Using this as a warm up after our first day of curve sketching. Feel free to use or offer feedback, if you have any!

## Monday, November 20, 2017

## Wednesday, November 15, 2017

### Find My Mistake Activity- CPCTC

A CPCTC activity where each proof has something wrong and students need to find and correct it! I usually have students work in teams at stations around the room and record what they find wrong with each. Often, I'll put in one "correct" proof so they have to find the one that has no mistakes, but I decided not to on this one. Since I'm using this for my Geometry with Lab class, I wanted to give them a chance to practice proof analysis without the extra confusion. I'll add in that layer as we move on into more sophisticated proofs.

Side Note: I don't let my kids say CPCTC until like February. By that time, some tutor or another has told them my well-kept secret and they're begging to use it. Until they can perfectly explain to me what it means, they don't touch it. You'll see no mention of it in these proofs! We instead talk about the fact that is triangles are congruent, the corresponding sides or corresponding angles.

### Mean Value Theorem Free Response Critique

Every year the justification of Mean Value Theorem is something we spend a lot of time finessing (a new favorite word of the senior class here...any other schools seeing this?) over the course of a year in AP Calculus. The students understand the concept, but struggle with accurately justifying the situation. We started MVT last class and as a warm up today I did this activity with them.

I gave each set of partners about 5 minutes to complete the front page and then we discussed- what are the "giveaways" that you should be thinking about MVT? What are the conditions that need to apply? How would YOU answer this?

Then, I had them flip over to the back and do a critique of 3 arguments with their partner. Each one could some tweaking, although one did receive full credit on the AP Exam.

The third section I left blank intentionally, so I could move around the room and see what students were putting on the front side of the page. This way they could critique their own answers in light of the responses they saw. Here's what I had them write in based on what they were writing with their partners:

I gave each set of partners about 5 minutes to complete the front page and then we discussed- what are the "giveaways" that you should be thinking about MVT? What are the conditions that need to apply? How would YOU answer this?

Then, I had them flip over to the back and do a critique of 3 arguments with their partner. Each one could some tweaking, although one did receive full credit on the AP Exam.

The third section I left blank intentionally, so I could move around the room and see what students were putting on the front side of the page. This way they could critique their own answers in light of the responses they saw. Here's what I had them write in based on what they were writing with their partners:

We got to discuss the importance of using the same notation for the function in the problem (using g, not f) and the importance of the justification part.

Here's the activity!

We will be building on this next class as we spend an entire day trying to differentiate between when to use which existence theorem and looking at some more interesting AP style questions. Feel free to send any suggestions or other favorite MVT activities my way!

## Sunday, November 12, 2017

### Basic Triangle Congruence Proof Tools

I'll be honest- I wasn't quite sure how the start of triangle proofs would go with my Geo with Lab students this year. Not because they aren't capable, but because they were so scared! With students who already have some math anxiety, the anticipation of starting a famously formidable topic was hanging ominously over the classroom our very first day. They had heard things from their older sibling and friends and judged proofs before they ever even gave them a chance. So far, so good, though. No tears. A few "why did everyone make such a big deal of this?" comments. I count all of those in the W column.

I've been scaffolding proofs slowly, a little more each day. We've been using this super basic graphic organizer to plan before writing anything, making a constant analogy to how your English teacher asks you to outline a paper before you write the final draft. Knowing where your headed before you ever start makes the destination easier to get to, for sure. I printed about 8 of these to a page and have them in sheet protectors in my room so kids can write on them with dry erase markers with no commitment as they plan. I also have a bunch of extras that they can pick up for homework or use on quizzes/tests if it helps them.

Here's how it looked in action on our first day:

Here's a link if you're interested in using or adapting:

I also designed this really basic sorting activity for triangle congruence. I know there are a ton of these out there already, but I wanted something targeted for my type of kiddos, who need to build some confidence and hadn't been exposed to everything yet. I didn't even use this with my standard level class because they were ready for more open-ended activities more quickly. There are 3 proofs and all the statements and reasons scrambled for each. My students at this point hadn't seen HL or CPCTC yet, so these are really just getting them to engage with the very first steps of proof. It went well with my kiddos and made them feel some success, which is really half the battle in a lab class.

Steal away if this would be helpful to you! And as always, feel free to offer suggestions if you see room for improvement! Happy proving!

