Solving 2-step Equations (Alternate Method)

Blogging Challenge:  Day 14
Something you did in class...

Solving 2-step equations can be a tricky subject.  The idea of undoing, inverse, and solving for an X is above the heads of some students.  ("But yesterday you said X was 5????")

I talk about a lot of the typical things when teaching equations typically.  The balance of the equation, the equal sign means one side is equal to the other side, and we have to undo the operations to find the value of X.  

This year I even added a game "DragonBox" that teaches the basics in a game-like format.  The game overall, was somewhat successful but some students could not make the connection between the abstract math equations and the game.  Although I will say that when I was helping some students and had the following conversation more than once.

Student: "I am not sure what to do."
Me: "This X is like your Dragonbox."
Student: "Oh, so I do this and this?"
Me: "yep, good job."

However, some students could not get it down.  So I introduced this alternate method of solving equations.  It doesn't address the balance of the equation issue, but really focuses on the inverse operations idea.  I am not sure where I picked this up.  

www.screencast.com/t/rg9E9N5LIikd

Many of the students who could not solve equations in the more traditional way, really picked up on this method.  They seem to enjoy and understand it more than any other way.  

What I am not sure about is the long term significance of using this method over other methods.  Time will tell...

Chris
@CjSieling34

Kahoot is a hoot, but is it a formative assessment?

Blogging Challenge Day 11
A website

Today I used a website I have never used before.  getkahoot.com   The website is set up like a quiz game in a restaurant.  There are multiple choice questions and a timer that counts down.  Players get points for correct answers, and there are slightly higher points for using less time.  

The teacher has a main game on his computer and it is projected onto the screen/smartboard.  The questions and four choices are displayed along with a timer that is counting down.  The timer can be set by the teacher for 30, 60, 90 sec or more per question . 

Students go to kahoot.it and sign in using a game pin # and a nickname.  The teacher thens starts the kahoot.  The students watch the smartboard for the first question.  Each student then answers the question on their iPad, phone, or any mobile device.  When all answers are registered the compter then displays the correct answer.  

The students are told various information on their device.
     1.  Correct or incorrect
     2. Points earned
     3. Place in the class
     4. how many points behind they are from the student in front of them

The teacher then clicks next and the computer displays the points of the top 5 in the class.  The cycle then repeats for the 2nd question.  

I like Kahoot for several reasons:
The format is very engaging and exciting to the students.  They were hooked today.  Very involved and asked if we could play more often.  

It is an engaging and non-threatening way to stimulate discussion among the students about the problems.  

The quizzes were very easy to create.  I just screen grabbed various inequality questions I already had and imported them into the kahoot quiz.  Very easy.  

It is free.  

The results are downloadable and can be saved.  

My first ever kahoot is here.  

I also have several concerns:
The timer makes some anxious, this is a problem especially for math.  I have never valued how quickly a student can accomplish a math task.  

I am not a big fan of multiple choice.  

With a timer and multiple choice format, it can push many struggling students to guess.  

The students can put in their own nicknames.  This allows them to put in pretty much whatever they want.  I asked them to use either their first or last name.  I got some "variations."  Nothing super inappropriate, but it was only the first time.  This could also throw off the validity of this as a formative assessment.  


The Big Question:  Is this a formative assessment?
From kahoot, I do get data and it does help drive my instruction.  The activities that we will do tomorrow are partly shaped by the questions the students struggled with today.  However, I am not sure how valid the data is or whether I should rely on it to shape instruction.  

As I use kahoot more often, we will see how the results align with learning.  

Chris
@CjSieling34

Gamifying the Class, but not the learning

Gamification
Blogging Challenge Day 10

Gamification has a certain appeal to me.  Gamification is applying game type mechanics to the classroom.  Students earn points, badges, and can "level up."  Gamification at its best is a good motivator and helps makes class fun and engaging for students.  

It appeals to me because I loved video games growing up.  Many hours of my life were spent playing Nintendo and blowing the dust and static out of the bottom of those cartridges.  

