Math = Love: April 2015

Thursday, April 30, 2015

Logic Puzzle Love: Shikaku Edition

I'm not sure why I'm still surprised when the #MTBoS comes through for me.

Last week, I tweeted about doing griddler logic puzzles with my students.  Bowen Kerins tweeted back with a suggestion of a different type of logic puzzle that could be tied to the math curriculum: shikaku.


Guess what type of puzzle we did the next day in class?

A quick google search revealed an article in NCTM's Mathematics Teaching in the Middle School May 2010 issue by Jeffrey J. Wanko.  Dr. Wanko wrote about a process of introducing students to logic puzzles by first showing them a completed puzzle and having them determine the rules of the puzzle.

I placed the unsolved shikaku puzzle from the article on the SMARTBoard.  I asked students to speculate as to what the rules of the puzzle were.  After a few suggestions, I asked students if it would help to see a completed puzzle.  They were eager to see this.


At first several students proclaimed that this was too hard or impossible.  And, of course, I followed this up with "This will take some time and effort."  In some class periods, a student said this second line instead of me.  #growthmindset  It was really cool to see the light bulbs going off as students studied the screen.  Soon, they decided that the circles told how many boxes were in each section.

Though, the room quickly erupted when one student claimed that each section must be a rectangle.  Other students argued that squares were also allowed.  Some students claimed that every square was a rectangle.  Several classmates were less than convinced.

We also discussed the fact that the rectangles could not overlap, and the circle could be placed anywhere in the rectangle.  With these rules, students were antsy to start a puzzle.  I put up a puzzle on the board to do as a class from the same NCTM article.  Students came up one at a time and drew a rectangle where they thought it went.  Some students were not using logic to place their rectangles.  But, I didn't say a word.  I figured the class would figure this out eventually.  And, they did.  They worked together to fix the mistakes.


After doing one puzzle as a class, I gave students an activity sheet with 4 more shikaku puzzles.  To receive their points for the day, they had to successfully complete two of the puzzles.  Most of the students agreed that they liked these puzzles better than the griddler puzzles from the previous day.

It was eye-opening to listen to students' thinking as they worked these puzzles.  One student claimed that if the circled number was odd, the boxes would always be in a straight line.   I hope they eventually realized that 9 broke this pattern.  What they were actually noticing was the difference between prime and composite numbers!

I could see using this as a fun introduction to factoring.  A 12 rectangle can have dimensions 1X12, 2X6, or 3X4.  Students had to consider each of these possibilities when solving the puzzle.  I can also see using this as part of an investigation into comparing area and perimeter.



These got my students thinking which is exactly what I want them to be doing during these last few weeks after testing and before the end of school.  Several students came in the next day and asked for more of these puzzles to do.  I even have students who aren't enrolled in my classes coming to me and asking for logic puzzles because they see their friends doing them.  These puzzles are definitely a keeper!

Here's a link to a pdf file by the author of the NCTM article with more logic puzzles (including some shikaku puzzles!) to use in the classroom.  Enjoy!


Monday, April 27, 2015

Logic Puzzle Love

I heart logic puzzles.  Give me a long road trip where I'm not the one driving, and I'll probably be doing one of two things when I'm awake: reading or working logic puzzles.

One of my favorite logic puzzles is one I learned about in high school.  My high school calculus teacher would leave us packets of logic puzzles to solve on days when we would have a substitute.  In one packet, there was a certain puzzle that frustrated me.  There was a set of cells that were either colored in or not colored in.  And, there were clues around the edges to help determine which cells were which.  The numbers around the puzzle tell how many cells in a row are colored in.  This puzzle took me hours to solve, but I couldn't give up.  Once I figured out a strategy, I was so proud of myself.  And, I was also hungry for more puzzles like that to solve.  I found several free sources of these on the internet, and I've been solving them on and off ever since.

Here's an example from the puzzle handout I gave my students:

Source: https://www.griddlers.net/images/iGridd_Demo.pdf 
This file that I printed puzzles from for my students to do also has the best rule explanation I've seen for these type of puzzles.

