Math = Love: 2015

Wednesday, December 9, 2015

Unit Reflection Sheet Reflection

The first semester is wrapping up.  I've got a few more lessons to teach and semester tests to write/give/grade.  One new thing I've implemented this year is a unit reflection sheet.  At the end of each unit when students have demonstrated mastery on all of that unit's quizzes, students fill out this reflection sheet, staple their graded quizzes to it, and turn it in with their completed notebooks.

I ask my students to reflect on each unit.  I, on the other hand, am going to reflect on my first semester of using reflection sheets.

* Not putting a space for students to write their name on this sheet was a huge mistake.

* And, apparently putting a box between "Unit" and "Reflection" is not a big enough clue to students that they should write the unit number in the box...

* It's been interesting to read the students "Why?" answers for which skill they are most confident with and which skill they found most difficult.  Some students, of course, write things like "#2 because it's easy" or "#5 because it's hard."  Other students have actually taken the time to reflect on what made a specific skill easy or hard for them.

* Either way, I'm excited that when I had back the packets at the end of the year to review for the end-of-instruction exam that students will automatically have a list of which skill they need to work on the most in each unit to prepare.  If I choose to do this again, I will be more adamant about students explaining why something was easy/hard.

* I like that students have to go back and look at their errors and formulate a plan for avoiding those errors in the future.  Each reflection sheet is sort of a note to themselves to read/act on in the future.

* I had big hopes for the summary section, but it hasn't worked out exactly as I'd anticipated.  For the one word summary, I had meant for students to choose one math word that summed up the unit.  But, a lot of my students are picking words that describe how they feel about the unit such as "challenging."  Or, they're like my stats students who summarize our box plot unit as "boxy."

* For the one sentence summary, I'm realizing that many of my students don't know how to write a sentence.  One word is not a sentence!  These sentences are almost always their opinion of the unit.  I guess I'm still getting feedback about what they feel, so it's not what I was intending but it's also not useless.

*  Lastly, students have to do a  mind map summary.  Mind map.  Concept map.  Bubble map.  Web.  Whatever you want to call it.  I had this vision that students would comb through their notes and put a lot of thought into this.  They copy the titles of a few units into bubbles and call it good.  A few students have been making a number line of sorts and ranking the skills from easy to hard.  Basically, I've been letting students turn in their reflection sheets if they have something written there.

* I need to do a better job of holding kids accountable for doing things the way I want them to.

At the bottom of the form, there's a place for me to mark off if they submitted their reflection sheet, completed quizzes, and notebook for grading.  I keep the reflection sheet/quizzes in a filing cabinet, and I'll pass them back at the end of the year for them to review.  I'm hoping this makes review go much smoother.  

A copy of my file is uploaded here.

Tuesday, December 8, 2015

Looking at Radicals in Algebra 1

I've never really known what to do about teaching radicals in Algebra 1.  Oklahoma's Algebra 1 standards currently have students simplify expressions involving radicals in Algebra 1.  This is not the same as simplifying radicals - that happens in Algebra 2.

In the past, I've taken several approaches.  I either skip radicals altogether and tell students to type them in on their calculators come test time.  Or, I go all-out and teach simplifying radicals, adding/subtracting radicals, and multiplying/dividing radicals.  This year, I decided to just teach rationalizing and reducing.  It's better than just having kiddos type things in their calculators which teaches them nothing and just helps them pass the test.  And, I'm not wasting time by teaching things that won't be tested.  My Algebra 1 students are already far behind, so time is at a premium.  Plus, this is a high-stakes class.  They must pass the end-of-instruction exam to be eligible to graduate.  We are slowly but surely making progress, though.  

If you notice at the top of the page, this is skill 3 for the year.  It directly follows order of operations/integer operations and fraction operations.  I specifically taught it after fractions because I wanted to rely on the idea of equivalent fractions for teaching rationalizing the denominator instead of teaching kids to memorize the steps for how to rationalize.

In the past, I've been guilty of explaining rationalizing the denominator like this:  "If we want to get rid of a square root in the denominator, multiply the numerator and denominator by the square root you are trying to get rid of."  The radicals magically disappeared, but I never explained to them how they should know how to do that.  Of course, that strategy fell apart when there was a cube root in the denominator...

