Category Archives: #perplexity

The Overview:

This year I wanted to do Kyle Pearce’s Detention Buyout Program that Dan had highlighted in his Great Classroom Action series.  The problem was that in my new school we don’t have detentions, so I didn’t think I would get much buy-in from the students.  But there is something that all schools definitely do have:  Missing assignments!  So I created three “deals” that would allow students to pay me money in exchange for getting credit for an assignment they missed.

I used this assignment as an introduction to inequalities, but I also wanted to link the Missing Assignment Buyout Program to the linear equations we just finished covering.  That is the why as you look at this assignment, you will see a focus on connecting the information in the graphs to the information contained in the inequalities.

I sequenced this by first giving the assignment.  Then two days later I did another version of it as an opener / warmup.  And then lastly I put another version of it on their test.  Each new version offered slight modifications from the previous.

The Description:

I first offer students three possible deals for buying off their missing assignments.  I poker face the whole thing and enjoy all the “Is this legal” expressions on their faces.  I tell them to make sure they go home and talk to their parents about how much money they have budgeted for such as program.  The first question on the worksheet asks them which deal is better for them, so as an added bonus I printed out each students missing assignments and handed it to them.  This is that first worksheet:

There are a lot of interesting questions and explanations that came out of this first assignment.  For instance, having students see that x less than 5 was the same as saying x less than or equal to 4 since x could only take integer values.  Also having students see the connection between the intersection points of their graphs and the inequalities they wrote was time well spent.

A couple days later I came back to the Missing Assignment Buyout Program in the form of a opener or warmup question.  I handed the students this graph when they came into the room (two graphs per page to save paper):

Then I had students write a description of each deal, as well as the inequality and equation for each deal.  This was a slight inversion of the original assignment where I gave them the description and had them write the inequality, equation, and then graph.  Now I am giving them the graph and asking them to write the description, inequality, equation.  I have them in pairs and am checking homework and taking role while they work.  Then I randomly call on pair share partners and fill in the following table that I am projecting on the board:

Lastly to make sure that they really did understand the concept, I put a similar problem to the opener exercise in their inequalities chapter test.  The test had a slight twist in a scenario where a student would want to buy the Flat Fee plan based on their number of missing assignments, but based on the money they had to spend, they would need to pick their second best option.  Here’s that problem:

I initially thought having them graph each deal was kind of an unnatural excercise, because why would someone ever graph something like that?  But I think it ended up working because of how the Opener and Test question both refer to the graph.  All in all student engagement was high, even with the graphing portion so I think I’ll keep it next year.

The Extension:

(good idea courtesy of my principal)

Tell the students that you have decided to only offer one deal to the whole class, and they have to decide which deal they want for the class.  This could open up a nice debate about fairness and equity – this deal is best for you since you don’t have any missing assignments, but what about these other students?  Connect this debate to something current, like Obamacare.  Discuss how math influences decisions and that often decision makers have to make decisions based on their believe on the greater good, even when the numbers indicate that some people will be negatively affected by the decision.

The Goods:

Stacking Cups Assessment

When three of your favorite bloggers all write about the same lesson (Dan, Andrew, Fawn) it is a pretty safe bet that you should do the lesson.  I used Andrew’s 3Act video because my students can be pretty green and I might not hear the end of it if I couldn’t find an additional use for all these cups I was bringing into the class.

I don’t have anything to add to what was already said by Dan, Andrew, and Fawn, so I will just share a problem I created that you can put on your midterm that is a slight twist to the presentation of the original problem:

1.  How many cups would stack in a 250 cm door?

2.  What are the dimensions of the cup?  Draw it and label it with the dimensions.

I suppose you could ask for the y-intercept and slope and all that stuff too if you wanted.

Moving on from test questions – The actual lesson went great for me and I am definitely looking forward to doing it again next year.  When I did this problem in algebra I had the students make a Stacking Cups comic that was supposed to describe how to solve the stacking cups problem.

I like the comic concept because I think this is a very visual problem, and since I didn’t provide them with actual cups they needed to create their own visuals.  I have been trying to get students to give me a visual for every word problem they do this year.  My stated reasoning for that has been that visuals help you give a clearer and more convincing justification for your solution.

In order for students to learn how to construct a viable argument and critique the reasoning of others (Let’s hear it for MP.3!!!), we are going to have to have an iterative process on a couple problems where they essentially hand in drafts, and we keep having them make improvements.  I think this is a great problem to do for that since it has a couple nice extensions for system of equations (different sized cups) and geometry (here).

