It has been about 100,000 years since I have posted. Call it survival. Call it a CCSS learning curve.

I did want to mention my amazing colleague's blog, Mathy Murk, especially if you care about mathematical modeling, alternative assessment, and constructing viable arguments. Jessica Murk is a constant inspiration to me.

Mrs. Murk always says to her students, "I want you to be critical consumers of information." And if you are one of Murk's Geometry students, you are getting plenty of practice!

Go check it out!

# Ms. Z Teaches in Mathland

A High School Math Teacher/Poet/Crafter/Athlete/Mom

## Friday, April 4, 2014

## Tuesday, November 12, 2013

### A Post in Honor of the MTBoS and A Case For Dilberate Pseudo-Text

This post doesn't really fit into any of the MTBoS explorations this go round, maybe what makes my classroom uniquely mine round 2.

First off, I made the best smoothie of my green smoothie life, cures whatever ails you and gives you a mid morning nutrition blast that has become quite the habit. Pack it in a mason jar for that needed pick me up: Into a strong blender goes: 3 pitted dates, 1 pear, 1.5 carrots, rib of celery, 1/2 inch cube of ginger, two big handfuls of spinach, and .75 cup of water. Start blending on low, turn off, pack with a spoon, then blend on high until smooth. Heaven!

I have been working to pull my Advanced Algebra students out of the Algebra/Geometry For All model and into the "let's get ready for college thinking" mode. Instead of "here are three ways to know and graph quadratic functions", I let the graphs drive the equations, forcing the students to come up with silly scenarios to write model equations. They were a lot more fun to grade and a lot of pride went into them. Honestly, I am not certain yet that deeper learning happened, as the kids stressed about getting them done. I did do one CCSS tweak to the whole thing. The first round was so awful and so lacked understanding, that I made comments on sticky notes, and had the students revise them. I realize I could have had the students do this step, and I needed to get the project going in the right direction before the students would be able to comment.

I asked the students to come up with three equations to model quadratic functions, one that utilized vertex form, one that utilized factored form and one that required students to use a system of linear equations to find a, b, and c. A lot of good discussion came up around where to place the axes and what does it mean when a isn't negative, even when we know our graph should be upside down. The graphics, of course, were the best part. I thinking mapping the path of Skittles into the mouth of the a person across the room, frogs lapping up flies mid jump, and swan divers make a case for a little psuedo-text license. Just saying.

First off, I made the best smoothie of my green smoothie life, cures whatever ails you and gives you a mid morning nutrition blast that has become quite the habit. Pack it in a mason jar for that needed pick me up: Into a strong blender goes: 3 pitted dates, 1 pear, 1.5 carrots, rib of celery, 1/2 inch cube of ginger, two big handfuls of spinach, and .75 cup of water. Start blending on low, turn off, pack with a spoon, then blend on high until smooth. Heaven!

I have been working to pull my Advanced Algebra students out of the Algebra/Geometry For All model and into the "let's get ready for college thinking" mode. Instead of "here are three ways to know and graph quadratic functions", I let the graphs drive the equations, forcing the students to come up with silly scenarios to write model equations. They were a lot more fun to grade and a lot of pride went into them. Honestly, I am not certain yet that deeper learning happened, as the kids stressed about getting them done. I did do one CCSS tweak to the whole thing. The first round was so awful and so lacked understanding, that I made comments on sticky notes, and had the students revise them. I realize I could have had the students do this step, and I needed to get the project going in the right direction before the students would be able to comment.

I asked the students to come up with three equations to model quadratic functions, one that utilized vertex form, one that utilized factored form and one that required students to use a system of linear equations to find a, b, and c. A lot of good discussion came up around where to place the axes and what does it mean when a isn't negative, even when we know our graph should be upside down. The graphics, of course, were the best part. I thinking mapping the path of Skittles into the mouth of the a person across the room, frogs lapping up flies mid jump, and swan divers make a case for a little psuedo-text license. Just saying.

## Sunday, October 6, 2013

### MtBoS:What Makes My Classroom Uniquely Amy-ish

Ha! I am one of those veteran teachers that Sam Shah was referring to when he said,

Ack, I am even an emptynester

this year for the first time and don't even have a pipeline to popular culture. I doubt my students give a rip that I saw a 2 year old movie about a pharmacist obsessed with Woody Allen at the Jewish Film Festival, or Foyle's War on PBS, or what the latest Economist has to say on Freakonomics Radio.