This year, I decided to take a different approach.  I told them that our goal was to get rid of the radical on the bottom.  Then, I encouraged them to think of a radical that could be on the bottom that would simplify.  Now, what can we multiply the denominator by to make it into that radical?

This worked sooooooooooo much better.  If students had a radical five in the denominator, they recognized that if it was a radical twenty-five that the denominator would reduce to five.  Thus, they should multiply the numerator and denominator by radical five.

Some students caught on to the shortcut that I used to teach my students.  Other students get out their square root chart and think through the process of what to change the denominator to each time.  Either way, students are thinking about what they are doing instead of blindly following steps, and that has me so excited.  Why has it taken me so long to figure this out???

Download the file for this lesson here.

Tuesday, December 1, 2015

Cutting and Pasting to Combine Like Terms

This year, I decided to really emphasize combining like terms with my Algebra 1 students.  In retrospect, I should have done the same thing in Algebra 2 because they were still struggling with what they can and cannot combine.

I thought this would be a one day lesson, but it ended up taking my students two days to work through it.  There were lots of great conversations happening, so I think it was definitely worth it!  

I gave students a quarter sheet of paper that had a note box and three polynomial expressions.

We began by taking some notes over what like terms are.  I really wanted to emphasize to my students that xy and yx are like terms, so I really pushed the "order doesn't matter" this year.

I had them copy down the first polynomial strip in their interactive notebooks.

Then, the students had to cut the strip into terms.  This led to a great discussion of what a term is.  Students had to make sure they cut the strip so that each term contained the sign in front of it.  Students were super careful to make sure they were cutting the strips correctly which is exactly what I was hoping for.

Next, I instructed students to group the terms into groups that were like terms.  This is where the best conversations happened.  After students sorted their terms, I asked them how many groups they had.  When students realized they had sorted into a different number of groups, they started justifying their groupings to their classmates.  It was just awesome to see them pointing each other back to the definition of like terms.  Finally, we decided on how the terms should be grouped.  

Next, I instructed students to glue in their groupings.  I intentionally did not tell them how to group them in.  Luckily, the students glued them in different orders which let us discuss the fact the order of the terms doesn't matter.  

Finally, we circled the groups and combined the coefficients.  Since the students glued the groups in in different orders, their terms ended up in different orders.  I emphasized that this was okay as long as the sign in front of 21x was negative, the sign in front of 2x^2 was negative, and the sign in front of 4 was positive.  

Next, they proceeded to do the next two problems in their groups.

The zero coefficients and invisible one coefficients freaked some of my students out, but they persevered.

Last problem:

We finished the class period off with two additional practice problems.  The kids were quite miffed that I did not give them strips to cut because how else would they figure out what the terms were.  To remedy this, many students drew "cut lines" between the terms to separate them.

I like this activity got students actually separating terms, grouping them, and combining them.  I hope I made an abstract concept a little more concrete and understandable for my students.

File for this lesson found here (PDF and PUB).

Sunday, November 22, 2015

Stats Simulation: Hiring Discrimination

This year, I decided I wanted to start my statistics class off with a statistical simulation to give them a taste of what was in store for the year.  I ran across mention of a hiring discrimination simulation on another blog, and I thought it would make the perfect first activity.  The activity is from The Practice of Statistics.

I made the activity into a quick booklet foldable for students to glue into their interactive notebook.

Here's some more readable images.


Inside Left:

Inside Right: 

Instead of using a deck of playing cards to run the simulation, I decided to make a sheet of pilot cards to print and laminate for each group.  I love finding excuses to laminate things!  

Each group got a bowl of cards to run their simulation.  Well, they first had to cut their cards and put them in the bowl.  Next time I teach stats, the cards will already be cut, and they'll just get a bowl of cards.

They pulled out eight cards to simulation the random picking of the eight pilots.

After a group completed their five simulations, I gave them a sheet of circle stickers and asked them to make a dotplot.  Here was our class results:

Students then had to copy the class dotplot into their notes.  One girl asked if she could use stickers there, too.  Of course!

