# Category Archives: algebra

## 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

## Math Council

This is a group activity I created and have a lot of fun using in my classes.  It can be used as a review activity at anytime because all you need to do is create 10 or 12 problems.  It came from a desire to have a collaborative activity where each person in the group had their own distinct role to play.

The Overview

Students form a Math Council in groups of 4.  Each student then gets or chooses a role to play.  Each role has unique things that they are graded on.  The end goal is to create a poster that highlights the problems that the group worked on.  But in the creation of that end product, each member of the council has certain responsibilities.

Each student must do every problem on their own paper.  Then as a group they decide what the right method was and then that gets transferred onto a poster.

There are four roles:  Leader, Scribe, Sage, Runner.  Here are descriptions of each:

The Leader is in charge of making sure the poster finishes, as well as selecting the problems that group works on.  Each group is initially given an envelope of problems and the Leader chooses which ones the group works on.  Typically the envelope will have about 10 problems of which the leader selects 4 or 5 for the group to work on.  Interesting for me to see which ones they choose.

The Scribe is in charge of the poster.  Other members can help work on it, but their grade is most directly tied to the quality of the poster.

The Sage is responsible for coming up with key points for each problem.

The Runner is the only person who can ask me a question.  The Runner must report my answer back to the group.

– I do not answer any of the Runner’s questions near the group.  I make the Runner come to me and report my answer back to the group because I want to make sure that the group must rely on the Runner to explain to them what I’ve said, rather than them simply hearing me say it.

– I give each group an envelope with lots of problems in it, and then have the leader choose 4 or 5 for the group to work on.

– Each student must complete every problem on their own paper.  That is the “work shown” grade.

The Executive Council

This is a fun thing I added to mess with the students help students work on their collaborative ability to adapt to changing circumstances.  I have what I call the “Executive Council” and they call me periodically during the activity and make new demands upon the students.  I pretend to be receiving a phone call and then announce that the Execute Council just contacted me and they now want this or that.  Here are some common things the Execute Council calls for:

– They demand that every council has a name and that name goes on the poster.

– They require a certain problem out of the bunch to be on every poster.

– They require the Sage’s key points to be on every poster.

– They want a picture of a penguin drawn on every poster.

– They give extra credit for their favorite posters.

It’s pretty fun – after awhile when I act like I’m getting a phone call the students will call out “If that’s the Executive Council don’t answer it!”.  They will continuously ask who the Executive Council is – but of course I am not allowed to reveal that.

The Goods:

Runner

Sage

Scribe

## So I Guess I’m Making Videos Now

I had to be absent a couple days last week, and I wanted to the class to learn some new material.  We had just spent two days simplifiying radicals, and I wanted them to move onto adding and subtracting.  So I decided to make a quick video of myself explaining how to do it.

The next day basically every single student I have told me how much they loved the video.  The sub-report talked about how great it was.  A couple teachers and a teachers aid all told me at various times throughout the day that they heard I made some great video.  Then yesterday a student told me that she learns better from my videos than she does from me (thanks…  I think?).   And after multiple students asked if the video was online, I figured I should put it online.

And it’s kind of funny because they are nothing special at all – straight up direct instruction.  But it seems like some students got something out of them, so who I am to judge?  And just like Khan I suppose, I did them in one take so they are not time consuming to create.  I ended up making 1 for geometry, and 2 for algebra.

Oh yeah, and I am certainly not going to post them all to this blog.

## Teaching Mixture Problems With The Mixture Picture

I just want to throw my hat into the mix and say that I also have found Marlo Warburton’s “Mixture Picture” to be an extremely effective way of teaching mixture problems.  I mean you get to do a demonstration in an algebra class!  Just that alone makes it awesome, not to mention students like it and find it helpful.  So what is it? (You haven’t seen the video?  You are soo uncool)  The “Mixture Picture” is a graphical organizer that helps students make sense of mixture problems.  The above link directs you to the Teaching Channel that has a video of her giving the lesson, as well as handouts.

I have never had much success with mixture problems, so I was happy to try anything different.  I could not have been happier with the results – the entire class was engaged.  After the first example, a majority of the class was up and running on it.  I am not going into the details of it because it is all in the video, which I followed very closely.  I’ll just move into some advice I have gained from the experience.

1.  If you are going to use the worksheets from the Teaching Channel, then I would start with the worksheet “Homework Sheet for Day 1 of Mixture Problems” because problem #2 of the worksheet “8th Grade Mixture Problems” is too different from problem #1.

2.  Don’t give your students anything in Comic Sans – so retype the worksheet “Homework Sheet for Day 1 of Mixture Problems” with a different font.

3.  Do the demonstration.  I brought in some red food coloring and continued to go back to that demonstration throughout the class.  Check the video for how to do the demonstration.

4.  My students quickly grasped how to do it when there were three percentages given – but when only two percentages are given, the students initially struggle.  That’s why I brough the container of food coloring to class with me.  Because food coloring is a 100% food coloring!  That helped them know when to use 100%.

5.  The Seesaw example that Marlo does on the whiteboard is critical to show the students.   I would continue to go back to it every time the students were working on a mixture problem.

The Goods

All the handouts are on the Teaching Channel website.  But remember the Mixture Picture is a method – not a worksheet, so you can just use the mixture problems in your textbook.

## 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.

## Who Am I – Quadratics

Here’s another ‘Who Am I’ style worksheet.  I posted a few others a while back, which you can find here.  Some of the clues are intentionally general, and thus will have multiple answers.  The students must list all possible answers.  I used this worksheet the day after playing Quadratic Taboo.

The Goods

## Parabola Review Worksheet

I created the following worksheet to help students review what they learned about identifying the different characteristics of a parabola.