Source: https://www.griddlers.net/images/iGridd_Demo.pdf 
These puzzles have only about half a billion different names that they go by: Nonograms, Paint by Numbers, Griddlers, Pic-a-Pix, Picross, PrismaPixels, Pixel Puzzles, Crucipixel, Edel, FigurePic, Hanjie, HeroGlyphix, Illust-Logic, Japanese Crosswords, Japanese Puzzles, Kare Karala!, Logic Art, Logic Square, Logicolor, Logik-Puzzles, Logimage, Oekaki Logic, Oekaki-Mate, Paint Logic, Picture Logic, Tsunamii, Paint by Sudoku and Binary Coloring Books.  (And, yes, I did just copy and paste that from Wikipedia.)



Before giving my students 6 puzzles from this handout to solve on their own, we worked one puzzle together as a class. This puzzle was downloaded from Web Paint-by-Number.  I started by showing students a few strategies for filling in boxes.  Soon, they were full of their own ideas.

Their assignment was to complete 2 of the puzzles on their own during the class period.  Some students chose to do more than 2.  Others stopped after fulfilling the minimum requirement.

Source: http://webpbn.com/
One thing I've noticed about my students this year is that they really struggle with thinking logically.  Their main tendency is to narrow a situation down to two or so ways and then randomly choose one to go with.  The idea that it is possible to know something for certain is foreign to them.  But, we're working on that!

My favorite part of assigning my students these logic puzzle type tasks is eavesdropping on their conversations.  Hearing students explain their reasoning to one another makes my day.  It's something I need to make happen more often in my classroom.

Did all of my students love these puzzles?  No.  Did it push all of them out of their comfort zones?  Yes.  Several of my students enjoyed these puzzles so much that they downloaded apps to their phone to solve extra puzzles over the weekend.  Yay!  :D 



Saturday, April 25, 2015

Four Fours = Tons of Fun

My students took their end-of-instruction exam on April 13th.  That was two weeks ago, and we still have three weeks left in the school year.  My students and I worked extremely hard to cover the entire curriculum before Spring Break began.  Now that testing is over, it's been a full-time job keeping them busy.  I know a lot of people are probably reading this right now and thinking that I should still be teaching new content.  That just isn't feasible with how my school structures testing.  We started testing April 13th and will finish May 7th.  Of course, we aren't testing every day in that window.  That would be insane.  But, the kids who show up to each class period each day are a surprise.

So, I'm taking this opportunity to have my students reflect on the school year.  I'm taking this opportunity to pose problems that stretch their brains.  I'm taking this opportunity to engage them in the sorts of activities that are meaningful but don't tie directly into the tested curriculum.

My kids keep coming to my class expecting to watch a movie.  Eventually, they're going to realize that's not how Ms. Hagan rolls  :)

One of my favorite activities from the past week was called Four Fours.  I learned about this puzzle from the #MTBoS, but I'd never tried it out with my students.

The Task: Form the numbers 1-100 using exactly four fours.  Feel free to use addition, subtraction, multiplication, division, exponents, roots, factorials, decimals, and concatenation.

We played around using four fours and some math operations to figure out what they made.



My students had never been exposed to the idea of factorials before, so that was a fun mini-math lesson to give.  I've never used factorials with my students because they aren't included in my state's tested standards.  But, you know what, that shouldn't matter.  I need to stop worrying so much about what's on the test.  I'm selling my students short.  I have a chance to expose them to a side of mathematics they have never seen, and I need to take that.



Several of my students asked some really good questions about where factorial would fit in with the order of operations.  I wish I had asked them where they thought it fit in instead of just giving them an answer.  Actually, I think this is something I need to work on for next year.  I go back and forth with whether I should review the order of operations at the beginning of the school year.  Some years I do because I find that my students bring over so many misunderstandings from middle school.  But, I never feel like this reviewing does much good because students are convinced that this is review material and they understand the order of operations perfectly fine.



But, what if I took it further next year?  What if we talked about the order of operations, and then we discussed where to put all of the stuff that studying Algebra 1 and Algebra 2 and higher level math subjects brings with it?  We need to talk about factorials.  We need to talk about roots.  We need to talk about the vinculum.  (I love exposing my students to new math-y words!)  We need to talk about the difference between parentheses that signify grouping and parentheses that signify multiplication.

In other words, I need to step up my game.  


To structure this activity and my students' responses, I printed off the "Mind Your 4s" sheet from 17GoldenFish.

I wish I could say I passed out the pages for students to write their answers on and the room was instantly filled with rainbows, butterflies, and smiling students.