I've been scaffolding proofs slowly, a little more each day. We've been using this super basic graphic organizer to plan before writing anything, making a constant analogy to how your English teacher asks you to outline a paper before you write the final draft. Knowing where your headed before you ever start makes the destination easier to get to, for sure. I printed about 8 of these to a page and have them in sheet protectors in my room so kids can write on them with dry erase markers with no commitment as they plan. I also have a bunch of extras that they can pick up for homework or use on quizzes/tests if it helps them.

Here's how it looked in action on our first day:

Here's a link if you're interested in using or adapting:

I also designed this really basic sorting activity for triangle congruence. I know there are a ton of these out there already, but I wanted something targeted for my type of kiddos, who need to build some confidence and hadn't been exposed to everything yet. I didn't even use this with my standard level class because they were ready for more open-ended activities more quickly. There are 3 proofs and all the statements and reasons scrambled for each. My students at this point hadn't seen HL or CPCTC yet, so these are really just getting them to engage with the very first steps of proof. It went well with my kiddos and made them feel some success, which is really half the battle in a lab class.

Steal away if this would be helpful to you! And as always, feel free to offer suggestions if you see room for improvement! Happy proving!

## Sunday, October 29, 2017

### WODB- Differentiation Techniques

We just finished implicit differentiation last class and I wanted to get my students thinking about when to use which differentiation technique as we come to the close of this unit. I made this quick WODB to have students analyze differences among structures. This isn't as true to WODB form as I'd like, but it will still get them talking and thinking.

Comment suggestions if you have any!

A: Only one that uses implicit differentiation, only one where point is given (not just x coordinate)

B- Only one asking for general derivative, not derivative at a point

C- Only one that requires product rule, only one not in terms of y (in function notation with g(x)), only one with trig function

D- Only one that does not equal 1/2 (equals -1/2), only one from a table, only one that requires quotient rule

## Monday, October 9, 2017

### Limit Definition of the Derivative- Multiple Representation Reference Sheet

I pinned this picture years ago when I started teaching calculus and it's stuck with me every year. It's so simple and clean, but shows exactly where we came from and where we're going. Math is so elegant sometimes *sighhhhhhh*.

I really want my students this year to make concrete connections between representations as often as possible. The limit definition of the derivative is such a foundational and, at its core,

I'm giving this as a warm up in class tomorrow so I know I'll be tweaking, but if you see anything you think should be tweaked leave a comment!

I really want my students this year to make concrete connections between representations as often as possible. The limit definition of the derivative is such a foundational and, at its core,

*simple*concept.**It's slope. We know slope.****I made this reference sheet for my kids to get them talking, thinking, and connecting between representations of the derivative. I have them start with their Algebra I definition of slope, then progress through notational changes to derive the formula for slope of the tangent line. I've included the general formula on the front and the definition at a point on the back.**

I'm giving this as a warm up in class tomorrow so I know I'll be tweaking, but if you see anything you think should be tweaked leave a comment!

Limit Definition of Derivative- Multiple Representation Reference

UPDATE: Here is my filled in key from class! I really liked this and will incorporate it again next year for sure!

Limit Definition of Derivatives KEY

UPDATE: Here is my filled in key from class! I really liked this and will incorporate it again next year for sure!

Limit Definition of Derivatives KEY

## Wednesday, October 4, 2017

### Intermediate Value Theorem Justifications Gallery Walk

One of my favorite parts of AP Calculus is seeing my students' ability to make mathematical arguments develop. This is a long and drawn out process that takes the length of the course to complete. One thing that I found really useful last year was having students critique others' arguments.

To get students analyzing arguments for IVT, I used this gallery walk and a whole lot of post its.

To get students analyzing arguments for IVT, I used this gallery walk and a whole lot of post its.

Students were asked to critique arguments around the room, offering feedback and identifying one they thought made the best argument. They started to give specific feedback on how things could be improved and identify which was really "true dat."

We will do more like this throughout the year, but it's still one of my favorite ways to get into justifying!

## Wednesday, September 27, 2017

### Intro to Auxiliary Lines Warm Up & Activity

As we wrap up our first geometry unit this week, one thing we begin to discuss are auxiliary lines. My students already have so much background knowledge on parallel lines cut by a transversal from their middle school days (and our first few days of the year), so I wanted a short task to get them connecting what they've done before with where we are headed next.

