Friday, December 2, 2016

Simplifying Radicals Game

I created a game for students to learn about simplifying radicals before they actually learn how to simplify radicals.  The idea is for students to find matching numbers (or variables) and take them 'outside' the radical.

I had a student film this while I taught the students how to play.

Here is a link to the cards and square root mat.




Wednesday, November 23, 2016

SR Games - All (eventually) My Games in One Place

I was looking back at the views on my blog posts and I started to notice a pattern: The posts with the most views were the ones about games.  So, I decided to create a website that has all my games in one place.  I was going to wait until it was all complete and then publish the website, but why wait?  I published it early.  As of now there are 5 games finished on and 4 more to come soon.  Here is the link.  Go ahead, check it out, it's FREE!!!




Monday, November 21, 2016

Slope - Ping: A Classroom Game

Here's a new game for you all:  Slope-Ping.  I wanted a game that got this students up and out of their seats and this game delivered.  

Game Objective:  Create the most slopes with ping pong balls on the board.

Educational Objective:  Practice finding slopes from a graph.

Materials:
I created my boards from pizza boxes, push pins, glue, and 4 of these grids.  
12 ping pong balls (2 different colors).




I purchased a lot of ping pong balls on eBay and make Xs with sharpie to color half of them.

Game Set Up:
Divide the players into two teams.  Each team picks their color ping pong ball.
Place the Slope-Ping board on the playing surface between players. 
Shuffle the Slope cards and place them facedown to create the draw pile.


Game Play:

1) Draw four cards.  Each card has a different slope on it.

2) Bounce a ball.  All players “shoot” from the same side of the board (the “Negative y direction” sign will be closest to the shooter).  The ball must bounce at least once before it goes onto the board.  If your team has used all of its balls, take one off the board.  Teams take turns repeating this step until one team is able to…

3) Match any slope.  Line up 3 of your team’s balls to match the slope on one of the slope cards.  You must have 3 balls in line to match the slope.


4) Take the slope card and replace with a card from the deck.

5) Go back to step 2.


Winning the Game:
The first team to get 4 cards wins!



Note:  The students may become frustrated when their ping pong balls start bouncing all over.  I had the students create a barrier on three sides to help keep them on the board.  It also forced the students to shoot from the negative y direction. 


 









Wednesday, November 16, 2016

Keystone Algebra I - The Bowl Problems

There is this problem in our Algebra 1 state exam, well it's in the sampler I'm not allowed to actually see the exam.  Yesterday my Algebra 1B students took their assessment on writing linear equations, just the boring stuff no applications.  So for XP points (read about those here) I gave them the bowl problem.  I explained that it was something I didn't teach directly yet and that it was challenging, but I wanted to see what they could do with it.




My Method (very typical):

I create two ordered pairs (1, 2) and (5, 5) where x is the number of bowls and y is the height of the stack in inches.

I determine the slope: 3/4

and I find the y-intercept: 5/4

So my equation is y = 3/4x + 5/4

Then the height of a stack of 10 bowls is y = 3/4 (10) + 5/4 or 8.25 inches.  


Lily's Method:

The point of this post is to share the work of one of my students, Lily.  

I saw that her equation was y = 3/4x + 2 with no work, she says that she did it all in her head (I did see her working on it without writing anything down if that makes sense).  
So, I marked her y-intercept incorrect.

Then I saw how she labeled her variables:

x - variable: "The number of bowls on top of the first bowl."

y - variable:  "The height of the bowls."

And I crossed off her "on top of the first bowl" part because it wasn't the way I did it.

Then her answer for the height of 10 bowls was correct and I was like, "Wait? What?"  She plugged 9 into her equation instead of 10 and that's when it finally sunk into my thick skull.  She was composing functions!!!  Here is her work (and my comments) if you are interested.  




Monday, November 14, 2016

Unsupportive Parents



You've seen this comic before I'm sure.  When I first saw it, I wondered if I blow things out of proportion.  Did that parent really just attack me, or am I too sensitive?  Is she asking questions to prove I'm wrong, or is she just trying to gather more information?  However, I received an email recently that is clearly blaming me for their child's performance.  The closing wasn't "sincerely" or even "respectfully", it was "this is unacceptable".  I am being reprimanded by a parent who has been bamboozled by her son.

Just a few weeks ago a girl had an incident with my substitute teacher while I was at NCTM.  The incident had nothing to do with me, it was an exchange between the sub and this student.  However, the parent demanded that I send her a copy of the lesson plans that I left for the sub.  Wait?  What?  The lesson plan had nothing to do with the incident.