Concert Tickets Remix

Word Problem remix here.

I started by playing some Soulshine from Gov’t Mule to set the mood if you will.  From there I pretty much just showed the image below which is a screenshot from the Ticketmaster site when I went to buy the tickets.

This is not the exact image from Ticketmaster because I photoshopped out where they give the subtotal for the cost of the tickets and also where they again give the Tickets/items price because I wanted the students to have to take into consideration the order processing fee.

At this point I just let the black rectangle do it’s thing.  Student engagement was high.  I required each student to also draw a diagram of this situation that would be useful in explaining their thought process.

Then the reveal.

And lastly I give them the original textbook problem that inspired the remix:

A ticket agency sells tickets to a professional basketball game.  The agency charges \$32.50 for each ticket, a convenience charge of \$3.30 for each ticket, and a processing fee of \$5.90 for the entire order.  The total charge for an order is \$220.70.  How many tickets were purchased?

I had very high engagement in all three algebra classes even with the textbook problem.  The students felt confident with it and they wanted to figure it out.  Success!

As a side note, lead singer / guitar player Warren Haynes is one of my idols, so giving him some props in a lesson was fantastic.  A few year ago he headlined the High Sierra Music Festival and it was the greatest set I’ve ever experienced.  It’s here.  I recommend beginning with his rendition of “I’d Rather Go Blind” with Ruthie Foster (track 10)

My Day 1 Lessons For 2013

This year I am teaching algebra and geometry again – new school, same subjects.    I have decided to do no introduction or ice breaker activities.  No syllabus on day 1 (which I never have done) either.

Last year I did the straw bridge challenge and I loved it and definitely recommend it.  But I am scrapping it this year due to the time constraints of  focusing on CCSS in a district that is still giving the STAR test.  So I choose these two activities for their more direct relationship to standards I must teach, as well as their low entry point and interesting hooks.

Algebra

Day 1 in algebra is going to be my Getting to Vegas problem, which is simply a personalization of a problem Dan Meyer describes here.  When I was living in Forestville some friends and I decided to go to Vegas.  There are two airports that we could have used – the smaller local airport in Santa Rosa, or the larger airport in San Francisco.  Which airport should I have took, or will I take next time?  I have screen grabs of all relevant information in the slides.

A couple extensions:  How long would the Vegas trip need to be in order for the Santa Rosa airport to be cheaper?  (Eventually the more expensive parking at SFO takes over).  Or Dan’s scenario of taking a shuttle from Santa Rosa to the San Francisco airport vs. driving directly to San Francisco.

The Goods:

GettingToVegas

Geometry:

In geometry I’m starting with Dan’s Taco Cart problem.  I am just going to go to keep it as Dan vs. Ben, because I am a bit intimated on day1 to follow Fawn’s more interactive implementation allowing students to choose their own paths.

This is an exercise with the Pythagorean Theorem, which is great for day 1 because they have all seen it before.

The Goods:

TacoCartWS

TacoCartWS

Running Off The Burger

How far would you have to run to burn off all the calories from this burger?

The Overview:

This is a slight remix of a traditional calorie problem in a math text.  Bascially I first show the students 4 burgers with the calorie count blacked out, and have them guess what it is for each burger.  Then I ask them to figure out how many miles they would have to run in order to burn off the calories from each burger.

The number of calories burned depends on how many miles you run and your weight:

# calories burned = 0.75(your weight)(miles ran)

Runners use the general rule of thumb that you burn 100 calories per mile.  You might what to use that fact for something – maybe ask them for what weight is that actually true.

– The problem asks students to use their weight.  I offer up my weight and ask if some students could help me by doing the calculations for me.  That way they can choose to do it for themselves or me.

– I do not initially give them the relation for calories burnt vs. miles.  I make them request that information based on their need to solve the problem.

– If you want to incorporate a comparison between running and walking, here is the relationship for walking:

calories burned = 0.53 (your weight)(miles ran)

– I got these functions from Runner’s World:

The Goods:

RunningOffTheBurgerHandout

RunningOffTheBurgerPresentation

The Extension:

How many times around the track would you have to run to burn off this burger?

This burger is called “The 8th Wonder”.  Although the calories of it have not been calculated, we know it’s 105lbs.  I have the students use the fact that “The Beast” is 15lbs and 18,000 calories.  Discuss with them if a linear model is sufficient for this calculation.