~~But~~, AND here I am trying to share what I know and get better. That's the thing, right, 28 years and I can do better, get better, learn how new minds think and what gifts you all bring to the table.

I am not the teacher who invents fancy new dances like the Dishwasher and Gravity, I don't play the guitar, (I used to beat the crap out my football players doing pull-ups (not chin-ups) until I broke my arm last summer), AND what I do have is SPUNK. I can be 50 and still be S.P.U.N.K.Y. One of my new students commented, "you are optimistic aren't you?" Yup, yup, I am. I am so sure you can do this thing, because I did, I have and believe you me, you are better than I am because I am pretty confident you didn't have to go through what I did to get here. (and thank goodness for that...living on my own from age 14-15...not what I would wish for any teenager.) I never, ever, sit down. That's my schtick and I am sticking to it.

I do want to share with you a super fun activity that occurred in my Geometry class the other day.

I gave each group of four students a statement. (Thanks to Julie Reulbach for the inspiration). (

The students needed to write the statement as a conditional statement, decide whether or not it was true, and draw or explain how they knew what they knew.They did this on whiteboards.

We had the best conversations. Are three collinear points always coplanar? Are all right triangles congruent? Etc...And here is the twist. REVISION! Pick one, take it home, make it yours, and make it better!

Happy Fall Everyone! and Thank you for welcoming me into your MTBoS. You are the best.

*If you feel like you aren’t awesome at teaching, welcome to the club. If you feel constantly like everything else you see out there is better, welcome to the club.***I love you Sam!**Ack, I am even an emptynester

this year for the first time and don't even have a pipeline to popular culture. I doubt my students give a rip that I saw a 2 year old movie about a pharmacist obsessed with Woody Allen at the Jewish Film Festival, or Foyle's War on PBS, or what the latest Economist has to say on Freakonomics Radio.

I am not the teacher who invents fancy new dances like the Dishwasher and Gravity, I don't play the guitar, (I used to beat the crap out my football players doing pull-ups (not chin-ups) until I broke my arm last summer), AND what I do have is SPUNK. I can be 50 and still be S.P.U.N.K.Y. One of my new students commented, "you are optimistic aren't you?" Yup, yup, I am. I am so sure you can do this thing, because I did, I have and believe you me, you are better than I am because I am pretty confident you didn't have to go through what I did to get here. (and thank goodness for that...living on my own from age 14-15...not what I would wish for any teenager.) I never, ever, sit down. That's my schtick and I am sticking to it.

I do want to share with you a super fun activity that occurred in my Geometry class the other day.

I gave each group of four students a statement. (Thanks to Julie Reulbach for the inspiration). (

**I love you too, Julie!**) I always give the students some way to assign tasks like materials getter, writer, speaker, time keeper, by having them figure out little details, like who has the most pets, who lives farthest from school, who has the youngest sibling, who has the "most expensive" first name (118 for Gustavo),etc...That is something I think makes my classroom "mine."The students needed to write the statement as a conditional statement, decide whether or not it was true, and draw or explain how they knew what they knew.They did this on whiteboards.

We had the best conversations. Are three collinear points always coplanar? Are all right triangles congruent? Etc...And here is the twist. REVISION! Pick one, take it home, make it yours, and make it better!

**Rewrite the whole darn thing,**especially if you don't agree with the conclusion, and for fun, I added, write the converse, inverse, and contrapositive and determine whether or not each of those statements was true or false. If I had stuck to the "lesson schedule," I would never had the wherewithall to extend the activity into homework that has some nice chewy bits.Happy Fall Everyone! and Thank you for welcoming me into your MTBoS. You are the best.

## Saturday, September 21, 2013

### The CCSS Mindset

I just inherited two sections of Geometry. I mean, called in Tuesday, start teaching Wednesday. Yeah, so trying to figure what the kids know and don't know starting on day 10 of their 95 minute block schedules. There is so much I want to share with them, so much rich, yummy math.

Tuesday Evening I took a quick peak at the book (The previous teacher took down her website and wiped the board clean...I don't blame her...) found a few terms they should know and gave them a relatively easy worksheet on pairs of angles. The first eight problems were identification, last 14, find x.

Nothing too interesting. However, in going over the assignment in class, a CCSS click occurred. While it isn't earth shattering, the idea is that if my head wasn't in a constant state of CCSS-ness, I would have not been so clever. Already CCSS is working...on me.