I'm at a loss as to why I have to defend my almost every move.  I have to defend my lesson plans.  I have to defend my grading procedures.  I have to defend the grades they students earn.  I even had to defend my sick days to parents in the past (or at least was asked to).

Why have we lost support and respect?

My next move:  Write an email home to a parent whose child is doing fantastic work.  That always cheers me up.

Tuesday, November 8, 2016

Writing Linear Equations (Days 3 and 4)

Yesterday (day 3) I had a substitute cover my afternoon classes so that I could attend my own children's parent-teacher conferences.  So, I left a worksheet for my students to practice writing equations.  Here is a link to the worksheet if you're interested.  The posters will still available for the students to use as a model.

Today (day 4) I did nothing.  Well, in period 6 I did nothing and the student worked hard.  In period 7 I ran around the room begging students to do work and they came up with any excuse they could to do nothing.  I gave them 6 problems and the period to get things done.  Here are the 6 problems:



1) Write the equation of the line that has a y-intercept of 4 and an x-intercept of -6.
y = 2/3x + 4

2) Write the equation of the line that has a y-intercept of 7 and a slope of -4/3.
y = -4/3x + 7

3) Write the equation of the line that has an x-intercept of 2 and a slope of -4
y = -4x + 8

4) Write the equation of the line that has a slope of 3/2 and passes through the point (4, 5).
y = 3/2x - 1

5) Write the equation of the line that passes through the points (-4, 3) and (2, -9).
y = -2x - 5

6) Write the equation of this graph:
Graph created on desmos.com

y = -1/2x + 6



I printed the problems each on it's own paper so the students could easily share and rearrange the problems with each other. 



I heard one girl shout, "Oh yes!  I'm going to desmos for help!"  I took a picture of her screen to prove it.  



Students hard a work, me lazy with an iPad.




I mixed together problems that we have covered in class and problems we have not.  I found it interesting that some groups struggled with number 2 where the slope and y-intercept were given, while others realized to go straight to the answer.

The conversations were fantastic again (in 6th period anyway).  One group was getting quite aggressive in their explanations of how to do the problems, but I love to see students so passionate about Algebra.

Absolute Value Equation Stations (In progress)

My classes just finished day 3 of working on the Absolute Value Equation stations.  Tomorrow will be the last day. Here are a few tidbits for you:

Let them decide how to use their time (with limits):

On day 1 I saw a 'reliable' student doing work for another class.  I didn't say anything, I wanted to see if she was going to work double the next day.  Ummm, no.  She came into class and started doing work again for another class.  I pulled her aside and explained that I was getting worried, I wanted to know her plan to completing the work.  Today (day 3) I received three of the assignments from her.

Another student completed one of the assignments and then got her crocheting out (I love crocheting).  Again I let this go, but to my surprise, she came in the next day and kept working.  She is doing well with this arrangement and seems to be relish in the freedom.

Don't Forget to Give Score Feedback:

As the students are turning in their work, I am grading it.  At first I wasn't going to put their scores in the grade book because some parents don't understand when I put 'unfinished' grades in.  But when I saw some student relaxing, I felt it was time.  You can see their running totals below for one my of classes.  These scores are out of 50 points and there is only 1 day left.  I'm holding on to hope that some students have finished papers that they are waiting to turn in.  Hopefully, maybe, please!!



Students are Trying to Cheat (Gasp!):

Yes, one day left and some students have zeros.  With the desperation of getting good grades, they are copying (or attempting to copy) from their friends.  Can I prevent all copying? No, of course not.  But copying the assignments on color paper was a huge help.  When I see one student with two papers the same color, I can easily see that they are copying.


Overall:

Overall things are going well.  Most students are using the time wisely.  Most are doing their own work or working together with other students.  I think that once students get use to the stations things will go smoother.  I guess that means I have to create more stations.



Friday, November 4, 2016

Writing Equations Given Two Ordered Pairs (Day 2)

We started class today by listing all of the formulas we have used in class so far.  Here is the list they came up with:

1) The Slope Formula:  m = (y2 - y1)/(x2 - x1)

2) Vertex Formula:  y = m(x - h) + k

3) Slope-Intercept: y = mx + b

And I finally showed them point-slope form

4) Point-Slope:  y - y1 = m (x - x1)


We discuss what is similar and different about each of the formulas.  I show them how to convert the slope formula to point-slope, then point-slope to vertex, and if we substitute h with 0 in vertex form we get slope-intercept.  It was beautiful!!

Next, we discussed the two methods the students used yesterday to write the equation of the line that passes through the points (6, 7) and (10, 9).  The two methods they came up with are graphing or using the vertex formula.

Then I showed them how they could use the slope formula, or slope-intercept, or even our new one Point-Slope.