Gamification of the classroom is a little worrisome to me.  I got into standards-based grading because it made the focus the learning and not the points.  Gamification seems to put the emphasis back on the points.  

However, I had two brainstorms recently in terms of gamification.  
1. Math Team
I think gamifying math team practice and points earned during the year could really help motivation.  I could award points for finishing extra practice, watching help videos, scoring points during competition, making help videos, etc...  A leaderboard is nothing new to math league as I always keep current standings posted in my room during the season.  Badges could be given for different accomplishments, scoring points, making the team, a perfect paper, as well as other things I hope to think of later.  This definitely has some possibilities for next year...

2. iPad expectations
I posted a while ago about iPad expectations in the classroom.  I am worried about students' proper use of technology in the classroom.  Of course we can use our discipline policy to help, but this seems so punitive.  Gamifying the expectations creates the possibility of mainly rewarding positive behavior and sometimes, when needed, punishing negative behaviors.  Using a google doc to track points for students would be pretty easy.  Teachers would just have to decide how to awards points and badges.  I am sure there would be issues, but I think this idea has some potential.  The students could compete as individuals, or we could have them form teams.  

Now I just have to find some tech resources to make the leaderboards and badges as easy as possible.  

Chris
@CjSieling34

Practice, the Game, and the Series

Blogging Challenge Day 9
Something you are doing this week in class...

I posted recently about my assessment strategy and how I grade. My biggest surprise came when I got a question from my principal about the post.  First, he reads my blog? Crazy cool.  Only one of the many reasons he is a great principal, I think our staff is super lucky to have him.  I am not just saying that because I know he reads this. :) (i better clean up the grammar mistakes, he used to be a language teacher...)

His question was about the analogy of formative assessment as the practice and the summative assessment as the game.  My short answer is that I see where the analogy is handy when teaching someone about formative and summative, there are some problems with the analogy in general.  

Summative Assessment = The Game?
First, to me a grade should indicate the amount of learning the student has done in regards to the learning target.  

In sports, a game is a snapshot of how the team is doing at that moment.  There is a final score.  The result can not be changed.  (unless one team has cheated somehow and a governing body goes back and takes away wins from the cheaters)  This doesn't happen a whole lot in schools.  (hopefully)

So the summative assessment is the game?  Summative has such a 'final' connotation to it.  When I hear the word summative, it tells me the learning is over.  Which means there is a final score (grade) and the results can't be changed later?  I question this idea.  

Formative Assessment = Practice?
Practice is the main area where sports teams learn and get better. During practice there is constant feedback and repetition to help everyone get better.  Isn't this what is happening in a class at all times?  Formative assessment is a great non-graded way to give feedback, but shouldn't this be happening all the time?  There are many things in the classroom that are practice.  They are purely to get better at the learning target and are not graded.  In terms of assessment I use a 1-4 style on any "graded" assessment.  I also try to include feedback on how to "get to the next level."  I just recently found this picture on twitter that perfectly explains the 1-4 grading system.  I showed it to students and they finally fully understood the 1-4 system.  

  

Assessment = The Series
To continue the sports analogy of assessment, and the grade the students receives from the assessment, I propose that assessment is much more like a 7-game series.  The grade the student receives for a learning target is like being rated on a performance in a seven game series.  It involves preparation, practice, a game, adjustments, practice between games, another game, more adjustments, more, practice, more games, and so on.  The biggest point is that all the preparation, practice and games all contribute to the outcome of the performance.  

Conclusion 
I would like to ditch the terms formative assessment and summative assessment completely.  I read the phrase "Assessment for learning" somewhere and have fallen in love with that term.  Whether the assessment is graded, non-graded, formative, summative or some other category, the assessment should be used to help student learning.  The student's final grade should consider all evidence, with emphasis on the most recent (whether it summative or formative).  