I designed this task as a way to get students thinking independently about how auxiliary lines might help us. The above diagram was given to them, along with a bunch of questions about angle pairs and measures. I had them work on this individually after they finished a quiz, then find a high five partner around the room with whom they could discuss their answers. For many this was a "duh" kind of activity. It transitioned well into more complicated diagrams, giving us a foundation to which we could refer.

I was inspired by this one from Math=Love Two Truths and a Lie Activity Template post, in which she had students create their own version of Two Truths and a Lie on a particular topic. This brief activity had students decide which statement was a lie and then explain why. They worked in partners and we debriefed as a class. In my more talkative classes it sparked a lot of debate. In my less talkative it involved a LOT of creeping on students' papers and calling on the right kids to share their answers (which some did not appreciate, especially on a 90 degree day during first block). Overall, though, I liked it and would the format again for other topics!

Nothing groundbreaking but if anyone can use it, please steal!

__Auxiliary Lines Warm Up__I designed this task as a way to get students thinking independently about how auxiliary lines might help us. The above diagram was given to them, along with a bunch of questions about angle pairs and measures. I had them work on this individually after they finished a quiz, then find a high five partner around the room with whom they could discuss their answers. For many this was a "duh" kind of activity. It transitioned well into more complicated diagrams, giving us a foundation to which we could refer.

Here's the actual Word file:

__Two Truths and a Lie__I was inspired by this one from Math=Love Two Truths and a Lie Activity Template post, in which she had students create their own version of Two Truths and a Lie on a particular topic. This brief activity had students decide which statement was a lie and then explain why. They worked in partners and we debriefed as a class. In my more talkative classes it sparked a lot of debate. In my less talkative it involved a LOT of creeping on students' papers and calling on the right kids to share their answers (which some did not appreciate, especially on a 90 degree day during first block). Overall, though, I liked it and would the format again for other topics!

Again, the Word file:

Nothing groundbreaking but if anyone can use it, please steal!

## Monday, September 11, 2017

### Storyboarding to Introduce Limits

I had the rare opportunity this year to start from scratch with my AP Calc students when introducing limits. Due to adjustment to anew curriculum, our Pre-Calc PLC just didn't get there last year so we are doing more thorough coverage in class than I've done since my Pre-Calc teaching days. I wanted to try something new this year to get my kids thinking about the concept of a limit.

I was planning to put this slide on the board:

I'd then asked for 4 volunteers, 2 to be a part of Scene #1 and 2 to be a part of Scene #3. Scene #2 was a mystery that would come back later. I'd give each group a set of a secret directions only they got to see and about 30 seconds to plan, then had to pose to represent their "scene" for the class.

**:**

__Scene #1__
Two friends are having a frisbee toss. Friend #1 is ready to toss frisbee to friend #2, who is wearing sunglasses.

**:**

__Scene #3__
Friend #2 is holding broken sunglasses, having clearly gotten hit in the face with a frisbee. Friend #1 is reacting to having just hit his/her friend.

The class has to study the scenes and make a prediction as to what Scene #2 would look like. Most would go for the obvious choice. A few would go for something crazy (a bird flew in his eye, he got punched in the face, etc), which is great. We start to discuss what it looks like should have happened in that scenario, given the information we were given. We also discuss the fact that this predicted scenario doesn't necessarily have to be what

*actually*happened. The kids grasp on to this pretty easily and it becomes an easy framework through which we can view a limit, especially a limit where the defined value of the function and the limit are not equal. And it's a goofy, fun way to get seniors out of their seat!
But, of course, I forgot we had a senior assembly this morning and I would lose 45 minutes of my 2nd period.....teacher problems for sure. It remains hypothetical, but I have a lot of hope for it. Sharing if it can be a fun and goofy thinking activity for anyone else and storing it away for a rainy day for myself!

## Saturday, September 9, 2017

### The First Week: Building a Triad of Responsibility

First Week 2015 |

First Week 2009 |

NYC Math Lab Triad of Responsibility |

This week was, by far, my favorite first week I've had in my 7 years. I loved all of my classes, felt like I got to know more than usual about my kids, and it's been the most perfect September weather here in Upstate NY. I tried a bunch of new things and brought out some old favorites. I celebrated with coworkers and went to bed by 8:30 pm on Friday.