I was a bit disappointed with how little my students wanted to critically think through the scenario to decide if discrimination was present or not.  It seemed like they just wanted to guess and not use statistics or math of any sort to back up their hunches.

I guess this does mean the activity gave me insight into how my students would likely approach our study of statistics.  Getting my students to write out a full sentence with fully explained thinking for the TELL section was difficult.  This has proved true for the entire year.  My students hate to write and explain.

I do think this was a worthwhile activity to start out the year!  If you want the files, you can download them here.

Friday, November 20, 2015

Statistics: Game of Greed

I've been looking for fun ways to collect quantitative data in my statistics class.  Let's just say my students are tired of surveys of how many siblings they have or how many states they've visited.

I got this activity from @druinok.  Here's the word document version she posted.  She calls it the "Game of Greed," but I've played a slightly different version with students before called Greedy Pig.

I modified it in just the slightest way to make it into a booklet foldable that will glue into my students' interactive notebooks.    

Here's the questions that students worked through:


Inside Left: 
Inside Right: 

I was really impressed by my students' answers to the benefits of the various types of graphs.  They had been really hating on boxplots lately, but they did note that they could come in handy for various things.

Want to know what made the activity?  We didn't just roll any die.  We rolled this jumbo blow-up die that a coworker gave me last year.

Had I known how big this die was, I probably would have changed my mind.  But, it was new and in the package, and just looked like a fun die.  This thing is huuuuuuuuuge.  It took forever to blow up!

My students had a lot of fun playing this game, and they seemed legitimately interested in the data analysis because they wanted to know if boys or girls were better at the game.  Of course, I had a group of boys decide they were all going to stay in/go out at the same time, so that definitely influenced our data.

They've also wanted to keep playing with the die ever since.  I can't exactly just stick this thing in the cabinet to keep it hidden away...

Want my (only slightly) modified version of this activity?  I've uploaded it as a PUB and a PDF file here.

Thursday, November 19, 2015

Rational Expressions Question Stack

Sorry my posting has been so sporadic of late.  It turns out that teaching, grad school, and wedding planning is waaaaaaaaaaaay more than a full-time job.  Today, I want to share another self-checking practice activity I made for my Algebra 2 students.  It's a Question Stack to practice simplifying and adding/subtracting rational expressions.

Here's a quick overview of how a Question Stack works:

  • Lay out all of the cards with the answers facing up.
  • Flip over one card to reveal a question.
  • Work that question out.  
  • Find the answer on another card. 
  • Flip that card over and lay it on top of the first question card to start a stack of questions and answers.
  • Work the new problem that was just revealed.
  • Repeat until you run out of cards. 

I have my students work through these in groups with mini dry erase boards.

This was very hastily put together because 1) I am a procrastinator and 2) I have first hour planning period.  That is NOT a good combination.  So, if it bothers you that I copied and pasted some questions and typed others, I apologize.  If your kids are super astute and will notice the font differences, you should probably fix this.  My kids were so stressed out about rationals that they didn't seem to notice.  

I put a Q on the question side of the cards to avoid confusion.  I still had one group waste a lot of time trying to solve a problem.  They couldn't figure it out.  I couldn't figure out why it wouldn't simplify.  Finally, I realized that they were looking at the answer side of the card that was already simplified.  The rest of the class gave them a whole lot of grief over that!  

Here are the questions I used:

And, here are the answers.  The cards do not print with the question and answer on the same card when printed double sided.  This is by design.  The cards should form a sort of loop.  

Download the file (PDF or Publisher) here.

Tuesday, November 17, 2015

Slope Dude Says

Last week, we got to play one of my favorite algebra games ever: Slope Dude Says.

Before playing the game, I had to make sure my students had been introduced to Slope Dude.

I told them that we were going to watch my most favorite math video in the whole world.

Some students had seen it before, but others hadn't.

Here's the link to the video on Youtube.  It's only 2 minutes long, and I think it's well worth your time.  It's a newer version of the video with improved sound quality and captions.

The kids always groan and make fun of it, but I know that they truly love it deep down in their heart.  Honestly, I don't really care what they think about the video.  I just know that it's hard to forget the four types of slope after watching this!  