The worksheet looks like this: (From Kuta Software)

I had the students mark it like this:

Then we took problems 13-22 and categorized them. The final product looked like this:

The students had to justify and critique each other's placement of the remaining problems. (Math Practices Constructing the Viable Arguments and Critiquing the Reasoning of Others).

High engagement, low prep. I like it!

Tuesday Evening I took a quick peak at the book (The previous teacher took down her website and wiped the board clean...I don't blame her...) found a few terms they should know and gave them a relatively easy worksheet on pairs of angles. The first eight problems were identification, last 14, find x.

Nothing too interesting. However, in going over the assignment in class, a CCSS click occurred. While it isn't earth shattering, the idea is that if my head wasn't in a constant state of CCSS-ness, I would have not been so clever. Already CCSS is working...on me.

The worksheet looks like this: (From Kuta Software)

I had the students mark it like this:

The students had to justify and critique each other's placement of the remaining problems. (Math Practices Constructing the Viable Arguments and Critiquing the Reasoning of Others).

High engagement, low prep. I like it!

## Sunday, September 15, 2013

### Noticing and Wonder in High School (Algebra 2)

Ack! I didn' save one image! However, don't stop reading, okay, you can if you want...

Systems of Linear Equations is a review for Algebra 2 students, and I hope, now that the students ARE Algebra 2 students, they will finally make the connection between the Algebraic solution to the system and its graph.

I started with this slide:

from the most recent Woman's Day (how I got that subscription, I will never know, it just appeared one day).

Then I gave them a graph with some (fake) linear data.

The conversation was rich in two ways, the math was great, AND the opportunity to have a conversation with teenagers about health, diet, and exercise was FANTASTIC. Lots of questions about how they lost the weight, they wanted to know how long it took them to weigh their current weights, were they doing any weight training, have they maintained their weights, what kind of help did they have. Why did Michelle lose more weight, is Brian more muscular, how tall are they?

I know the issue can be extremely sensitive and I did notice one "husky" boy shifting in his seat. I emphasized that they didn't gain the weight overnight, so they weren't going to lose it quickly if they were going to maintain healthy weights. I emphasized the portion control, exercise, and cutting empty calories like alcohol (one girl told us how her mom quit drinking and lost 30 lbs!), I did emphasize body types (I have bird bones and 150 lbs would look ridiculous on me, however my daughter has her dad's bones, and 145 looks marvelous on her).

Noticing and wondering turned procedural proficiency (Blech) into something engaging and meaningful. It turns out

Systems of Linear Equations is a review for Algebra 2 students, and I hope, now that the students ARE Algebra 2 students, they will finally make the connection between the Algebraic solution to the system and its graph.

I started with this slide:

Michelle and Brian Look Fabulous! |

Then I gave them a graph with some (fake) linear data.

The conversation was rich in two ways, the math was great, AND the opportunity to have a conversation with teenagers about health, diet, and exercise was FANTASTIC. Lots of questions about how they lost the weight, they wanted to know how long it took them to weigh their current weights, were they doing any weight training, have they maintained their weights, what kind of help did they have. Why did Michelle lose more weight, is Brian more muscular, how tall are they?

I know the issue can be extremely sensitive and I did notice one "husky" boy shifting in his seat. I emphasized that they didn't gain the weight overnight, so they weren't going to lose it quickly if they were going to maintain healthy weights. I emphasized the portion control, exercise, and cutting empty calories like alcohol (one girl told us how her mom quit drinking and lost 30 lbs!), I did emphasize body types (I have bird bones and 150 lbs would look ridiculous on me, however my daughter has her dad's bones, and 145 looks marvelous on her).

Noticing and wondering turned procedural proficiency (Blech) into something engaging and meaningful. It turns out

__Andrew Stadel tweeted about Noticing and Wondering in this Blog Post from Max at the Math Forum. I didn't see it until this morning after the fact. After reading the article, I can't wait until Monday!__## Friday, August 30, 2013

### Constructing Viable Arguments and NOT Critiquing The Reasoning of Others, Yet

I am still so catching the teachable moments. I am happy and annoyed that the CCSS chatter won't shut up in my head every minute of my teaching day. I know I can do better. I need to get the procedural stuff down too. I have to be patient.

