Category Archives: #collaboration

Visual Patterns and VNPS & VRG!

I feel like I’ve been preaching the gospel of vertical non-permanent surfaces and visible random groups everywhere I go these days.  The norm is set in my room – I pose the problem, give them a couple minutes of silent thought, put them in groups, and away they go.

Below is a pattern I made up quickly one morning.  It doesn’t look exciting – but guess what?  It’s doesn’t have to be.  It was close enough to full class engagement for me, which was due to a nice combination of:

1.  They believed they could do it.

2.  Vertical non-permanent surfaces and visible random groupings.

3.  Probably some other things I can’t quite pin down yet.


I’ve settled on these as my go-to questions for visual patterns.  I know I got the sketch the 10th idea from Fawn’s blog.  I never used to have them do that but when I started requiring it I was impressed with how helpful it was for a lot of my students when they ultimately wrote the equation.

1.  Sketch the 10th

(helps them immensely when writing the equation)

(sketches aren’t exact drawings.  I tell them I should be able to have them sketch the 1,000,000th)

2. How many blocks are in the 49th?

(too big for a table!  For students struggling to write an equation, having them sketch the 49th usually gets them to get it)

3. How many blocks are in the nth?

(I start the year asking it this way:  “Write an equation that relates the step number to the number of blocks in that step.  (another way to ask this question is:  How many blocks are in the nth step?)”

I would literally have that parenthesis in each problem, until I finally got to drop it.)

4. What is the largest step I could build with 1000 blocks?

The first extension.  My true goal here is the equation in #3.

5. How much of the sequence could I build with 1000 blocks?

 A second extension.  It’s quadratic and I haven’t directly covered quadratics, so it will challenge those kids.  We have talked about Gauss addition so it is not completely out of their range.

On the whiteboards below you will see graphs because in this particular case I also asked them to graph the number of blocks per step, and the total number of blocks needed to build the entire sequence per step. I wanted them to have to graph something non-linear.  I think it helps further highlight what makes things linear when they work with things that aren’t.

They don’t go directly to the whiteboards.  I first give them about 5 minutes to develop their own thoughts in quiet.  Then I group them and they do their thing.

After class I always look at every whiteboard and judge how much of the conclusions are in their writing vs my writing.  I’m not sure what I gain from that but it is a research point for me right now.  There is a little bit of my writing on boards 7 and 5, but they are supplementary thoughts and not the main thinking that I wanted to the students to do.  Here are some of the whiteboards after the activity:





Lastly, after it was finished I had them go back to that paper with their initial thoughts and complete the problem on paper. I give them graph paper and rulers and have them make nice graphs to turn into me.  In some sense, one could think of the paper as the assignment as the whiteboard as a giant scaffolding.  But in another sense the whiteboards could be the assignment, and the paper is something that goes in the notes.  Or in another sense…

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.


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:



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: 



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.


The Advice

– 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:





Taboo – Quadratic Functions

The Overview

Improve student literacy by focusing in on the math terms surrounding quadratic functions, and then play Taboo using those terms.


The Description

Warning:  Your students will have a lot of fun with this.

Taboo is a game where you try to get your team members to say the word on your card, but there are a list of restricted words that you cannot use in your descriptions.

I read Fawn Nygun’s Taboo activity and I wanted to do it with my class.  I love how she implemented it by having her students create the cards.  But I decided to control the words in Taboo by creating the cards myself.  This allowed me to scaffold it by first focusing on improving student literacy on the words that I had put into the game.

To scaffold the words that were going into Taboo I decided to use Frayer Models.  I created the packet “My book of Frayer Models” and we did two each day for a week.  It was a warmup activity that they did when they first walked into class, probably took 20 to 30 minutes each day.  Below is an example of one of the pages of a students Frayer Model book.  I would give students the page number where the word could be found in their textbook, and I had them do the model themselves while I did the routines of checking off homework and taking role.


After I was done checking homework, taking role, I would randomly call on students and get my Frayer Model completed on the whiteboard.  Lastly for each Frayer Model, I would put the word on the whiteboard and ask students for key words that describe it.   This portion of the lesson acted as my substitute for when Fawn’s students wrote out their own taboo cards.  We were essentially writing out a Taboo card as a class, and it allowed me to see what words the students deemed important.

After we finished their book of Frayer Models – It was time for Taboo!

The taboo cards focus on quadratic functions.  I didn’t make them all related to quadratic functions in order to give students the illusion that the game was covering the entire book.  The restricted words were choosen to leave the door open for good mathematical descriptions and not make the game too difficult.  Thus for the word “parabola” I didn’t include “quadratic” as a restricted word.    For me, the restricted words were really meant to try and take away the cheap clues, rather than the good mathematical clues – like for instance with the card “Domain” I restricted “Range” but I did not restrict “x” or “value”.

The rules for Taboo were basically the same as Fawn’s, but here they are:

  1. Class is divided into 2 teams, Team X and Team Y.
  2. Team X goes first: two people from Team X come up to front.
  3. Skipping a word is not allowed.
  4. Team has 1 minute to get as many right as possible.
  5. No hand gestures.

The Keynote slides attached below have a description of how I explained the Taboo game to the students.

For the final round, I was describing each card and giving points to the team that could guess it first.