The biggest difference maker for me this year was the marriage of 2 different activities I learned about this summer. First, I had my classes participate in Sara Van Der Werf's 1-100 Task as one of our first day activities. I decided to fuse this with one of my experiences from NYC Math Lab this summer. In Math Lab, we used the Triad of Responsibility to help set norms for the students. I loved this idea and thought it was a natural fit for the first day.

Before we started the activity, I had my students individually brainstorm their responsibilities to themselves as students. It was amazing to see the difference between answers in a Geometry with Lab class (1.5 times the class minutes of a typical Geometry class) and an AP Calculus class.

Side Note: The Calc ones almost made me sad....so grade oriented, no examination of yourself as a whole person. It would have been how I answered in high school and it's part of the reason I love doing this particular work with these kids. I hope they all begin to see that they are valuable for more than just a number.

Next, I had the students perform the 1-100 task as described in Sara's blog. Overall, we did it 3 times and discussed group norms or "Responsibilities to My Group" in reference to the activity.

Lastly, we discussed "Responsibilities to our Classroom Community" in reference to our whole group discussion. Each class had common themes, but brought many unique answers. Even if lot of math teachers aren't into them, it was a warm, fuzzy day and I ate it up.

Here are what my kids generated from our conversations:

These are nice to hang in the classroom, sure, and I've already found myself referring back to them in our first 3 days of instruction. But you cannot imagine the difference this short activity made with my students.

**I have seen the type of group work I normally don't see until November or December during the 3rd day of class.**I have seen students checking in with each other to make sure everyone in the group understands. I have seen communication from*every*student in a group. Students are taking small risks, testing the reactions of their classmates and seeing that it is okay to be wrong. And they're asking questions! I'm very interested to see how this initial sense of community carries on through the year and I feel a huge responsibility to live up to the expectations of a safe environment that I've set from the first day. Anyone have any favorite ways to keep that sense of community and safety going all year long?
Best of all, the posters got approval from a very harsh and deciphering academic who only wags her tail at her favorite first day strategies.

## Wednesday, August 30, 2017

### Basic Algebraic Limits Circuit

Given our high number of snow days last year and changes in curriculum, our Pre-calc classes didn't get as far into the Limits unit as they have gotten in the past. With that in mind, our PLC has tried to put some extra umph into our limits unit to cover not only the advanced applications, but also the basics. This is a practice activity for the first day of algebraic limits and covers evaluating by algebraic simplification with factoring, rationalizing, and trig identities. This just requires students' basic knowledge of trig identities- none of the special trig limits needs need to be memorized for this!

This would work for the end of the year with Pre-Calc too! Let me know if you see anything that needs fixing! (And don't mind my name line....I always put some pun or saying there and I've been watching too much Game of Thrones sooooo here we are).

## Monday, August 21, 2017

### NYS Common Core Geometry Standards and Assessment

Happy Eclipse Day!

As the new school year inches closer and closer, my thoughts are turning back to my classroom. After having our first PLC meeting of the year this morning, I'm at least being productive today!

Wanted to share a resource for any other NYS Geometry teachers who might be interested. I spent a lot (....like a lot...) of time this summer going through every released Common Core Geo Regents and sorting the questions by standard (side note....I am sure there was an easier way to do this as the Regents already has an alignment document and would love to be enlightened if anyone has ideas!). I recorded next to each standard how it has historically been assessed on the Regents and 18 pages later, we have this. These are sorted according to our pacing and unit layout, but can easily be adapted to whatever your school does.

As the new school year inches closer and closer, my thoughts are turning back to my classroom. After having our first PLC meeting of the year this morning, I'm at least being productive today!

Wanted to share a resource for any other NYS Geometry teachers who might be interested. I spent a lot (....like a lot...) of time this summer going through every released Common Core Geo Regents and sorting the questions by standard (side note....I am sure there was an easier way to do this as the Regents already has an alignment document and would love to be enlightened if anyone has ideas!). I recorded next to each standard how it has historically been assessed on the Regents and 18 pages later, we have this. These are sorted according to our pacing and unit layout, but can easily be adapted to whatever your school does.

Feel free to send me ideas if there are things you would add! I made this to be used, so please steal, adapt, and keep sharing more ideas!

## Tuesday, August 8, 2017

### WOBD Limits #3

I feel like this needs a tweak for some reason. Letter D seems a little...forced?....to me. Anyone have any feedback that might help? I will update if anyone has any great ideas!