After printing it out I decided that I wanted to make it an error analysis exercise instead, so I filled it out myself and made one or two mistakes for each parabola.   I had students put check marks by the correct answers, circle and fix the wrong answers.  Here’s that worksheet:

The Goods:

ParabolasCharacteristics

ParabolaCharacteristicsError

## Investigator Training

The Description:

The goal here was to use Dan Meyer’s “Bone Collector” 3Act problem, as the motivation for a series of lessons on scaling.

The basic premise is as follows:  I show the Bone Collector clip first (see the link above for the clip), tell them we need to figure out the shoe size of the killer because we need to make sure that the killer is not in the room.   Then I concede that I realize they are not trained investigators.  Thus I tell them that over the next couple days we will be doing some investigator training, to get them ready to take on this case.   I help a lot during the first two cases, but I provide little help during the Bone Collector case – and the good news is that they didn’t need much help on it after the investigator training.

CASE 1 “The Drug House”

For their first case, I used a google maps images (see Keynote or PowerPoint file below) of a huge house that I was calling a “known drug” house (It’s actually Michael Jordan’s house).  The goal is for them to calculate the area of the very suspicious large building at the bottom right of the picture, where a lot of cars are located.  I tell them the FBI wants to perform a raid but they do not know how many agents to send, because they don’t know the size of the building.  And they are waiting for our calculations to proceed.

I handout the above picture to each student.  Then do a little strategy session where they write down how they are going to calculate the size of the building.  At that point they are given time to solve it with their pair/share partner.

The next day  I come and say that althought the FBI was happy that we correctly calculated the size of the building, unfortunately after performing the raid they learned that this was not a drug house, it was in fact Michael Jordan’s house.  And that big building is a basketball court.

CASE 2 “The Statue Thief”

I use a picture of the Surfer Memorial Statue in Santa Cruz.  Then I show a the same picture but with the statue photoshopped out.  I then tell them that a security camera picked up a very suspecious person who had visited the statue multiple times before night of the theft , and that the FBI needs us to find the height of the suspect in the picture.  This case is very similar to the Bone Collector.

(awesome statue)

(but we have a suspect)

Students get a copy of the image above.  We again do a strategy session, where I require them to write a strategy for finding the suspects height.

The next day I reveal that the suspect was captured and he is 6ft.  Most students calculate something around 6″3′, so we spend some time talking about possible sources of error.

CASE #3 The Bootprint

Here we do the actual Bone Collector problem, delievered in much the same way that is described in Dan’s blog.

– I have students work in groups of two.

– I don’t spend the entire class period on these.  I do investigator training for the first 20 minutes or so, and then move on to something else.  Thus I essentially make this investigator training week.

– I help the students with the strategy sessions for the two practice cases, and then leave it up to them for the Bone Collector problem.

– Definitely play up the investigation aspect of these cases.  I tell them how much investigator make and that they should take these cases to the polic department and interview for a job.  If a couple students complain the quality of the bootprint picture is not very good, respond with “Yeah, I’m not sure why the FBI would provide such a low quality image”.

– That is me in the picture for the “Statue Thief” problem.  That is definitely an added bonus if you can do it.  It allows me to completley deny it’s me, while also saying “Look it’s not enough to just tell the police the suspect is extremely good looking, we have to get them information about his height”.

The Results:

High level of engagement.  Take a listen to student reaction when they hear that the shoe print is a size 10.

Bone Collecter student reaction

The students were upset (yes, actually upset) because all their solutions were between size 13.5 and size 16.5 .  They all calculated a larger size because they used the bootprint, rather than the actual size of the foot inside the boot to convert to shoe size.   I ended the lesson with a great back and forth with the students about what happened with their calculations.

One of my lowest performing students asked me if her proportion she setup was correct…  it was.

Using the Bone Collector clip without the associated investigator training works too, but not as well for me.  I really enjoyed these lessons, and I felt like my two initial cases put the students in a place to be successful with the Bone Collector problem.

The Goods:

Dan Meyer – Bone Collector problem

The Drug House Handout

The Statue Thief Handout

Bone Collector Bootprint  (just pick one – my girlfriend and I messed around with the image in photoshop to get the best quality for different printers)

InvestigatorTraining   (Keynote and PowerPoint)  I created this in Keynote, and highly recommend using Keynote.

Update 1:

To see whether or not the students retained any of this, I put the following picture into the chapter test.  The question was:  How tall is the tree?

The guy in the picture was brave enough to take me on as his student teacher and I am a profoundly better teacher because of it.  His name is Walt Hays.  His height is 6ft.

Update 2: 3/23

Based on Debbie’s comment, I have fixed the typos in the Keynote and Powerpoint files and adjusted the scaling to result in an answer that is consistent with the size of the tennis court next to the basketball court building.

## Factoring Puzzle – Practice Version

The Overview:

I wrote about a factoring puzzle I found online here.  That puzzle is difficult because it has trinomials with a leading coefficients other than 1, as well as special products.  I wanted to create a puzzle that would be a simple review on factoring trinomials where the leading coefficient is always 1, or could be 1 if the GCF is factored out first.  Thus when they eventually challenge the more difficult puzzle, their questions will be focused on factoring, rather that “I don’t get what to do?”.

I did not create a scrambled version, so obviously you will need have a TA cut out the pieces and put them into envelopes.

The Goods:

FactorPuzzlePractice

FactorPuzzleChallenge

Update 1:

Thanks to a great comment from John, I have created one that does not have a border, thus allowing us to differentiate for the excelling students.  That puzzle is now included above in the original post.  The puzzle without the border is the exact same on the inside as the puzzle with the border, I will eventually make that different too when I get some time.