Category Archives: geometry

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.

Math Hospital Remix

I decided to remix the Math Hospital.  All the steps are the same that I outline in my original post about the activity, which can be found here.   The only difference is the handout, where I now embed the problem that we are fixing into the worksheet.  This allows students to circle and point to the things that they like, or believe are right or wrong.  I also have them fix the patient (correct the problem) right there on the worksheet.

Sell the hospital.  To have them quite down, tell them the patient is sleeping.  If correcting the problem becomes homework, say “I want to have this patient looking healthy by tomorrow”.  And so forth…

I’ve done this in groups of four, but typically it is done individually.

Congruent Triangles Worksheet

The Overview

Here are two worksheets I created for triangle congruency – one of them is focused soley on SSS, the other on SAS.  Both worksheets begin with two problems where all the information necessary is given in the diagram, then they have two problems where the students need to identify a piece of inherent information, and then two problems where they need to intrepret both inherent and given information.  Then the last three problems are a combination of those.

The Method:

I first put the worksheet into Keynote so I can setup my timers and have my board look like their worksheet.  After that, this is my general recipe.

1. I do the first problem on the board myself.
2. I put up a 1 – minute timer and have the students work on the second problem.
3. After that minute is done, I have them share with their pair share partner.
4. I pull a popsickle stick and call on one group to come to the board and work the problem.
5. I then repeat this process again – where I do problem 3, they do 4.  I do 5, they do 6.  Then I have them finish the worksheet on their own.

The Goods:

SSS

SAS

Dig a Hole to China

The Description:

Show them this website and ask them if they can figure out what it is all about:

This site shows the exact opposite side of the earth from anywhere on earth.  So if you dug a hole straight down through the center of the earth, this site shows you were you would end up.  Every student in my class had heard the old saying about “dig a hole to China”, where it is believed that if you dug a hole straight through the earth, you would end up in China.  Apparently it’s not true, you would end up in the middle of the Atlantic.  Students will definitely ask you to find where you would need to start digging if you wanted to end up in China (Argentina).

That is about all you need to pose the question “If you were to dig a hole to China, how deep would the hole be?”

I give the students the circumference of the earth.   This lesson is teaching them to find the radius from the circumference.

C = 2(pi)r

At the end of class come back to the fact that if you give them radius, they would be able to give you diameter and circumference.  If you give them circumference, they should be able to give you radius and diameter.

The Goods:

I do not give any handouts.

Bracketology

The Description

Bracketology is a review game based on the NCAA basketball tournanment.  Basically you pick problems, setup the bracket, and the goal of the game is to figure out which is the most difficult problem.   You setup the intial matches, and then students use whiteboards to vote for the most difficult problem.  Then they work the losing problem on a piece of paper.  Here’s how it works:

– Intially pick 4 problems from the first part of a chapter, and then 4 problems from the second part of a chapter.  Then rank them from #1-4 based on how difficult you think the problems are.  The #1 seed should be the problem you consider most difficult of the group, the 4th seed should be the easiest.

– Draw the bracket on the whiteboard, the highest seed should play the lowest seed, so put #1 vs #4 and #2 vs #3.

– Have students in groups of two.  Each group gets one whiteboard, and each student needs their own piece of paper.

– Pick a match and have each group use their whiteboard to vote for the problem they think is the most difficult.

– The winning problem is the one that is voted the most difficult.  Take that problem and draw it into the next round.  All the students should work on the losing problem.

– When you finally get to a champion problem, offer extra credit to any student who can take down the champion.

– I would write on the whiteboard the two basic steps that the students are doing:
1. Vote for most difficult problem.
2. Work on the losing problem.

– That above advice is key because students will get confused intially about which problem they should be working on.

– I have two whiteboards in my room.  I use on of them for the bracket, and then I work the problems on the other.

The Goods

I do not use any handouts with this game.  Students take out their own piece of paper and I write the problems all on the whiteboard.

World Cafe

The Description:

This is a math adaption of the World Cafe, which according to its website is “a powerful social technology for engaging people in coverasations that matter”.   I recommend reading their website for a complete description.   The World Cafe also has an extensive online community that can be found here.  I have authored several posts about my experiences implementing it in a math class, which can be found there.  As far as I know, I am the only person implementing this in a math class.

For the World Cafe you put desks in groups of four, and cover the desks with butcher paper, which I call the table cloth.  The butcher paper is like their scratch paper, and they should be doing all the problems on it.  Once they have finished working on the problem, they discuss with eachother about what answer is correct.  Once they have decided on a correct answer, they must write it, along with all the steps, onto their World Cafe Menu.