That's NOT what happened

In fact, for the first 30 minutes of first period, I thought I had made the biggest mistake in the world by assigning this task to my students.  There was complaining.  There was grumbling.  Yes, I realize those are kinda the same thing.  I guess I just want you to realize that the vibe in my classroom was not a good thing.  Students were asking, "Ms. Hagan, why do you hate us?"  To this, I answered, "I don't hate you.  I love you.  That's why I'm trying to stretch your brain today."

The Growth Mindset Bulletin Board was working overtime.

Student: This is too hard!
Me: This will take some time and effort!

Student: I give up.
Another Student: I will use some of the strategies I've learned.



Seriously, it wasn't pretty.  I have only about 9 students in my first period Algebra 1 class.  4 of the students were working semi-diligently.  The other 5 students were sitting and complaining.  They tried to just sit and play on their cellphones, but I stopped that by threatening to take them away for the rest of the day.  No one wants to lose their phone for the entire day during first period!  I didn't think my students were getting anything out of this activity.

But, thirty minutes into class, something changed.  One kid excitedly announced that he had figured out how to find a certain number.  Another student asked how he had found it.  Instead of telling what he did, he gave a hint about using factorials.  This led to a couple of other students figuring it out and exclaiming happily as a result.  Pretty soon, the kids were going crazy with excitement each time they found a new number.  They were helping each other, coaching each other, encouraging each other.

Students who sat idle for the first half of class were talking about how they didn't find as many solutions as their classmates because the rest of the class had gotten a head start.  Teenagers...


The same cycle continued for much of the day.  The class would start off grumbling.  But, the excitement of a student or two would somehow turn the class around.  The sheet I gave students to fill out had 5/100 answers already filled in.  To get their participation grade for the class period, students had to fill in 25 additional answers.  Of course, they were encouraged to do more than that.  

It was fun to see students make observations during this activity.  For example, in almost every class period, one student would exclaim that the majority of the answers they had found were in the far right hand column.  To this, I said, "Well, it makes sense since that column is multiples of four."  I'm kicking myself now, though.  What I should have said: "How interesting!  Why do you think that is?"  #stilllearning 

I did have a problem with a student looking up answers on their phone.  I'm just skeptical when the completed assignment looks like this.  I know that as I worked on the activity that my answers were much more sporadic and spread out.  


I had several students remark that this activity would have been so much easier if we were using the number 5 instead of the number 4.  I joked that they had just found the next day's activity for me: Five Fives.  In fact, when I gave the students a logic puzzle the next day, they complained that they would rather be solving Five Fives.

It was a great brain stretching activity.  It was a good review of the order of operations.  It let my students experience factorials.  And, they learned what the word concatenate meant.  It kept them busy for an entire fifty minute period.  And, I think it was a lot of fun.  Definitely doing this again!


Friday, April 24, 2015

What Worked; What Didn't: Calculator Storage



For the past two years, I've been frustrated by calculator storage in my classroom.  I had calculator tubs, but the calculators never seemed to make it back in the tubs.  My school provides calculators for all of our students instead of asking our students to purchase their own calculators.  Because these are the school's calculators, my students sadly don't take as good of care of them as they should.

This summer, I bought three shoe hangers at Tuesday Morning (pretty much my fav store!) to keep the calculators more organized.  I had to do some rearranging in order to even find wall space to hang up the shoe hangers.


I had this idea that I thought was pretty brilliant.  Students would enter my classroom.  They would take a calculator out of a pocket.  They would place their cell phone in the pocket.  At the end of class, they would return their calculator and retrieve their cell phone.  This would leave my room cleaner at the end of the day, and there would be no distractions from phones.

There was something I failed to account for with this plan.  My students.


During the first week of school, one student stole another student's phone out of their pocket to be silly.  So, that was the end of having students put their phones in the pockets.

I've found that my students are much more likely to put their calculators back in the shoe holders than they were when I was using a tub.  I have found that my students do a better job of putting them away if I give them a verbal reminder at the end of class to put away their calculators.  I shouldn't have to do this.  But, I haven't found a better way.

I don't want my students packing up until the very end of class, so I can't really hold the class until all of the calculators are put away.  I do like that hanging the calculators on the wall has cleared up flat table space.

Did these solve all of my problems?  No.  Have they helped?  Definitely.

Tweak I'm thinking about for next year: numbers on each calculator that match up with numbers on the pockets.