A- Taking limit at a real number x value(not negative infinity), limit is one sided, limit is taken at an infinite discontinuity

B- Function is continuous, does not have an infinite discontinuity

C- Limit exists

D- Limit approaches positive infinity **This is the one I want to make better. Ideas?

## Friday, August 4, 2017

### WODB- Limits #2

Here's the 2nd in the Limits WODB series. I am open to ideas and feedback on any of these, so please feel free to suggest improvements!

A- Can be evaluated with direct substitution

B- Limit exists at a point where function is undefined

C- Limit does not equal

**defined**value of function, not as x approaches 2, is a graph
D- Limit does not equal 5, Limit DNE

### NYC Math Lab (Alternate Title: Elementary Teachers are Superheroes)

Real talk: one of the joys of teaching is summer....time to step back from the day to day grind and reflect on the year behind us, while looking to the year ahead. I make it my mission every summer to get outside my comfort zone for at least one major challenge. Know what's outside my comfort zone?

10 year olds.

Most of my best friends are elementary school teachers and I genuinely believe they are superheroes. I hug crying kids who didn't get into their first choice college or whose boyfriend broke up with them and I live through the day in and day out struggles with factoring, but they teach little humans

The Math Lab is the most unique professional development I've ever experienced. Each day, the teachers in attendance were able to observe instruction for a group of rising 5th graders in a "fish bowl" environment and then begin to work individually with a student as the week went on. Afternoons were spent analyzing the lesson and sharing ideas while looking ahead to what would be best for kids as the week progressed. It was a collection of people there to learn from each other- the students, the lab instructors, the participants. Everyone was working towards a common goal of students' individual conceptual understanding and sense-making and that made it feel like a true professional learning community. These weren't hypothetical kids....they were

While the content was far below the level I teach daily, I learned so much and have so many new routines I want to try in my classroom this year. The thoughtful way you must present complex ideas to young minds to help them understand is a lesson for all of us and it explained so much of why some of my students struggle to build on a shaky foundation. My biggest takeaways were:

I have learned more and more each year how much I believe that I teach students, not math. I love the rapport I have with my kids, but I have been trying to find new ways to build student confidence, voice, and engagement in my room. One of the key focuses of the math lab is building a mathematical community. Much of this community centered around the Triad of Responsibility, which had 3 key components:

As teachers, we put a lot of the responsibility for students' learning on ourselves. I think it's in our nature...we love our kids, care about their success, and are judged by the world around us by a test score. I

Before the students walked in the first day, we were specifically asked to not interact with the students on the first day. Observing in a "fish bowl" environment means you can't interrupt...you're a fly on the wall. I challenged myself throughout the week to really

10 year olds.

Most of my best friends are elementary school teachers and I genuinely believe they are superheroes. I hug crying kids who didn't get into their first choice college or whose boyfriend broke up with them and I live through the day in and day out struggles with factoring, but they teach little humans

*how to read*....how to*share*....how to exist in regular society. They work with the same group of kids all day (no bell to save the day when little Johnny is having a rough one and you're ready for him to go to history now kthanksbye) and they have to be masters of every subject. They are magicians of classroom management and engagement. They still clean up bathroom accidents (and they do it with a smile). Seriously....superheroes. I've always known I have a lot to learn from them and NYC Math Lab was an amazing opportunity to do so.The Math Lab is the most unique professional development I've ever experienced. Each day, the teachers in attendance were able to observe instruction for a group of rising 5th graders in a "fish bowl" environment and then begin to work individually with a student as the week went on. Afternoons were spent analyzing the lesson and sharing ideas while looking ahead to what would be best for kids as the week progressed. It was a collection of people there to learn from each other- the students, the lab instructors, the participants. Everyone was working towards a common goal of students' individual conceptual understanding and sense-making and that made it feel like a true professional learning community. These weren't hypothetical kids....they were

*our*kids. They had funny shirts and favorite books and bad days and amazing successes.While the content was far below the level I teach daily, I learned so much and have so many new routines I want to try in my classroom this year. The thoughtful way you must present complex ideas to young minds to help them understand is a lesson for all of us and it explained so much of why some of my students struggle to build on a shaky foundation. My biggest takeaways were:

**A Math Community is Built Intentionally**I have learned more and more each year how much I believe that I teach students, not math. I love the rapport I have with my kids, but I have been trying to find new ways to build student confidence, voice, and engagement in my room. One of the key focuses of the math lab is building a mathematical community. Much of this community centered around the Triad of Responsibility, which had 3 key components:

- Responsibility to Self
- Responsibility to Partner
- Responsibility to Community

This frame of reference for students to participate in the community gave all students power- not just those who understood the fastest, but also those who needed to most intervention. Praise was never given for being right; it was given for being an active participant in the community.