Getting called out by my SBG hero on Twitter

Blogging Challenge Day 8
A professional read.
(repost, because I accidentally deleted the old post)

Last spring I finished my Master's program with a double emphasis in teaching/leading/learning and mathematics (pause for applause).
My action research paper was all about grading.  A couple of years before I started, I had read about Standards Based Grading from a couple of different sources.  Dan Meyer was probably the most influential.  

I then read Ken O'Connor's book How to Grade for Learning.  I used this book prominently in my action research paper and how I designed my grading system for the study.  

Read until the end to see how Ken O'Connor responded to me on Twitter...

It really awoke from my traditional grading practices to start seeing grades as a way to promote learning, not judge students and their academic behaviors.  I started to think about what I wanted out of a grade.  I then started combining the resources I had compiled over the years to get rid of a points based grading system to install a standards-based 1-4 rubric grading system.  

Radical Things I did that first year (and mostly still do)

• I ditched any kind of unit test
• Weekly quizzes scored 1-4 sorted by concept
• Unlimited re-takes on any assessment (with some remediation)
• No points for homework
• NO extra credit
• No participation points

When a student asks how they can raise their grade, I respond well you need to re-take the concept quiz.  They have stopped asking for extra credit because I make a really big deal out it the first week.  I have a slide in my classroom expectations presentation that says at the top "EXTRA CREDIT."  Then using animation the following lines are revealed one by one.  

1. No Extra Credit

2. Never

3. Ever

4. Seriously

5. Don't even ask

The kids usually find it funny and it drives the point home.  If you want a better grade you need to learn something.  

Of course I am the only teacher in my school in 7th-12th grade who does this.  So I do need to use a conversion scale to turn the grade into a percentage to enter in the gradebook.  

Here is that process.  

1.  Each grade entered into the gradebook is a learning target/concept.  (whatever word you like to use).

2. The score is entered, but can change as evidence is gathered.  

3. I enter each concept score in as a score out of 100.  Parents love percentages.

4. I usually wait until I have two assessments on a 1-4 scale to enter a score.  

4,4 = A

3,4 = A-

3,3 = B

3,2 = C+

2,2 = C-

1,2 = D

1,1 = F

I sometimes feel like Neo in the Matrix when I am entering grades. I have this vast spreadsheet of 1s, 2s, 3s, and 4s and all I see are the grades and the story that the numbers create.  

It works well.  My grades really seem to represent what the student learned about math.  I owe this mostly to Dan Meyer and Ken O'Connor.  

By the way,  I was taking part in the standards-based grading twitter chat (one of my first chats) and I was trying to describe my grading system in 140 characters.  It didn't work very well and received the following tweet from my hero Ken O Connor.

@CjSieling34 #sbgchat Sorry Chris that is not right - practice is practice and the score for practice isn't the score at the start of game.
— Ken O'Connor (@kenoc7) September 26, 2013

So in my first twitter chat, where I dipped 1 toe in the water and posted something, I got called out by my SBG hero.  Awesome right?

It really was all over the terms formative assessment and summative assessment.  Really I don't like either term.  I read somewhere the phrase "assessment for learning."  I like that term.

So anyway, definitely read Ken O'Connor's book "How to Grade for Learning" just don't challenge him on Twitter over it.  :)

Chris
@CjSieling34

1:1 Device Classroom Expectations Poster

Blogging Challenge Day 7
Classroom Management Tip

Our high school went 1:1 last year.  The teachers have struggled with management of them in the classroom.  Kids using them more for games, being off task, the usual stuff.  

Next year, our plan is go to 1:1 in the junior high.  We thought the classroom management would be easier if the teachers used common language with expectations about the iPads.  So  sub-committee was formed in investigate this, (the sub-committee was me, my Google skills, and Twitter).  

After much perusing around the internet and sending emails back and forth with some other schools I came up with the following graphic that would summarize our expectations about iPads.  

Know that the elementary is a PBIS school with the following expectations posted everywhere in their hallways.  
    1. Be Responsible
    2. Be Safe
    3. Be Respectful
    4. Be Prepared

So I decided to use those as a basis for the expectations.  The results of my first draft is below.    