Also, I need to come up with a better system for students to check out calculators to use on their ACT exams.  Writing names and calculator numbers on post-it notes and losing them in the mess on my desk is not cutting it.


Thursday, April 23, 2015

Q & A: Practice Problem Conundrum

Today, I want to answer a couple of questions I received in my e-mail. I hope that my answer can help more than just the teacher who sent in the question. Since I'm hoping this will become a regular thing on the blog, I even made a cute picture for these posts. :)

By the way, I'm terrible at replying to e-mails with questions. Hopefully this will help me get better at answering these types of e-mails.




The Question


Right now I use the textbook to give my students practice problems that they write over in their notes and can reference back to later how they did something (for a quiz, test, etc.). On your blog you mention whiteboards which I think are great, but the work that students did is erased and lost. So:

1) How do you give your students practice problems (where do you get them from, how do you present them)?

2) Do you have students write down their working out of practice problems in their INBs or do you find that it's not necessary?

My Answer

This is one way in which my approach to interactive notebooks is changing. When I first started doing interactive notebooks with my students, I was very controlling of what went on each page. I wanted my students to have notebooks that were identical to mine. We would do a few problems in our notebooks, but the majority of our practice happened on individual white boards. Several of my students started asking if they could include some of the whiteboard problems in their notebooks. I tried to making up a modified page numbering system to accommodate this. If we took notes on page 7 and students wanted to take extra notes, I would have them number these extra pages as 7B, 7C, etc. This was a hassle, and my students never really caught on. 

This year, I've given up on page numbers. As long as my students have the notes in their notebooks, I've decided it doesn't really matter what page the notes are on. It is nice to be able to tell the class to open up to page 52 to reference something, but I think it's more important to have my students taken ownership of their notebooks. I've started to recognize that some of my students need lots and lots of practice problems in their notebooks. Other students benefit more from having a few practice problems in their notebooks and doing the rest of the problems on their dry erase boards.

So, I've started giving my kids an option. We start a new concept by getting out our notebooks. After taking notes and doing a few practice problems, I pause and give them the option to keep their notebooks out or to transition to a dry erase board for the rest of our practice time. My students who need the notes know that they need the notes. My students who prefer the boards often do so because they know that they are more willing to take risks in solving problems when mistakes can be wiped away with a swipe of the finger.

For next year, I think I'm going to have students number pages according to the learning goal. So, I can say turn to the notes for learning goal 14. This may be a different page number for each student, but we should still be able to reference our notes together as a class when necessary.

It comes down to knowing your students and what they need. I'm learning to be less controlling in certain areas because I know it's what's best for my students.

As to your first question, I get practice problems from a variety of sources. I frequently use problems from the free sample Kuta worksheets. I also keep a textbook or two around to steal problems from. But, my most frequent source for problems is the Test and Item Specs and Released EOI Items from the Oklahoma Department of Education. I try to expose my students to the wording they will see on their end-of-instruction exams. I also frequently just do google searches for various topics and steal worksheets and practice problems from other teachers on the Internet.


Wednesday, April 22, 2015

Algebra 2 Learning Goals

Yesterday, I shared my Algebra 1 Learning Goals for this year.  Overall, I think I'm much happier with them than I am with my Algebra 2 Learning Goals.  Though, I think the problem wasn't my Algebra 2 Learning Goals.  Instead, it was how I structured my Algebra 2 class into units.

I'm still trying to figure out how to better structure my course.  This was my 3rd year teaching Algebra 2, and I still haven't found a unit structure that seems to flow and make sense to me and my students.  I've still got hope that there's a better structuring system out there.  Any advice would be greatly appreciated.  

Algebra 2 Learning Goals
2014-2015


Unit 1 - Graphing and Describing Graphs
I can graph and identify key aspects (domain, range, intercepts, intervals of increasing and decreasing, and relative maxes and mins) of functions (quadratic, radical, logarithmic, exponential, polynomial, and rational).
I can identify parent functions based on graph, equation, description, or set of data points.
I can find and graph the inverse of a function, if it exists.
I can identify, graph, and describe conic sections.