One of my favorite moments came when a student, who was much younger than others in the room, felt pushed beyond what he was ready to think about that morning. I saw him getting teary as he spoke to the other instructor and I asked if he wanted to take a break in the hallway. Once we got outside, he told me how he felt overwhelmed and we talked about how proud I was of his perseverance and hard work. Just then, another instructor walked over behind me and pointed how what a huge contributor he'd be to the math community's discussions and that the community needed

*him*and needed*his*ideas. He agreed to head back in and within 15 minutes was up at the board explaining his idea to the group. His exit slip that day explained how he had loved "being brave" and would be even braver tomorrow. He felt important, included, and valuable and he saw growth because of that throughout the week.

**It is the students job to make sense for themselves**As teachers, we put a lot of the responsibility for students' learning on ourselves. I think it's in our nature...we love our kids, care about their success, and are judged by the world around us by a test score. I

*know*students need to understand conceptually to have a truly sound foundation on which they can build their knowledge and I try to achieve this in my planning, but so often in the craziness of the school year I wind up thinking "What else can I do for them?" instead of "How else can I give them an opportunity to make sense of this?" Too often it comes down to time. But I'm realizing the further I get into my career, the more I need to slow down and dedicate time to that sense-making for THEM. I can't make sense of it for them, I can only create favorable conditions for their success. What we spend time doing in class is a good indication to our kids of what we value, so I am working on learning to slow down and show kids that I truly value their understanding.
Students were encouraged to talk

*to each other*in a very methodical way. Instructors never said anything a student could say, often just reframing or encouraging points and debates among students. If it was clear a student has a question, the instructor would instruct the student to ask "What do you mean by that?" or "Could you explain ____ more?" Since it was up to the student to understand, it was up to the student to ask. They were learning responsibility for their own level of understanding. This is cliff notes from another great resource that we discussed, which is high on my reading list now.**Sometimes the Best Thing You Can Say is Nothing**Before the students walked in the first day, we were specifically asked to not interact with the students on the first day. Observing in a "fish bowl" environment means you can't interrupt...you're a fly on the wall. I challenged myself throughout the week to really

*listen*to what the students were saying, something I know I don't always take the one on one time necessary to do well. It's*hard*to listen to students talk on and on at you about a misconception, but we worked the whole week from a place of "You know SOMETHING. Let's build on that." Often this meant inching backwards in the progression of understanding until you found something that you and the student could both meaningfully agree upon and using that as a building block for your conversation. I don't think in the week I was there we came to the right answer of how to implement this given the time constraints you have when covering a whole curriculum in a classroom of 25 kids and 1 teacher, especially given the confines a state test places upon the teacher. However, it made me deeply reflect on how much I assume when I talk to my students daily. They may say something that isn't quite right, but it sounds close and I let it go for the sake of time.....building a misconception that we might have been able to nip in the bud then and there. Below is the document we were given on "Nudges" and how to consult meaningfully with students one on one while not giving them too much (with some of my notes added for extra seasoning).
Since this wasn't my curriculum, these weren't students in classroom, and there wasn't the pressure of a test, I was truly able to treat this experience as a "lab"....a scenario where I could experiment with my own practice and analyze the impact on a student's understanding. I saw a difference.

I am taking so much from the experience into my planning for the upcoming school year and I am so grateful to have had the opportunity to reflect, observe, and learn with these other teachers and students. Elementary teaching is, much like all teaching, both an art and a science and there is so much to be learned from seeing where my kids start before they ever step foot in my room. My gaze has shifted and I know I'll be doing more elementary PD as the years progress. So to all the participants from that high school teacher from upstate that seems a little out of place in the intense 3rd/4th/5th grade conversation- thank you. Being out of place is my favorite way to grow.

## Thursday, August 3, 2017

### WODB- Limits #1

Taking July off from blogging has been extremely restorative after a long school year and I'm ready to get back in action! I'm starting to create a series of WOBDs for warm ups in AP Calculus and am looking first at my limits unit. This one is just a start, but it's getting my blog moving back in a productive direction as August gets underway! MTBOSBlaugust was pretty powerful for me, so while I may not post daily, I'm trying to get back on the wagon this summer!