Stay on Task:  
    Off task kids are going to do off task things.  However the 1:1 seems to enable this behavior even more.  Next year, this will be a major point of emphasis during the first month. 

Use for Learning:
    I would like to reword this one somehow, but I can't seem to think of anything better.  The devices should be used for learning.  The students seem to think otherwise.  

No Meanness:
   The high school struggled during the first part of year with the devices being used for cyberbullying and just plain bullying.  Posting mean things, taking photos/videos, the list was large and unacceptable.  I read Dave Burgess' book "Teaching Like a Pirate" this summer and used his No Meanness rule in my room this year.  It has gone pretty well.  So I thought using similar terminology with the iPads would be helpful.  

Flip When Told:
    Flipping the screen toward the teacher whenever asked to lets the teacher check on on-task behavior.  Another plus is it takes the students eyes off the screen and focuses them on the teacher.  This can also be used to have the student flip the iPad screen down on their desk when not in use.  
  
Charged and Silent:
  Keep them charged, (parents will need to be trained in) and keep them silent.  Pretty obvious.  

Keep Updated:  
    We had problems with kids refusing to download apps that were pushed out by the school.  I think this is better now.  I am not sure if it was a lack of training or teenagers being teenagers.

Protect Privacy:
    Where do students learn this?  Shouldn't this be an essential outcome in every school?

Stand up to Cyberbullying:
   Students need skills to deal with mean people on the internet.  They are everywhere.  The best bullying book I ever read was Love & Logic's "BullyProof my Child" or something like that.  Those skills are invaluable in cyberspace as well.  


I am hoping this language can help us address the most common issues in a 1:1 classroom.  Anybody have any feedback about missing areas, or areas we should change?

Thanks
Chris
@CjSieling34

Desk = Mess

Blogging Challenge day 6

Something I wish I did better

I need to be better organized.  Plain and simple my classroom is always a disaster.  My desk is always a sea of random papers.  Every year I get one of those big desk calendars thinking it will help me be better organized.  Then 1-2 weeks into school it is buried in the paper waves of disorganization.  I usually don't see it again until the end of the year.

I have used apps, post its, small white boards, and anything else to keep better organized.  Nothing seems to stick.  I just can't seem to regularly commit my time to it.  I feel I would be a better teacher if I was better organized, but I just can't seem to make it happen.

This year I am implementing a self paced/flipped/differentiated/leveled 8th grade math class.  I have created a google doc that contains information on every student and their progress on every learning target.  What they have finished, quiz scores, pre-quiz scores levels of proficiency... and I am barely above the waves. Luckily I have a very understanding wife who understands I need at least half a day every weekend just to keep up with this project.  

I need some steps to stay better organized.  I can see some steps to be ether organized, but like my desk calendar, I probably won't look at them until summer.

@CjSieling34

  

Scatterplots, Correlation, & Mythbusters

Blogging Challenge Day 5
Assessment

One of my favorite assessments of the year is based off of a Mythbusters episode (season 10, episode 145).  The episode is Waterslide Wipeout.  Jamie and Adam investigate this YouTube video.

Jamie and Adam build a giant waterslide and slide down it a couple of times each at various distances during the episodes.  I thought this would be a great opportunity for students to apply their knowledge of scatterplots, correlation and line of best fit.

To start, we watch the above video.  We then pause for discussion about whether this video is real or fake.  We then watch various parts of the episode, cut down to the essentials, to see how Jamie and Adam faired in their investigation.

I then present them with the data from the episode.  Their task is to use www.desmos.com to create a scatterplot and line of best fit from the data.  Then use the line of best fit to help their decision about whether or not the video was real or fake.


Slide Distance (ft)      80     121      165     123      162
Flying Distance (ft)     4       40        70       43       72


The students then create short videos reporting their findings.  Last year they used Educreations to create the video, this year I will probably use iMovie.

A couple notes:
I used to do have students do this by hand, desmos has really made this problem much better.
We have covered exponential equations at this point, although most students go with a linear line of best fit, I have had students use exponential as well.
The students do enjoy this assessment.