This is what my boards looked like at the end of class.  The formulas on the right board and our work on posters on the left board.



Graphing method



Vertex Form

Point-Slope



Slope-Intercept



Slope Formula


Absolute Value Equation Stations

For the next few days in the class, my students will be working on different assignments to practice and learn about Absolute Value Equations.  I did this last year, but had some tweaking to do, so I thought I would share it again.  Here is the link to last year's lesson.

What changed from last year.  The students don't have to complete every single station.  I made this activity worth 50 points, but there is a total of 68 points they can earn.  All points earned over 50 will be included in the XP category (read more about that here).

I no longer include the answer with each station.  That wasn't an issue last year, but if I'm grading on correctness this year I didn't feel it was a good idea to leave the answers.

I did change the worksheet.  I was rushed last year and just printed the first one I found online.  This year's version is much better.


Absolute Value Equation Stations


Each station is worth a certain amount of points.  Students must earn a minimum of 50 points to complete the activity.  Any excess points are awarded to their XP category.

Station 1:  Play Absolutely Valuable (10 points)

Station 2:  Worksheet (10 points)

Station 3:  Challenge Questions (each question answered correctly is worth 3 points)

Station 4:  Error Analysis (each problem analyzed correctly is worth 2 points)

Station 5:  Card Sort (worth 8 points if completely correct)

Station 6:  Educreations Video (worth 16 points)

Here is a link to the materials.  The link for the game is above.




I've been trying to make lessons that follow more of what I read in Drive by Daniel Pink.  This setup allows for that.  The students pick which stations they want to complete, they pick who they work with, they pick the technique they want for the problems (graphically or algebraically) and the video (Educreations or something else), mastery (those challenging problems are something to master), time (they can choose to work on this at home), and purpose (the videos will be available for others to watch).

Here are some pictures from today's classes:









Thursday, November 3, 2016

Writing Equations from Two Ordered Pairs

The students have practiced writing linear equations given slope and a point, today we start learning how to write equations given two ordered pairs.  They do have enough information/knowledge to do this without instruction.  Let's see how it goes.

Introduction:
Review the problems we did yesterday (given slope and point).  Discuss the two pieces of an equation in slope-intercept form (slope and y-intercept), discuss what those two things look like on a graph.  Emphasize that in order to write an equation in slope-intercept form, you have to have the slope and y-intercept.  If it's not given to you, go find it!!

Group Work:
Give each group a large white board and remind them that they have access to any supplies on the supply table (rulers, graph paper, etc).  Student may also use desmos, but it will have to be their idea, I won't suggest it.

Write this on the board, "Determine the equation of the line that passes through the points (6, 7) and (10, 9)."  The answer is y = 1/2x + 4

Each group is to write on their boards how they figured out the equation.  We will share with the rest of the class.  I'm hoping for different methods.  If they don't have different methods, I will have to show them myself I suppose.

Any group that finishes early will get a more challenging problem.  "Write the equation of the line that passes through the points (-3, -1) and (6, 5)."  Answer: y = 2/3x + 1

Exit Ticket:
A) Write the equation of the line that has a slope of 3 and passes through the point (4, 2).
B) Write the equation of the line that passes through the points (4, 5) and (6, 8).


What Really Happened:

Many students were still confused when given slope and a point, so I spent more time on that than I would have liked.  We ran out of time for the exit ticket.


This group understood/remembered how to find the slope algebraically using the slope formula.  Unfortunately, they use the formula incorrectly.  They were considering using the point-slope formula but were afraid of being wrong, so they did nothing at that point.




This group decided to use graph paper and determine the slope and y-intercept graphically.  All groups forgot that reducing was an option.  This particular group couldn't "find" the y-intercept because they didn't graph a point there.  I encouraged them to get a ruler just to see what would happen.




This group correctly found the slope algebraically.  They wanted to try guess and check, but couldn't figure out the "check" part.  



This group found the slope graphically, then found the y-intercept algebraically.  Interesting.



Students hard at work.


Students notice I have a camera.






One group double-checked their work by substituting both points into the equation.




This group never gave up.  They argued, they bickered, they struggled, but they never gave up.  I'm so proud.







Solved by graphing in about 2 minutes.  Fantastic!!


Solved algebraically.



I wanted to challenge this group to not use a graph by giving the ordered pairs (24, 6) and (-3, -3).  They surprised me by getting another graph out.  haha. Jokes on me.


Another algebraic.


This blew me away.  I was so impressed with this group and their use of slope and understanding.  


The group that only graphed, I finally challenged to find another method.  They did it!!


Another group that graphed.


This group did the (24, 6) (-3, -3) problem by graphing.  They used a scaled graph.  How stinkin' awesome is that!?!?!