## Authentic Math Task Lesson Reflection

Right now, in Algebra 2 Honors, we’re reviewing linear functions (from Algebra 1).  In previous years, I have not really done anything with modeling, other than the “story problems” in the textbook.  I found a lesson by Robert Kaplinsky that he titled “How much does a 100x100 In-N-Out cheeseburger cost?”  There were a couple of other lessons I was thinking about using it, but when I read this:
“This awesomely gross lesson provides students with a real world context for building linear functions.”
Bam, that was it, I was sold.

My goal was to hit the following points:
• Make a table of values
• Calculator graphing
• Write an equation based on points
• Have the kids ask any other questions that could be solved using math

I decided that as long as I hit those goals, I would call it a success and try this again later in the year.  I knew going into it that it wasn’t going to be perfect the first time.  But hey, this is new for me.  Also, this is Algebra 2 Honors.  I figured I couldn’t mess them up too bad at this point.  This was kind of a review for them.

This is what I did:
• Then, I put this picture on the board and didn’t say a word.  Also, this class period is right before lunch :)  The class was almost silent during bellwork.  The class erupted.
• We has a quick discussion about how we’re hungry.  Then, I showed the picture of the Double-Double cheeseburger.  When I showed them the picture of the 100x100 cheeseburger they started throwing out all kinds of great questions.  The question “How much does that thing cost?” came up quickly.  I made them give me an estimate that they knew was too low, and an estimate that they knew was too high.
• I handed out student answer sheets and displayed the picture of the menu and prices.  I told them that they had to find out how much the 100x100 cost, but then they could also answer any other question they thought of.  They worked in partners.
• After I gave the directions and let them work a few minutes, I realized that I was a little too vague.  We looked at the answer sheet together and I explained that I wanted them to come up with a function and represent it in four different ways.
• It was interesting to me to watch them work.  Every single one of my groups wrote their equation as   cost = 0.9(# of patties) + 0.85    I expected some of the groups to use the cost of the Double-Double and some to use the cost of the single cheeseburger.  They weren’t copying off of each other either.

• When all of the groups figured out the cost, I showed them the picture of the receipt.  I didn’t expect it to be a big deal, but there was a huge jackpot payoff for them to see the actual receipt.  I didn’t realize it before I used it in class, but there needs to be some sort of payoff for their work.
• Then, I let them choose another question and answer it themselves.  Most of the kids asked something based off of the number of calories.  My favorite was “If no one could eat more than 2,000 calories, how many people would it take to eat all of that?”  Another group found out how many patties they could eat to fit within their daily calorie allowance.

Reflections and Thoughts:
• I totally forgot to do some type of summary before the bell rang.  I only teach one section of this class, so I didn’t get a chance to do better the next class period.
• My kids were really excited about this.  Crazy excited.  However, I think that I need to be careful and reel them in a little next time.  It’s only September; I’m nervous to see what crazy excited looks like in April.  They worked hard and talked math the whole period, but I want to keep a tighter ship next time.
• I’m glad I practiced with a review type lesson before I jumped into something that was new material for them.  Now, I know a little more what to expect and how to guide them when I do use more tasks in the future.
• Their biggest hurdle was getting started.  Having a loose framework for them (like an answer sheet) is essential, in my opinion.  It helps them sort their thoughts.
• Some kids worked much faster than others (duh!).  This was great because I could just say, “Great, what else can you tell me?” and they could work on another question.  However, I think I need to provide a little more guidance to the struggling groups next time.
• I had my students work in partners.  Next time, I’ll have them work in groups of four.  They need more discussion.

I plan to do a few more of these types of lessons this year.

## 6 Reasons I Love Card Sorts

It’s no secret that I love card sorts.  I have several sets in my Teachers Pay Teachers store and several more that I have made or downloaded from other places.  Here are just a few reasons that I love them:

1.  Card sorts are self-explanatory.  I don’t have to give the kids instructions at all.  When I spread out the plastic baggies on the counter, the kids know exactly what to do.

2.  Card sorts promote discourse.  Whenever I use matching cards, I hear great mathematical conversations among my students.

3.  Card sorts help kinesthetic learners.  Many of my ADHD students can sit and focus while matching cards because they have something in their hands to manipulate and work with.

4.  Card sorts are low stress for students.  There aren’t blank spaces on a worksheet staring them in the face.  Students feel like they are making progress as they are matching cards.

5.  Card sorts give students a starting point.  If students are stuck, they have an answer bank where they can look for hints.  I’ve found that this makes kids much more willing to use their notes and other resources.

6.  Card sorts break up the monotony of worksheets.

Have you used matching cards in your classroom?  What do you like or dislike about them?

## Conditional Statements and Law of Syllogism

The other day, I wanted to review conditional statements and the Law of Syllogism before we started proofs.

I split the class into two teams and gave each team a set of cards.  First, I had them practice putting the cards in order.  A few of them had played a version of the game before in middle school, so it went pretty smoothly.  After about 10 minutes, I collected the cards, shuffled them, and passed them back out.  I had the two teams compete against each other.  The winning team got one bonus point.  My kids enjoyed it and I kept hearing funny things like, “Come on guys, look!  If I do my homework, then my parents are happy!”  I liked this because I didn’t have to answer any questions or anything, but my kids were talking about math and working the entire time.  Awesome!