@CjSieling34

Square Root Game

Blogging Challenge Day 4
Something you did in class this week.

Today the 7th graders played what I call the "Square Root Game" to start class.  The term game is kind of a stretch.  The rules are very simple.

1. I will write a square root on the board.  For example sqrt(12)
2. The students will on their own write down their best estimate of the square root.
3. After about a minute or so pencils are put down, and they share their guess with their neighbors.
4. The answer is revealed.  (with some theatrics of course)
5. We decide who is the closest, and they get a small candy prize.  (Jolly Rancher, Werther's, etc...)

For some reason, the kids love this.  We played 4 rounds this morning and they were begging for more.  We usually play this game during the end of our exponents/square roots learning target.  We will play this every day to start off class.

By the end the kids get really good at it and need to pretty much be right on two decimal spots to win.  I also love this game because there is a little luck involved, and really anybody can win.  I usually try to keep playing in class until everyone has won at least once over the couple weeks.

This is an example how a simple idea, some theatrics, some energy, and a small candy prize can go a long way to energize a room and get the learning going.

@CjSieling34

Online Homework

Blogging Challenge: Day 3
What is a website you can not live without?
     (A summary of how I use websites to assign homework)

When I assign homework, I have two guiding principles.

1.  Give the students space and time to get it done.  
I assign homework once a week.  I give the assignment to the students on the first day of the week,   and it is due on the last day of the week.  I feel this respects the students time commitments and      
helps the student learn to manage their time.  Every year there are some students who wait until Thursday night to start their homework.  They quickly learn they should start it earlier in the week.

2.  Give the students choice.
When assigning the homework students always have a choice between two assignments.  There is an "A-level" and "B-level" homework assignment.  I tell the students the "B-level" homework will prepare them for the B-level quiz, while the "A-level homework will prepare them for the A-level quiz.  (all my assessments are also differentiated)  Students vary in their choice.  Many choose the B-level homework every time, some choose the A-level every time.

Comedian George Carlin has a great bit about how we have the "Illusion of Choice" in this country.  (1000 bagels to choose from, 2 people to choose from for president).  Giving students this type of choice helps them feel like they are in control in some way.  They still are going to do math homework, but they get to choose how hard the assignment will be for them.

I used to do this by hand.  I created A-level and B-level packets every week and killed many trees copying them and laying them out for students to take each week.  It was time consuming and wasteful, but good for the students.  Grading them was also a pain and never happened in a timely basis.

How this ties into the Website topic.
All of this got easier and more efficient with the website www.ixl.com and www.buzzmath.com.  I no longer spend time and resources creating the packets or correcting the packets.  Students get immediate feedback as they work.  Students enjoy the fact that they have so much control.  They get to decide which assignment (A-level) or (B-level) and how far they will work the assignment.

IXL gives the students a smartscore from 0-100 based on how many questions they have gotten correct or incorrect.  Students can work as many problems as they need to get to the score they want.  I use the following scale.

SmartScore     Grade    
100                  A
95-99              A-
90-94              B
80-89              C
70-79              D
0-69               not done

This homework provides the base level practice many students need to be successful in math.  We save the higher level Bloom's for classtime.

Do I have students that always choose the B-level and work it only to a minimum level?  Of course.  These are the same students that typically wouldn't do their homework at all. So at least they are getting their homework done.  I have had many students come to me in the middle of year and tell me they tried the A-level homework for the first time and they got it done.  They are always so proud.  At the same time I have students who complete both the A-level and B-level homework and always work everything to the highest score possible.

There are technological worries of course.  Students at our school do have a study hall and a homeroom every day.  So some students with no internet at home have priority at those times to get their homework done.  In the past couple years I have had no student not be able to get the homework done because of technological concerns.

Overall there are some definite cons (I know Dan Meyer would not approve)  however I feel the pros outweigh them.  Giving students the illusion of choice and the time and space to get their homework done really helps with student buy-in on the math homework.