I did get to have this moment with my Algebra 2 students:

We first did a Frayer Model for Linear Functions in our INB's. It looked like this:

Then I stopped and said, "prove to yourself, your neighbor, and me that xy =12 is not a linear function." (At the end of the day, I got looser and said, choose any one of the Non-Linears). OMG, it was so interesting! Granted this is only their 4th day of Alg 2 AND I thought they just had a year of Geometry with proofs and stuff. Proofs and Viable Arguments are clearly two completely different animals!

I loved that the students were engaged and active. I gave one person in the groups of four a whiteboard pen and spread them around the available whiteboard space (and two large whiteboards in the middle of the room). Guess what, NOT A SINGLE GROUP in one of my classes tried to show the function wasn't linear by graphing!

I commended the students on what was good, I teased them (am I allowed to that?) about their lack of plotting points and looking at the graphs of the functions (when do the students understand the relationship between x, f(x) and a graph), I loved looking at their faces and "getting" what an argument means. I also loved KNOWING that the students were seeing that this was the math that connected to the rest of their academic life.

Happy Three Day Weekend Everyone!

Any thoughts, suggestions, concerns, next steps would be greatly appreciated.

I did get to have this moment with my Algebra 2 students:

We first did a Frayer Model for Linear Functions in our INB's. It looked like this:

Then I stopped and said, "prove to yourself, your neighbor, and me that xy =12 is not a linear function." (At the end of the day, I got looser and said, choose any one of the Non-Linears). OMG, it was so interesting! Granted this is only their 4th day of Alg 2 AND I thought they just had a year of Geometry with proofs and stuff. Proofs and Viable Arguments are clearly two completely different animals!

I loved that the students were engaged and active. I gave one person in the groups of four a whiteboard pen and spread them around the available whiteboard space (and two large whiteboards in the middle of the room). Guess what, NOT A SINGLE GROUP in one of my classes tried to show the function wasn't linear by graphing!

Nice!

The word "formula" made me cringe, and they got it!

I thought their last argument went nicely with the one above.

These guys got stuck so I fed them a possible argument

I commended the students on what was good, I teased them (am I allowed to that?) about their lack of plotting points and looking at the graphs of the functions (when do the students understand the relationship between x, f(x) and a graph), I loved looking at their faces and "getting" what an argument means. I also loved KNOWING that the students were seeing that this was the math that connected to the rest of their academic life.

Happy Three Day Weekend Everyone!

Any thoughts, suggestions, concerns, next steps would be greatly appreciated.

## Wednesday, August 21, 2013

### First Day Conversation Stall...

My first day bell ringer for Algebra 2 came from Fawn Nyugen's lovely site, http://www.visualpatterns.org/:

(Her's looks WAY more professional):

I gave the students quiet time. Then opened the conversation to the entire class:

I was a bit flummoxed when no table emerged at first. It was both WONDERFUL and odd that NO ONE after the first block class (the next 2 classes) made a table. The part I liked about the conversation was this:

Ss: I notice that the perimeter grows by 6 each time.

T: So you mean after the first term you get + 6 and then the next one you +6 again?

Ss: Yeah

T: How do you say that with your big girl/big boy pants on? I mean, if we want that to happen on every nth term?

Ss: Times Six

T: So if we said 6n, what does the "n" represent

Ss: The nth day, I mean the nth position

T: But does that work?

Ss: No! you have to add two for the ends that don't get shared.

T: So which of the various answers are now reasonable to eliminate? How can we test the answers that left ?

Blah, blah.

MTBoS, please let me know if I could have done a better job with the generalization of this pattern. What parts were good? I was completely unsure of how to end this lovely conversation. Suggestions?

(Her's looks WAY more professional):

I gave the students quiet time. Then opened the conversation to the entire class:

I was a bit flummoxed when no table emerged at first. It was both WONDERFUL and odd that NO ONE after the first block class (the next 2 classes) made a table. The part I liked about the conversation was this:

Ss: I notice that the perimeter grows by 6 each time.

T: So you mean after the first term you get + 6 and then the next one you +6 again?

Ss: Yeah

T: How do you say that with your big girl/big boy pants on? I mean, if we want that to happen on every nth term?

Ss: Times Six

T: So if we said 6n, what does the "n" represent

Ss: The nth day, I mean the nth position

T: But does that work?

Ss: No! you have to add two for the ends that don't get shared.

T: So which of the various answers are now reasonable to eliminate? How can we test the answers that left ?

Blah, blah.

MTBoS, please let me know if I could have done a better job with the generalization of this pattern. What parts were good? I was completely unsure of how to end this lovely conversation. Suggestions?

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