I want my kids thinking about both continuity and limits in this one, so I've tried to vary the reason I see things "don't belong." These are just my thoughts, but we know the kids will always find more:

A- Continuous

B- Removable Discontinuity

C- Limit Does Not Exist at x=1

D- Does Not Have Y Intercept of 2 OR Limit DNE at x=0

More to come, but wanted to get this blog train back on track!

## Saturday, June 3, 2017

### Integration by Parts Circuit

Let's face it....it's hard to keep kiddos engaged after the AP exam. Especially when they already took their final, know they got a "5" on it, and are starting to hit up the graduation party circuit. Luckily, I have great kids who are buying in to the whole "If I learn this now it might make my first week of college a little less stressful." (Huge shoutout to my former student rocking his engineering major at NC State whose email from the beginning of this year I've been able to show them!)

After learning Integration by Parts, I wanted to give the kids something self checking that they could work on with peers for practice, so I created this quick little circuit. I ended the lesson by having one student put a question on the board where tabular was appropriate and one student put a question where it wasn't and we talked more about why they made the decision they did.

Feel free to use as is or modify! I got all the problems from this Kuta worksheet. It took the kids about 15-20 minutes to complete.

## Wednesday, May 24, 2017

### Standards Based Review in AP Calculus- Student Feedback

After reading through 50 thoughtful and heartfelt course evaluations from my kiddos, I have pulled out the major themes from the section on standards based review. Overall, the reactions were very positive. These were their favorite parts:

- Liked opportunity to improve grade
- Pushed kids to study what they didn't know, not just what felt easy
- Getting a "4" on a topic built confidence for the exam on that topic
- Loved having to take them "cold"- gave a real picture of current understanding without stress of low score
- Gave accurate portrayal of what AP questions would be like
- Enabled you to correct your mistakes and feel okay being wrong/asking questions

As expected, it wasn't all sunshine and daisies....the kids has some (mostly) constructive feedback on things they didn't like too:

- Didn't like having to remediate to retake; just wanted to be able to retake
- Deadlines for retakes stressed some kids out since we were doing multiple per week
- Frustrating for students who understand concepts but make small algebraic or arithmetic errors and don't get the "4" they want so badly
- Wanted time in class to retake since finding time outside class can be difficult
- "Annoying" (Such helpful feedback, I know)
- Hard to find motivation with senioritis kicking in big time

Overall, I thought it was a success and will definitely be using this strategy again in the future. I was able to see a huge amount of growth in the students that took it seriously and we were able to comb through misconceptions with a fine-toothed comb. I was able to grade extremely critically since students were striving for a perfect "4" instead of settling for a 95% or 97% and not really examining what they did wrong. I whole-heartedly agree that it was a lot condensed into a small time period and the deadlines were constrictive for some students and I'll be adjusting for some of that next year.

The Google Form I used as a sign up was an absolute must - I could check it daily and was able to track student data through it, as shown here:

Overall, kids took 82 retakes on the 9 quick checks. Most kids said they wish they'd done more. And the growth mindset message seems to be getting through:

Can't believe we're so close to the end!

## Monday, May 8, 2017

## Friday, April 28, 2017

### Math Teachers at Play Blog Carnival #107

*The Math Teachers at Play (MTaP) blog carnival is a monthly collection of tips, tidbits, games, and activities for students and teachers of preschool through pre-college mathematics. We welcome entries from parents, students, teachers, homeschoolers, and just plain folks. If you like to learn new things and play around with ideas, you are sure to find something of interest.*

I'm so excited to be hosting this edition of the MTaP Blog Carnival at Give Me a Sine! If this is your first carnival, welcome! This is a great way to find some new bloggers you'll love and even share your ideas in the future! I am a high school teacher, so it has been particularly

*awesome*for me to get to explore so many new middle and elementary level blogs as I prepared to host this month.
Want more information about the MTaP Blog Carnival? Want to host it at your blog? Want to submit a favorite blog post? Click here for more info.

Since this is edition #107, let's ask the question on everyone's mind....What's so special about 107?