@CjSieling34

Monday Morning Math Game: "you down with WBG, yeah you know me..."

Blogging Challenge:  Day 2
Share an organizational tip from your classroom.

When I started, I struggled with the idea of bell work, especially on a Monday.  I solved it with this idea, that I totally stole from some teacher at a MN Teacher's Conference (MCTM) many years ago.

Every Monday, we start class with what the kids call the "White Board Game" (WBG for short).  The "game" is pretty simple and takes the first 10 minutes of class.

1. The students are grouped into teams of 3-4.  My room is always arranged in a groups so this is no problem.  Each team gets 1 small piece of white board and a white board marker.  (hence the name of the game).

2.  I display 3-4 questions on the smartboard.  They are math related questions.  Sometimes they are related to our current learning target, sometimes they are more math puzzles.  I get a lot of the questions from the MathCounts handbook.  (here)  

3. The timer begins when the bell rings to begin class.  I give them anywhere from 4-7 minutes depending on the questions.  They must place all their answers (only their answers) on the white board and place the white board at the front of the room before the time is up.  (with answers facing the whiteboard, hidden from the class).  If they get their board up in time, they get a bonus point.

"Wait, where do I get that many pieces of white board" - a lot of teachers ask
The trick is go to to a Home Depot type store.  I found a 8' x 4' sheet of whiteboard.  I had them cut it into roughly 1 foot by 1 foot squares.  I suddenly had 32 small white boards for less than $20.

4. Students must also write down the problems and work in their notebook.  This just helps with everyone participating.

5. A scorekeeper is assigned each week.  They turn the boards around, reveal the answers on the smartboard, and of course, keep score.  The winning team(s) get a small reward (jolly rancher, werther's, small sucker, etc...)  Students then volunteer strategies to solve the questions and it becomes some review as well.

This starts off every Monday in a fun way and I rarely have anyone late on Monday.  Even when students have to go to the bathroom they will either hold it or get yelled at by their group for abandoning them during WBG.

I am sorry to the teacher that I stole this from.  It was years ago and I can not remember your name.   Thank you though, your idea has given my students and myself years of fun and excitement.

Chris
@CjSieling34

Jim & the Beanstalk: An Adventure in Geometry, Literature and Bread

20 Day Blogging Challenge:  Day 1
Share a favorite book and an extension lesson.

As a math teacher, I was worried about this Day 1 challenge.  I then realized I was approaching it wrong.  Every year after we talk about similarity, surface area, and volume in 7th grade I read the class a book.  "Jim and the Beanstalk" by Raymond Briggs.

I got this idea from a Marilyn Burns book titled Math and Literature Grades 6-8.  (here)  However I have added some parts to the problem to take it further.

The story is about a giant and a boy who meets and helps the Giant.  The giant is of course a typical giant and allows me to get very theatrical as I read the book.  I really get to have fun as I walk around the room reading this book.  I get into it and do the different voices and really try to act it out.

At one point the giant says something about eating 3 boys on a slice of bread.  The math begins when I ask them to get into groups of 3-4, give them a piece of bread, and tell them to scale the bread up to be big enough for their group.

The students have to use ideas of similarity (it must look like a piece of bread), surface area and volume (calculated for the original piece of bread and the giant piece of bread) to answer the questions "how many times bigger is the piece of bread?"

The students must produce a taped out area on the ground to represent the dimensions of the piece of bread.  When students are confident of their answer and tape, the students lay down to prove they fit on the piece of bread.  They must also calculate out the height (or thickness) of the piece of bread.

Each group is given a worksheet and a piece of bread.  Even after all the students in the group and handled and measured the bread, usually someone in the group eats it.  I find this gross, but the students are kids and kids will eat just about anything.  My son, who is currently 8, once ate gum of the bottom of a bench in church when he was 5.  (not the grossest story involving my son either, but that is for another day)

I wish I had some student work to post along with this, (maybe in the spring), it is a really fun day or two in class.

Chris
@CjSieling34