The Advice:

– I would let one student volunteer to come up and I would randomly select a second student to join them.  I had students who never volunteer for anything, volunteering for this.

– Ultimately if the students knew the goal of Taboo was to work vocabulary of quadratics, then they could just list off all those key words every round.  So it’s important to do the following two things in order to give the students the illusion that any term in the book is possible.

  1. Do not tell the students that they are going to use the terms from the Frayer Models to play Taboo.  Even though every term from the Frayer Models are in the game, the students don’t need to know that.  I even collected the Frayer Models to day before playing Taboo.
  2. Throw in some math terms that do not have to do with quadratics.

– Students liked to say things like “the opposite of” – so if you have a card for maximum, make sure minimum is a restricted word.

– Use the restricted words to keep students from being able to use a non-math description.

– Have your TA cutout the Taboo cards and glue them to playing cards.

The Results:

A high level of engagement.  Definitely an animated class and everyone enjoyed the activity.  Students were shouting out a lot of great vocabulary, and I felt good that the Frayer Models had given them improved math literacy.

The Goods:


QuadraticTabooCards  (There are only enough cards here for 2 or 3 one minute rounds if you have two teams)


Solve / Crumble / Toss

A colleague of mine told me about this activity, and it has been a lot of fun for the class.

The Description

The basics are that the students are in pairs and do one problem on a whiteboard.  I check all their answers.  Then they crumble that problem up and throw it across the room. When I say stop, they all stop throwing, and pick up a new problem.  They uncrumble their new problem, do it on the whiteboard, and the process starts over again.

Each problem has a number, and it’s important that each group puts the number of the problem on the whiteboard, so I can know which problem they did when they hold up their whiteboards.  I have the answer key in front of me so I can quickly check if they are right or wrong.

I generally use about 8 different problems.  There is a chance that students will pick up a problem they have already done, so if that happens, I just tell them to pick up a new one.  At the end of the activity I like to give them a worksheet that has all of the problems from the activity on it.

I use colored paper to make sure that only the problems are getting thrown.  I use two colors, and make one color for easier problems, and the other color for more challenging problems.

The Advice

– I let the student throw paper back and forth, which gets hectic, but they love it.  If you want a more controlled scenario, only allow them one throw.

– Make it clear – they must stop throwing exactly when you say “Stop”, and cannot throw until you say “Throw”.

– Use colored paper, and make sure no white paper is thrown.

– A full sheet of paper can be thrown to hard, so be sure to use a half sheet for each problem.  Some students may try to crumble a couple of problems together to make a larger ball – big time no no.

– I arrange the desks so that half of the class is facing the other half of the class.  Let the students know the back row is the safest place.

– The problems can be hard to read when crumbled a lot, so use a large font.

The Goods

Here is the one I did for a review on Inequalities in algebra 1.



The Update 1

– Yesterday (at the advice of a colleague) at the end of class I stood in front of the recycle bin and told the students to all throw their papers at me.  It has two great benefits:  The students love it.  It makes cleanup easier because all the paper ends up in the same general area.

– I like to handout fresh problems (meaning problems on paper that has not been crumbled) for the first round of each class because the problems get harder to read the more the paper is crumbled.  It also allows me to intentally differentiate by ensuring that high achieving students get the more difficult problems.

Straw Bridge Challenge

This year I used the Straw Bridge Challenge on the first day of school as an ice breaker, an introduction to engineering, and a way to get their minds engaged.  There are several versions of this activity around, I used the one that was given to me by an engineer at Lockheed.

The Description

Goal:  Build a bridge that can span a 12″ gap and hold a 1lb weight for 5 seconds.

Materials:  20 straws.  24 inches of tape.  That’s it.

Design Specifications:  

  1. The bridge must span a 12-inch gap between two desks.
  2. The bridge must be free standing, meaning it may not be taped to the desk
  3. The 1lb weight is a full 16oz water bottle.
  4. The bridge must support the weight for at least 5 seconds without the bottle falling over and without the assistance of humans.
  5. Only supplied materials may be used.  Nothing else.

The Advice

My first class struggled the most with it because I had no examples to show.  I was able to use my 1st classes bridges as examples for the rest of my classes, and the bridges got progressively better as the day went on.  You may want to have a couple examples available for the students to look at.  Although expect the a lot of the groups to try to copy the examples, rather than create something new.

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 Advice:

– 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:

World Cafe Menu


These are a listing of hastags that I use to catagorize my lessons plans.  Each catagory represents a different style lesson plan.  My instructional goal is typically to make sure that I use each hashtag at least once a month.  The goal of this blog is to share all the lesson plans that I use under each hashtag.

My detailed lesson plans are my Keynote slides.  But along with those, I make a quick, calendar-style overview to me a general idea of what I am doing.  It’s on this calender where I place the hashtags at the bottom of each day.  This allows me  to quickly look back at what I have been doing, and know whether of not I am differentiating.  For example, here is two weeks worth of my lesson plans in geometry.  Notice that I can quickly see whether or not I have differentiated my instruction, without having to analyze each specific lesson plan.  The hashtags allow me to get a quick sense of what I have been doing, and what I have not been doing.


*Notes –

-The term “perplexity” is being used as described by Dan Meyer here