When I brought the class back together, we talked a little bit about starting proofs.  Most kids have heard horror stories about geometry proofs, so I usually like to prep them a little before “the big day”.  I tell my kids that proofs are like a mathematical story.  If you forget a detail of the story, it doesn’t make sense.  Also, if you tell the story out of order, it doesn’t make sense.  Proofs are our geometric story that needs the details in an order that makes sense.

Next, we did an activity that I totally ripped off of Crafty Math.  It was such a good idea and it turned out better than I expected.  Win!  I'm so glad I checked out her blog.  I used the overall idea and copied the robot story.

I put my students in partners and gave each group generic “If…, then…” statements.  They had to cut them out, put them in order, and use the Law of Syllogism to come up with a conclusion.

When they were finished they had to glue them on paper.  I also had them do the same thing with a short story.  If they finished early, they could decorate their pictures.

(Cookie cards are kind of a big deal at my school among the underclassmen.  They buy punch cards for \$10 and can buy treats in the cafeteria with them.  There are these fantastic chocolate chip cookies that are 25¢ each.)  I hung these cute pictures for Back to School Night.  Proofs are next!

## 5 Questioning Strategies That Work

When I first started teaching, I would just ask my students questions like, “So, what is the answer to this problem?”  I would also answer my own questions if my students didn’t answer quickly.  Teacher fail.  I didn’t know any better.  I read lots of articles, blog posts, and observed other teachers.  I’ve gotten much better.  Today, I’m sharing my favorite tips.  I use these strategies almost everyday and also use them in conjunction with each other.

“Two angles are supplementary.  The measure of one angle is 20 degrees less than 3 times the measure of the other.  Find the measures of the two angles.
By raise of hand, someone tell me how to start solving this problem.  Do not tell me the answer.”
“You need to set up an equation.  Drawing a diagram can help.”
“Ok, tell me how to set up the equation.”
Student gives an equation.
“Ok, tell me why this works.”

2.  Intentionally make mistakes.  This is different than the accidental mistakes :)  This is what it usually looks like:
“Let’s factor x squared plus 1.  So, we can just use the difference of squares, right?”
This gives students that would make that mistake a no pressure way to see why the mistake is incorrect.  Also, they benefit from hearing the explanation in the words of their classmates.

3.  Ask for another way to work a problem.  Once you have solved a problem in class, ask if the problem could have been solved a different way.  Nine times out of ten, you will get an excellent answer.  This strategy in particular gives me insight to how my students are thinking.  Even if your students give you an incorrect answer, you have created a valuable teaching moment.

4.  “Explain this to me like I’m not in this class.”  I use this line all the time.  Only write down exactly what your students tell you.  They will quickly realize that they need to be very specific in their language.

5.  Tell kids that “they’re out”.  Often, when a few students are answering most of the questions, I tell them that “they’re out”.  Every time a student answers a question, “they’re out”.  As more and more students are “out”, I start saying, “Someone that’s not out, tell me…”.  Once a large percentage of the class has spoken, I tell them that everyone is back in.  I’ve never actually explained how this works to a class; I’ve never had to.  They pick up on it very quickly, even my low performing classes.

Do you use any of these strategies in your classes?  What do you do that you think is particularly effective?

## Factoring Practice!

Today in Algebra 2 Honors, my students practiced factoring.  Yesterday, their homework was to look through their notes and textbook to find the three hardest factoring problems they could find.  I told them they could work with friends and bring the same problems, as long as they could tell me why they thought the problem was difficult.  My students thought I was joking at first.  One boy said, “This is like the easiest homework ever!” and a girl glared at him and hissed, “shut. up. now.”.  Super funny.  Their bellwork today was to list the “hard problems” on the board.  Some of the problems they chose were from their Factoring with Symbols worksheet.

Once all the problems were on the board, we worked the problems together.  I had a few reasons for doing this:
• I wanted the students to practice articulating why they didn’t understand something.  As a class, we talked about why a problem “looked scary”, then broke it apart together.  I kept stressing patterns.
• I wanted them to get used to seeing challenging problems, and actually working through them.  This is a tiny baby step I’m taking to try to teach perseverance in problem solving.
• My students were much more focused because I was working “their” problems.  A few of them were impressed that I could factor the problems on command.  Come on guys, it’s my 4th year teaching the same course using the same textbook.  I practically have those problems memorized.

When we finished working the “hard problems”, I had my kids do a set of matching cards with a partner.  They were supposed to match a polynomial with the factored polynomial.

I also gave them dry erase markers so that they could use their desks as scratch paper.  They LOVE writing on their desks.

I like to copy the problems in a different color from the solutions when I make matching cards.  It's easier for the kids to start working when they know what they're supposed to match.

If you’d like to use these cards in your classroom, you can download them for free from my Teachers Pay Teachers store, just click on the picture below!

## Factoring with Symbols

I’m starting factoring this week with my Algebra 2 Honors students.

I really like using this worksheet to reinforce the fact that factoring is all about patterns.  My students always think it’s impossible at first.  I do one or two problems with them, and they finish it quickly.  This worksheet is not my creation.  I think it’s been around in various forms for a long time.  However, it works well for my students, so I hope it will help yours!