Unit 2 - Add/Subtract/Multiply/Divide/Simplify/Convert Expressions
I can factor out the GCF of an expression.
I can factor quadratic trinomials.
I can perform polynomial long division.
I can simplify radical expressions.
I can add and subtract radical expressions.
I can multiply and divide radical expressions.
I can convert between radical notation and rational exponent notation.
I can simplify rational expressions.
I can add and subtract rational expressions.
I can multiply and divide rational expressions.
I can simplify complex fractions.
I can add/subtract/multiply/divide/simplify complex numbers.
I can add/subtract/multiply/divide functions in function notation.
I can simplify (evaluate) logarithmic expressions.
I can convert between logarithmic and exponential form.
I can use the properties of logarithms and the change of base formula to rewrite logarithmic expressions.
I can compose functions in function notation.


Unit 3 - Solving Equations
I can solve quadratics by graphing.
I can solve quadratics by factoring.
I can solve quadratics by completing the square.
I can solve quadratics by taking the square root of both sides.
I can solve quadratics using the quadratic formula.
I can solve systems of equations by graphing.
I can solve logarithmic equations.
I can solve exponential equations.
I can solve polynomial equations.
I can solve rational equations.


Unit 4 - Sequences and Series
I can identify a sequence, series, or situation as arithmetic or geometric.
I can find the nth term in a sequence.
I can find the sum of the first n terms in a series.


Unit 5 - Modeling
I can write a system of equations that models a situation.
I can use the model of a function to answer questions about a situation.


Tuesday, April 21, 2015

Algebra 1 Learning Goals

This was my first year implementing SBG (Standards Based Grading) in all of my classes. I had used it for a unit or two last year in Algebra 2. As the year wraps up, I'm ready to start reflecting on what worked and what didn't and how I plan to proceed for next year. But, before that I think I should share the learning goals I created for my students. So, for the next few days, I'll be sharing these learning goals here on my blog.

Are they perfect? Definitely not!!! I wrote goals for all three of my preps over the course of about a day and a half. Let's just say I kinda decided at the last minute to do SBG. But, I know that I benefited by looking at other people's learning goals online. So, I hope that this helps someone out.

Algebra 1 Learning Goals2014-2015


Unit 1 - Relations and Functions
I can label the parts of the coordinate plane.
I can correctly graph ordered pairs.
I can represent a relation four different ways.
I can classify a relation as a function/not a function and justify my answer.
I can classify variables as independent and dependent.
I can evaluate a function using tables, equations, or graphs.
I can graph a function on the coordinate plane.

Unit 2 - Linear Functions
I can identify the four types of slope.
I can find the rate of change given a graph, a table, or a set of points and interpret its meaning.
I can classify a set of data as linear/non-linear and justify my answer.
I can identify the slope, x-intercept, and y-intercept from a graph, table, equation, or set of points.
I can graph horizontal and vertical lines and recognize their equations.
I can develop the equation of a line given slope and y-intercept, slope and one point on the line, two points on the line, x-intercept and y-intercept, or a set of data points.
I can rewrite a linear function in a given form.
I can construct lines that are parallel, perpendicular, or neither parallel nor perpendicular to a given line.

Unit 3 - Inequalities and Systems of Equations
I can solve a system of linear equations by graphing.
I can solve a system of linear equations by elimination.
I can solve and graph simple inequalities in one variable.
I can solve and graph compound inequalities in one variable.
I can graph and interpret the solution of inequalities in two variables.

Unit 4 - Polynomials and Expressions
I can name polynomials according to their degrees and numbers of terms.
I can use exponent rules to simplify expressions.
I can add, subtract, and multiply polynomials.
I can factor the GCF out of a polynomial.
I can factor quadratic trinomials.
I can simplify rational expressions.

Unit 5 - Absolute Value Functions
I can define absolute value and identify the absolute value of a number.
I can evaluate expressions involving absolute value.
I can graph absolute value functions.
I can predict the effects of transformations on the absolute value parent graph.

Unit 6 - Radical Expressions
I can simplify radicals.
I can add and subtract radicals.
I can multiply radicals.
I can rationalize the denominator of a fraction.

Unit 7 - Algebraic Problem Solving
I can translate between written expressions and algebraic expressions.
I can solve linear equations for x.
I can solve literal equations for a given variable.
I can use algebra to solve problems.



Monday, April 20, 2015

Stuff Worth Sharing: Big Ideas Game Closet

So, I tweeted a link to this a couple of weeks ago, but I want to write a blog post about it too.  My own twitter use is sporadic, and I'm even worse about trying to keep up with reading everybody's tweets when life gets kinda crazy.  I know plenty of people haven't found out about this awesome resource.  But, if you already saw the link, forgive me.



