required to put their thoughts into words to answer or ask the question.

Please use my powerpoint to inspire you - I feel like this would be an amazing activity to use for transformations of parabolas too!

Speed Dating in the Math Classroom

on Monday, November 18, 2013

Okay - it's not actually speed dating. Since I have whiteboards for each table of 2 in my room, I have been trying to find ways to incorporate them into the work we do. Kelly O'Shea has a phenomenal blog about what happens in her Physics classes. She explained this idea of Whiteboard Speed dating, and I knew I had to give it a shot.

The Setup:
Set desks up in a circle with two kids per desk. There is 1 white board for every group of 2 kids. You give everyone the same problem to work on. After a short length of time you tell the student everyone is going to move. You tell each team of 2 to volunteer one kid to raise their hand. Once you have kids raising their hand, tell them to move one whiteboard to the left. Tell the kids who didn't raise their hands to move one whiteboard to the right. The whiteboard should stay where it is, untouched. Then, a new group of 2 is working on a new whiteboard with someone else's chicken scratch on it. Students need to figure out where the last group left of and keep going. Every few minutes you do the same rotation, but have kids continue to go in the same direction they did the first time. (Kelly has a great visual of this rotation - check it out!). When it looks like everyone is done, you can have a board meeting and showcase all of the whiteboards. This is a great time to compare methods or to figure out if people have gotten to the same conclusion for an answer.

What I learned:
(1) This does not work for short problems. Even the long word problems that you find at the end of a chapter in the math books are not long enough.
(2) It doesn't work well for students to make their own problem as one of the problems. (i.e. Don't give them this: Write an example of a linear equation and .... )
(3) You need to be ready for when a team of 2 students is stuck.
(4) Students should be encouraged not to erase the work they come to. They should try and spend some time deciphering it first before giving up and starting fresh.
(5) The board meeting at the end is key.

Would I do it again?
Yes. but, I would make some very key changes. The first time I used problems that were far too short. To get the effect of the "speed dating", I would have needed to call time every 60 seconds to get a few rounds in before students finished the problem. Also, I would not be discouraged after the first time going through it. Remember, for any new activity like this, students are trying to figure out the material as well as the activity at the same time. The more they "speed date" the more beneficial it can be. Also, students are super creative - they might come up with some variations that you never imagined!

Math Practice Scavenger Hunt

on Thursday, November 14, 2013
I love worksheets. I love that they are organized and that you can fit all kinds of problems on to them. Students love that they don't have to bring their book home - even though they don't realize they're pretty much the same problems! It seems like a win-win. However, I hate the monotony. If every day you keep doing worksheets or practice problems in the same format, it can get old.

To combat the monotony, I made a scavenger hunt for my students. We are currently working on solving systems of equations by graphing, substitution, elimination, and matrices. For our substitution day I created 8 substitution problems that had different ordered pairs as solutions. I typed them on a half sheet of paper with another system's solution on it.

A student starts with the SOLVE question. They copy it down onto their paper. When they come up with the solution they look around the room for the page with their solution. So if a student started doing the system above, they would come up with the solution (8, 4). Around the room somewhere is another page with the solution (8, 4) so they go to that page and solve the system on that paper. They keep going around until they reach the point where they started.
Link to the: pdf

I love this activity because it can be set up for any type of lesson where I want students to have a number of practice questions for. By having all the solutions there, students can also tell if they are on the right track. If they find their first coordinate is x = -14.5, and see that that is not part of any of the solutions, they know they need to check their work.

This set up also allows the students who understand the material to whip through it pretty quick. However, for students who are new to the concept, they have plenty of time and access to help during the activity. Also, as students are moving around the room at different paces, they are able to work with other students who are on the same problem. The students want to "win" and finish the scavenger hunt, so they help each other out and do a great job of explaining things to each other.

(1) On the back of each of the questions I wrote the answer to the system students were supposed to solve. I didn't tell the kids this, but it allowed me to sneakily tell a kid who was struggling to check what the answer was supposed to be and use that to help them.
(2) Be ready to field questions. I found having an answer key ready and accessible made my life easier.
(3) Have students spread out where they start, or else you'll get crowding happening at too many questions.
(4) Write the solution large so students can see where they're supposed to go. If it's too small and they can't see it from across the room they'll spend more time searching and being frustrated than actually doing the practice.
(5) Paste on bright colored paper so they're easy to find.

What have you done to encourage practice but get away from monotonous worksheets?

Why Study Math? A new way to begin the year...

on Wednesday, November 6, 2013

Syllabus Shock i.e. the first day of school.

Why do we do this to ourselves? To our kids? That, I don't know. But I do know that by the time my students get to my 4th hour class, their ears have stopped working. They can't listen to syllabi any more! Instead of participating in this cruel ritual, I start the year asking my students the question, "Why study math?" If we are going to spend the next 9 months learning math, there better be a pretty good reason as to why.

I adapt a lesson from Kuyers Mathematics to help my students who are suffering from syllabus shock. They have great resources for math teachers in Christian high schools and their first lesson entitled, Why Study Math? is the basis of my first week of class.

The first day students look at rationales for studying math provided by a variety of people throughout history - Descartes, Bertrand Russell, and St. Augustine compose a few of the quote sources provided. Since the text is fairly dense, and students brains are not quite awake after summer, we break into groups to analyze what reason for studying math each author suggests. The group collectively comes us with their reason, if they think it's a good reason or not, and why. Students write their group's work on a whiteboard and then they are able to have a visual to use when they explain their quote to the rest of the class. Usually this sharing and presenting will not get completely done in the first day, so that continues into day 2. This is a great introduction also to the expectation that every student should contribute to the collaboration, and that this will be a class where conversation is encouraged.

The second piece is to look at verses from the Bible, and how they help us think about why we should study math. We do this in a similar fashion - splitting into groups and sharing our discoveries.

On the third day students are asked to do some personal reflection on this topic. Students have not yet had a chance to reflect upon what they think in light of the work from the previous two days. I had students complete a reflection page in a google doc and submit it to me electronically. They were asked to reflect upon some of the quotes, probed about their understanding of why God made us able to comprehend mathematics, and led to create a document they can use later in a senior faith project (a requirement for Seniors at my school).

This activity sets up the the rest of the year. After these few days, students are able to understand key elements of my course that I don't know how to put into words for a syllabus. I want them to talk. I want them to collaborate. I want them to think deeply about things that matter.

What do you do during the first week of school to combat syllabus shock?

Live the Dream

on Thursday, October 31, 2013
I am a high school math teacher and absolutely love my job! This year I am in a room with all new furniture, a class set of whiteboards, an iPad and Apple TV, two projectors, not to mention our students have Chromebooks this year as well. My students have been great with the different activities I experiment with, and a few weeks ago we transitioned to a flipped classroom. Ironically, before this year I was very much against the flipped classroom model -- that story will come in time!

Recently it has gotten into my mind that I need to start writing again. However, in an age where everyone seems to have a blog about something, I don't want to be more noise without purpose. This will be a place to share my successes and failures in my classroom, a platform to share ideas and activities that work, and a sounding board for why things fell flat. Countless times I have used the math blogosphere to find ideas and spark creativity, and it is time for me to stop being a leech.

I'm ready to live the math blogosphere dream.