- 107 is a jackpot for prime number trivia!
- The 28th prime
- A Chen prime (since 107+2 is also a prime!)
- A safe prime (is of the form 2p+1 where p is also a prime)
- The smallest positive integer requiring six syllables in English (if you include the "and")
- The atomic number of bohrium
- The "911" of Argentina and Cape Town
- The number of legal acupuncture points
- 33 states and the US Virgin Islands have a highway numbered 107

And now, on to the posts!

__Elementary__
Talking to Parents about Math Explorations

While this post contained only a copy of a letter sent home to parents after a recent Math Exploration event, I loved the message that mathematics continues outside the classroom walls. So often, kids conceptions of math are influenced by their parents prior knowledge and experiences. I love the intentional outreach to parents to embrace the math of every day life!

While this post contained only a copy of a letter sent home to parents after a recent Math Exploration event, I loved the message that mathematics continues outside the classroom walls. So often, kids conceptions of math are influenced by their parents prior knowledge and experiences. I love the intentional outreach to parents to embrace the math of every day life!

Playing with symmetry in kindergarten

a) As a high school teacher, my heart basically melted here

b) I love all the different explorations the students used here to explore symmetry- from pattern blocks to mirrors to modeling with their bodies. The idea of symmetry is an integral part of my geometry and calculus classes daily, so building these intuitive understandings young is so promising!

### "Who Wants To Count My Windows?"

### This great post from Joe Schwartz on working with constraints in a 5th grade classroom. He builds off the "Ant Hotel" problem to create a fun-filled learning experience for his kiddos!

### Practice Math Facts Using Your Voice!

Cool and definitely fun to play with, this tool allows you to practice math facts with your computer just using you voice. Did my husband wonder why I was yelling numbers to myself in another room? Probably. But I can see littler ones loving this for practice! Just make sure you allow it to access your microphone.

# Origami Math Game {Tutorial}

I think making cootie catchers is a right of passage in the elementary days. Crystal Wagner shares a tutorial for turning this into a math game for your kids!

__Middle School__
My husband and I just closed on a house this week and I am so thankful to be a math teacher. I've gotten hit over the head with all the mathematics around me daily- even just buying the right amount of shelf liner for the kitchen or getting the right sized fire extinguisher. This post made me laugh out loud given all the high school math we've been doing and would be a great launching point to get kids talking about the geometry around them. You can also check out this one, on combinations, from the same blog: Three Sisters And Their PJ’s

Sort Students into Groups using Percents, Fractions and DecimalsThis fun activity will sort kids into groups AND get them thinking in the process. I can even see using this at the high school level- we all know fraction skills can always use a boost!

This activity draws on the proportional relationship that exists in linear functions and gets kids reasoning proportionally. This would provide a huge booster to the discussion of slope, too!

__High School__
Denise Gaskins shared this fun Patty Paper Trisection activity (complete with Hints and Solutions: Patty Paper Trisection). This puzzle gets the participant thinking about how to trisect an angle, using simple tools. Straight edge and compass aren't going to help you here, folks. Give this one a try!

MULTIPLE REPRESENTATIONS FOR TRIGONOMETRIC EQUATIONSSam Shah is one of my go-to's for quality and thought-provoking material in my upper level courses. This activity gets kids thinking conceptually about my all time favorite thing- the unit circle! Trig equations can be hard, but with the right conceptual understanding....BAM! You've got magic!

__Pedagogy__

To Whom it May Concern: Learn to Love the Why.This one is a keeper. Read the whole thing and listen to the voice clips. Kids can sometimes be our most honest and necessary feedback sources.

This isn't new, but it's been circulating in my mind for the past few weeks as we approach AP exam time. This is a Tuft's study that advocates practice testing as a shield from memory from stress. I've tried to integrate more practice testing into my review this year and I see a difference in what my kids are willing to take on. I don't have a fully formed opinion yet, but it definitely got me thinking.

A Brief Ode to Blank PaperSometimes we give

*too much*info to our kids. This piece by the amazing Tracy Zager (whose book is sitting on my nightstand and a must read) and advocates that by giving less, we cause kids to think more.

__General Mathiness__

These 2 posts from Mike Lawler will get your wheels turning with unsolved problems and the bridge between "pop math" and real math:

This post explores linear congruential generators and how they could be a source of mathematical play. It delves into computer programming, modular arithmetic, and more! Definitely worth an exploration!

Let me know if you had any other favorite posts of April and submit your posts for next month's carnival! Happy Math-ing!

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