This past summer, I was introduced to Big Ideas Learning through a Common Core workshop I attended.  We each received one of the Big Ideas textbooks to use in our classrooms.  These texts have been specifically written to meet the CCSS.  Of course, Oklahoma had already decided to drop Common Core at this point...  So, the book has been sitting on my shelf all year long.

Now that testing is over, I'm starting to think about ideas for next year.  I'm thinking of restructuring my algebra courses, so I'm looking for ideas.  While flipping through the Big Ideas Algebra 2 textbook , I saw a link to an assessment task that looked interesting on their website.  Going to the website led me to seeing a link to their Game Closet.  I clicked on that link, and I'm SO glad I did!


There are over 30 printable pdf games to use in your middle school / high school math classroom.  I haven't tried any of these in my classroom yet, but they look pretty and solid.  I'm super excited about trying out this logarithm board game next year.  If I taught geometry, I'd definitely be printing and laminating this war game to practice finding area.  I might modify this game a bit for my students, but I like this idea for turning graphing one variable inequality practice into a game.

This year, my students really struggled with identifying parallel and perpendicular lines.  Playing a game like this would probably have helped.  I also really like this dice game for practicing operations with polynomials.  I could keep linking to cool games, but I think you should really just visit the link for yourself.

Now, if you teach younger students or need remediation resources, they also have an alternate game closet.  This includes games to review the coordinate plane, integer operations, order of operations, fractions/decimals/percents, etc.  There is a bit of overlap between the two collections.  Here's the link to this other set of games to download.


If you find something cool, please share it on twitter or on your own blog.  Let the world know about it!




Sunday, April 19, 2015

Things Teenagers Say: Volume 32



Previous Volumes:
Volume 1 | Volume 2 | Volume 3 | Volume 4 | Volume 5
Volume 6 | Volume 7 | Volume 8 | Volume 9 | Volume 10
Volume 11 | Volume 12 | Volume 13 | Volume 14 | Volume 15
Volume 16 | Volume 17 | Volume 18 | Volume 19 | Volume 20
Volume 21 | Volume 22 | Volume 23 | Volume 24 | Volume 25
Volume 26 | Volume 27 | Volume 28 | Volume 29 | Volume 30
Volume 31

--

She's married to my ex-future-husband.

--

Student: Ms. Hagan, do you get cream in your slushies at Sonic?
Me: I don't get slushies at Sonic.
Student: You haven't experienced life as life itself, then.

--

My elbows sometimes look like elephant skin.

--

Your hair looks like a cheerleader's pom-pom.

--

Student: Ms. Hagan, this textbook is almost as old as you are.
Me: What year is it from?
Student: The first issue date was 1998.
Me: You do realize what year I was born in, right?
Student: 1989?
Me: Yeah.  That's quite a bit far away from 1998.

--

I don't know many old racist people.  But, then again, I don't know that many old people.

--

Male Student: What if you cut your cords?
Female Student: Do you mean tie your tubes?
Male Student: Oh...

--

My baby's going to listen to Alice Cooper!

--

Student 1: This doll has nice Barbie boobs!
Student 2: My doll has nice boobs, too!
Student 1: No, it doesn't.  See my doll's boobs are shiny.  Your doll's boobs are matte.

--

My eye feels like glass, and I can't deal with it.

--

Twitter is just for rich people.

--

Student 1: Guys, I've been married 30 times.
Student 2: Did you know you can get married in each state?

--

Student 1: There's a lot of product in her hair.
Student 2: Are you sure there's no quotient in her hair?

--

You have selective hearing, Ms. Hagan.  I used to get spankings for selective hearing.

--

I'm going to go home, eat some chocolate, and shave my legs at lunch.

--

Did you get your tattoo done professionally or in some alley by a guy named Berta?




Saturday, April 18, 2015

Group Board Work Strategy

Some days I have random ideas that work out well.  Other days, my random ideas flop.  Big time.  The other day while doing last minute test prep review, I tried one of those random ideas.

Here was the scenario:

For the first forty or so minutes of class, we had been reviewing various calculator strategies.  We had been practicing entering tables, turning stat plot on and off, and sketching inverses on the TI-84.  I'm annoyed that I have to teach these things because it's tedious and using Desmos would just be so much easier.  But, my kids don't get Desmos on their test.  They get a TI-84.