After watching the video, I announced we were going to play a fun game.  I put up this slide with the rules.  

It's just like Simon Says, but kids are asked to make various slope motions.  I always demonstrate the different types of slope for my students so they know what to expect with the game.  

I tell students to pretend they are looking at the graph as they make their motions.  When I'm judging them from the front of the room, their positive slopes look like negative slopes and vice versa.  

Here is a class demonstrating the movements for you.  

Positive Slope:

Negative Slope:

Zero Slope:

Undefined Slope: 

The first round or two, it's really easy to get students out.  All I have to do is start the game by saying "Positive Slope!"  Usually, a ton of kids will do it even though Slope Dude didn't say.  As we play more rounds, it gets harder and harder to get the kids out.  

They ask for days afterward if they can play again.  That's what I call a winning activity! :)  

One of my classroom aides was in my Algebra 1 class during my first year of teaching.  She even complained that her class never got to play it.  I love that I get to keep trying out new ideas every year.  I was once afraid that I would get bored teaching math all day long.  It turns out that no two math lessons go the same.  And, no two years of teaching are the same.  It's all new, all the time.  And, I wouldn't have it any other way!  

Friday, November 13, 2015

Interactive Notebook Resource Section

My students set up their interactive notebooks on the third day of school.  That was in August.  It's November, and I'm finally blogging about it.

Here are my three interactive notebooks for the year.  Algebra 1, Algebra 2, and Statistics.

Want to know what I'm most excited about?  Our individual unit tables of contents make tabs.  Instant organization.  :D

I decided to have the students create a resources tab at the front of their notebook to hold frequently referenced stuff.  It starts out with a unit mastery sheet.  My Algebra 1 class has 8 units.  As students finish each unit, they fill in the box.  When they are all filled in, they have demonstrated mastery of Algebra 1.

The other side of the tab has the table of contents for the resource section.  I pre-typed the names of the resources.  Students just had to fill in the page numbers.  

Up next was the hall pass I gave my students.  Students are allowed four hall passes per quarter.  This has drastically cut down on the number of times students are asking to leave my classroom this year.  I'm definitely considering this one a win!

Then, I had my students glue in two concept maps.  They complete one at the beginning of the year and one at the end of the year.

On the inside, they wrote the name of the subject in the center. Then, they made a concept map/mind map/bubble map/whatever you want to call it map to summarize what they thought Algebra 1/Algebra 2/or Statistics consisted of.  

After filling these out, we used stickers to seal them shut until May.  In May, we'll do another concept map and then open August's map to compare what they thought the class would be about to what it was actually about.

Next, I had my students make a pocket to hold their syllabus.  I had students read through their syllabus with a highlighter in hand to highlight the key information.

Next to the syllabus, students wrote out their goal for the year and how they planned to achieve that goal.  I think I would make a quick graphic organizer for this in the future.

Since they have to analyze all of their errors before retaking quizzes, I gave them a sheet summarizing different types of errors.  And, they made a pocket to hold sample error analysis sheets.

I didn't have my sample sheet in this pocket when I took my picture.  Sorry!  Basically, I took the first quiz of the year and made up fake answers.  Students had to grade it and fill out an error sheet for the fake quiz.

After this, student glued in a summary of the grading and retake policy.  I'm not sure if any students actually ever looked at this.  I'd probably leave this out next year.

Calculator tutorials came next.  Algebra 2 and Statistics glued in a TI-84.  Algebra 1 glued in a TI-30.  Then, they made a pocket to hold tutorials that will be given out throughout the year.

I don't have problem solving strategy posters on my wall this year, but I did give students a list of strategies to glue in their notebooks. They had to design a tiny icon to represent each strategy.  It was fun to see how creative my students got.

The last thing we glued in our resource section is probably the most used item.  I call it our mathematician's toolbox.

So far, my Algebra 1 students have referenced the square root chart while rationalizing the denominator.  My Algebra 2 students have referenced the prime number chart while working with radicals.  My Algebra 2 students have also used the multiplication chart while working on factoring quadratics.

The next day, we glued in our Unit 1 Table of Contents and jumped into the first unit of the year.