# Tag Archives: quadratic

## 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…

## T-Block Visual Pattern

I created this visual pattern as a followup to the I Rule! exercise from MVP.  It is intended to be more difficult than I Rule!.  When I gave this to my students, I included a linear T-Block just like MVP does for I Rule!

I asked them two questions:

1.  How many squares are in the 10th sequence

2.  How many squares are in the nth sequence

Only a couple of my students actually got to the right answer, but the effort was tremendous.  I had students coming to me during lunch and saying they had asked all their friends and they couldn’t figure it out.  Students were telling me they worked with their parents and couldn’t get it.  I had a student (who failed first semester mind you) tell me that her and her two math tutors stayed 45 minutes after their session working on it and couldn’t figure it out.  She had two pages of work.  I have a couple students who get 100% on everything they touch, and they didn’t figure it out.  So yay me!  I challenged them 🙂

Here’s the I Rule! pattern:

Check out many more visual patterns at visualpatterns.org – a site created and curated by my conference buddy Fawn Nguyen (@fawnpnguyen)

The Goods:

Here is the worksheet I used, not sure if I will include the linear T next year.

TBlockWithLinear

## 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

WhoAmI_Quadratics

## 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:

BookOfFrayerModels

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

TabooSlides