After finishing the calculator review, I asked my students what else they wanted to review before their standardized test.  This was their last chance to ask questions.  They voted on doing a dividing polynomial problem that resulted in a remainder.  I taught this using the box method this year, and it has been AWESOME.

This post isn't about the box method.  Though, I do need to still blog about it.  If I don't, please hold me to it.  It's pretty much life changing.  

This post is about how I handled a dilemma I had.  There was less than 10 minutes of class left.  It didn't seem like enough time to justify dragging out the dry erase boards, markers, and erasers.  My kids can easily waste a few minutes trying to pick the perfect dry erase marker out of the bucket.  I knew that I could ask students to get out a piece of paper.  But, I think you know how kids are during the last 10 minutes of class on Friday on the last day before the test.  If I did this, a few kids would, but more would probably just sit there and "pretend" to follow along without writing anything down.

In a moment of brilliance/insanity/not sure what, I told my students that we would just do the problem together.  No white boards.  No notebook paper.  Normally this is the recipe for complete chaos and student disengagement.  One person does the problem.  The rest of the class watches.  Or not.

But, I had a plan.  My students had to do the problem together.  With no help from me.  On the SMARTboard.  The twist?  No student could write more than 3 terms on the board.  And, no student could have more than one turn at the board.  

Here's what the finished problem looked like:

The class ACTUALLY worked together.  The top students weren't working ahead.  The lower students weren't off the hook.  Because no student could fill in more than 3 terms, they had to communicate with one another.  They had to pay attention to what the person ahead of them was doing.

Different students wanted to take slightly different approaches with writing out the process (highlighting versus circling like terms).  So, they had to justify these to the class.  Students who were confused about where we were in the process or where we were going were asking each other for help.

It was beautiful.  Students working together.  Students engaged.  Students asking questions.  Students answering each other's questions.  Students doing math.  Students talking about math.

I definitely wouldn't use this strategy every day.  But, for those odd few minutes when you want students to work together without dragging out loads of supplies, this worked perfectly.


Friday, April 17, 2015

Algebra 1 - Unit 2 Linear Functions INB Pages

Are you getting tired of seeing notebook pages yet?  Usually I try to space these out a bit more.  But, I'm so behind at getting them posted.  I want to get all of this year's notebook pages up before the end of the school year in one month!

Many of these are repeats from last year's unit on linear functions.  There are some tweaks and new pages, though.  You can view last year's pages here.

SBG Learning Goals for Algebra 1 Unit 2 - My students asked for separate columns to record their homework and quiz grades for each learning goal.


Unit 2 Table of Contents



Four Types of Slope:


Inside of The Adventures of Slope Dude:


This paper folds out and each quadrant is labeled to represent a different type of slope.  Students had to create 3 examples of each type of slope.


Slope name art project I've used before:



Slope Concept Map Graphic Organizer


Finding Slope from a Table or Points


We used our vertical number lines to help us find the delta y and delta x values.


Finding Slope From A Graph Graphic Organizer:


Interpreting Slope - My students have struggled with questions that ask them to interpret the slope of a table or graph in the past.  This year, we got lots and lots of practice with a poof booklet.


Inside of Booklet:




I don't think they'll forget that slope is all about the CHANGE this year!


Frayer Model for Linear Relationship:


Linear / Non-Linear Card Sort.  This was NEW this year!  Link to download file at the bottom of this post.



Practicing with Linear Patterns:


X and Y Intercept Notes:


Inside of Practice Poof Booklet:



Slope Intercept Form Notes


Inside of y=mx+b foldable:


HOY VUX Notes

And yet another poof book.  I kinda like these things!







Notes on converting equations to Slope-Intercept Form


Standard Form of a Linear Equation - I went back to this foldable from my first year of teaching this year.






Point-Slope Form Notes:


4 Practice Problems:





Inside stolen from Everybody is a Genius.


Parallel and Perpendicular Lines Foldable:


Inside:


These notes are the same as I normally use.


This year, I had students practice writing lines parallel, perpendicular, and neither parallel nor perpendicular to a set of equations.  This is a start at making this lesson better, but it still needs something.  I just can't put my finger on it.  Yet.

Parallel Practice:


Perpendicular Practice:


Neither Practice:



At the end of the unit, I had students create a summary foldable of the different forms of linear functions.  They had to write the steps to graph each function and make their own example problem.


Download files here.