Each problem is one round, and at the end of each round, all students must get up and go to a different table.  They are not allowed to follow the same people table to table, they must randomly disperse.

At the beginning of each round I give them a minute or so to introduce themselves to their new group, and I make them write their group members names on their menu.

– The actual World Cafe has a table host, but I do not use a host in my classes.

– Make sure that the students write the names of each of there group members in their own writing – passing the menu around for others to sign is not allowed.

– I give the students a two minute warning by playing my harmonica.  And then I play it again when it’s time to switch seats.  Maybe you can use music or something if you don’t play an instrument.

– Students should be allowed to doodle on the butcher paper.

– When you don’t give students colored markers, they tend to doodle less and they do more math.  So I don’t they them colored markers.

– Only final draft work hits the menu, and only right answers get credit.   I tell the students that I do not want to see eraser marks on the menu, that should all be done on the butcher paper.  Telling them I only accept correct answers provides motivation for them to figure out each problem.

– I through in extra credit for my favorite menus.  I have students take them home and turn them in the next day.

The Goods:

Teach/Pair/Share

The Description:

Teach/Pair/Share is my structured version of a pair/share.  It is structured more formally that the regular pair/share in that I have to be prepared to do the Teach/Pair/Share, whereas I can just have students do a pair/share at anytime without slide preparation.  The Teach/Pair/Share fits into #reasoning because it requires the students from group A to teach those in group B.

For the Teach/Pair/Share I have make sure each student has a partner, put those rows closer together, one row is group A, the other is group B.

Intially I will have one of the groups take notes, say group A, and the instruction for group B will be to listen.  I tell group B to just listen – and I make sure they do not have a pencil in their hand, because I do not want them writing anything.  Then I have group A take notes and help me solve the problem.  Once we have the whole problem on the whiteboard, I erase it, and switch the slide.

Now it is time for group A to teach group B, and for group B to take notes on what group A is telling them.  It is critical to be circulating at this point.  Randomly choose a group and ask the student in group B how to do the problem. If they explain it correctly, thank the group A students for great teaching, and the group B student for great learning.

Now repeat the same steps with jobs reversed.  At the end I have one problem that everyone needs to do.  I typically google translate the instructions into a language no one knows, and then I act upset when the students do not initially know what to do.

Math Hospital

The Description:

Math Hospital is an activity I try to do every other chapter.  I was given to me by my old district instructional coach.  He had given me a two page handout, but I have since lost it, and I don’t have a digital copy.   Here’s how it goes:

– The day before I give the students a problem to do on an exit ticket.  Then I look through those tickets for a common mistake, and scan that students work into my slides (student names redacted).

– The Initial slide for Math Hospital is always a reminder of the theme of Math Hospital – failure is helpful and not shameful.  I took that theme from a Dan Meyer post you can find here.  This is where I remind students that getting things wrong is a great opportunity to learn.

– Each student gets one exit ticket to do their work on.

– The 1st part of Math Hospital is called “Reading” and is simply where I ask a couple students to read the problem out loud.  It’s good that the class hears how other people interpret math language.

– The 2nd part is where we talk about things we like about the problem.  Common answers are asthetic things  – equal signs lined up, etc.  I tell the students here that “you have been in math for 10 years, you should develop a taste about what you think is good or not good.  Imagine if you were painting for 10 years, you would have an opinion about what makes good art”.  I have them all write down one thing that they like.

– The 3rd part is where we talk about things that are correct.  This is where I always say “remember, in every wrong answer, there is always something right about it”.  I have them all write down one thing that was correct about the problem.

– The 4th part is where we discuss what went wrong, and what corrections need to be made.  I have them all write down one thing that was wrong about the problem.

– The last part is where we discuss key points.  “What can we take from this problem, that is going to help us when we take the test?”.  I have them all write down one key point.

– After the Math Hospital is finished, I have the students work a similar problem to what they just analyzed.  I have them do it on the back of the exit ticket.

–   Lastly I tell them that if they are still confused then they might want to consult another physician.  In this case the other physician is Salman Khan,  and I show a slide that highlights the exact videos on Khan Academy that cover the topic we were discussing.

Here is the handout that I give each student the first time we do the Math Hospital.  It is basically the same as what my instructional coach had given me, but since I did not have it digital, I recreated it.