Exterior Angle Sum Theorem

extI made this quick activity for students to discover the exterior angle sum. I just printed several quadrilaterals and pentagons, cut out the exterior angles, and put them mixed up in a Ziplock bag. I gave students 5 minutes to work with a team of 3 to somehow figure out what all the angles added to. I didn’t give them much direction beyond saying they needed to put the color edges together to discover it. Walking around the room, students kept calling me over to check their hypothesis as got really into it to be the first to figure out the theorem. It was a quick way to have students discover a simply topic rather than me just directly telling them…and it worked…two groups found it out in the 5 minutes!

Entry Cards for Review

I can’t take credit* for this idea, but it is one I am loving and want to share…it’s quick entry question cards. Here’s how they work: I made about 10-12 cards and as each student came to the door, I stopped them, showed them a card and asked them the question. They told me their answer and if they were right, they got to come in and the next student behind them got a different card. If they were wrong, I told them a hint to help them answer correctly and then after they did, they were showed a new card with another question until they got one right and could come inside (if you have a long line of students, you could send them to the end of the line). Just be sure the questions are quick enough to answer in a few seconds. Kids liked this as another way to review before the test and to quickly check for understanding, I even had kids say, “ask me another!” I’m definitely going to start doing these more often with spiraled material and also on quiz/test days like today with the material for the test. capture-1

*Credit: A teacher from my team saw another teacher do this a few years ago.

New Beginnings

It’s been a while since my last post back in, eek, February!! But, a lot has changed and kept me quite busy. On May 31st, my husband and I welcomed our sweet baby boy, Roe, into our lives. And as if that wasn’t excitement enough, the following day, I accepted a position teaching at a different high school in our district. Summer was incredible with Roe. I learned a lot about being a mom and as I continue to learn more every day, I am so grateful my husband and I had 2 and a half full months with him at home.

School started last week with teacher in-service and the students arrived this following Monday. I was overwhelmed with how welcoming the teachers at my new school were. In-service gave me the opportunity to get to know the math department and work closely with my Algebra 1 team of teachers. I am looking forward to the year with these colleagues and so as I start out the new year, I want to make some new goals for the year.

#1.Utilize the textbook with distinct plans: This year, we are piloting a program at our school using the Springboard Algebra 1 textbook with fidelity. I, and several other teachers in the district, tried using the textbook last year, but because of its challenging and seemingly daunting approach, we all ended up abandoning the textbook and reverting back to comfortable ways of teaching the content. Now, typically I am not even an activist for using math textbooks, but this book had been so aligned with our state standards and rigor, that the district found that those who did use it more often in the classroom saw higher results on our state test and better academic performance in the classroom. So, our school agreed to be a pilot school for using the textbook with fidelity. Knowing that data will be drawn from our school, and most importantly knowing that previous data has proven high student success rates with this textbook, I want to stay ahead of myself with using it. I want to be sure I have done two things in planning each lesson with this new book (I  often do these while planning in my head, but writing it down here might make me more accountable…and I think these might be my goals for our Texas Teacher Standards, so I’m pre writing them out here).

1. Prepare for student misconceptions and errors (in planning each lesson, I will mark  an “E” in the text where I predict this.)

2. Create questions which delve deeper into student understanding and inquiry.

#2. Help students be organized: To do this, our team is using interactive notebooks with our students. I usually require binders and am pretty good at having students put things in their binders for the first month or so. But, after that I start to forget and before I know it, students have exploding binders and all hopes of organization have been crushed (along with their precious notes). I think our interactive notebooks are going to be a really beneficial place to keep their notes (foldables and non foldables) and examples as well as a great way to teach students how to stay organized. I’m excited for the team to help me stay on top of this as we work together to build these with the students.

So, with these in mind, the first week is almost over. I definitely miss and want to say thank you to the faculty and students at my old school that I was at for 7 years. Although I will miss them all, I am really looking forward to the year ahead with a new group of teachers, students, and traditions. I’m grateful for those who inspired me over the years and am motivated to continue learning and growing in this new adventure.


Julia Robinson Math Festival

This weekend I hosted a Julia Robinson Math Festival at Trinity University for students from my high school and one of our feeder middle schools. I stumbled across the Julia Robinson organization from a math colleague I follow on Twitter and reached out to him to find out more. He generously shared resources with me and as I began planning, I was happily surprised at how easy the organization was to work with by giving me financial and organizational support along the way.

Two of my past Trinity professors helped me work through the details of hosting the event at Trinity and also helped sort through the math problem sets that we thought would work best. We chose the following problem sets to be set up at tables for students to move through at their own pace: Indecisive Director, Leo the Rabbit, Tilings, Space Chips, and Tower of Hanoi. The math professor I worked with invited a few other university professors and undergraduate math club students to help run the tables (it was awesome to have the chance to facilitate the morning’s events and watch the learning take place instead of myself being a table leader at only one table). I also loved having the opportunity to reconnect with my university professors through this event.

There was so much success that took place…here are some of my favorite moments…

1. As students came in, I could tell from most of their initially shy demeanor’s that they were a little unsure of what to expect from a “math festival.” However, the university professors and undergraduates passion for math quickly transpired to the students. I watched as they adamantly listened to the professors and undergrads give hints, not answers, at how to work the problems. The way the table leaders facilitated their tables enabled kids to have many “ah-ha” moments that were really fun to see.

2. Several problem sets involved unique patterns that middle/high school students are not often exposed to in the general curriculum. One professor commented to me that a lot of students were trying to find the slope between the numbers but he had to stray them away from that and help them to look for a different type of pattern…I told him we focus so much on linear and geometric sequences and that students were not used to thinking there could be another type of pattern. The exposure to problems that were so different and complex required them to think creatively and again enabled them to have some exciting “ah-ha” moments. One student stated towards the end of the event that they felt like a lot of the problems were interconnected…a really interesting comment that proved they were finding patterns within the patterns.

3. The hands on activities of the Tower of Hanoi and the Space Chips were a hit. Kids loved creating physical things and I think they didn’t even realize they were using math especially in the Space Chips problem set. I am excited to use these when we get to 3D area and volume!

4. When the time was winding down at the event and parents were arriving to pick up their students, I made a quick announcement thanking the students for coming and putting in so much hard work into the morning. Not one student got up…I had to remind them several times that their parents were there to take them home, but they all wanted to finish up the problem set they were working on!

5. We had a very diverse group of students in attendance (G/T students, pre-AP and non pre-AP students, middle school, and high school students) but every kid found success at the event by finding patterns, creating something, or solving a puzzle without the direct help of a teacher telling them what to do. One girl who often struggles in my Geometry class told me at the end of the event (without me asking) that she had fun, she’s looking forward to next year, and can’t wait to come back!

6. Finally, I didn’t see a single cell phone out the entire morning…no need to say anything else about the level of engagement! 🙂

Thank you to all the table leaders (high school and middle school teachers, university professors, and undergrad students), the two university professors I coordinated the event with, my Twitter colleague, and those who work for the Julia Robinson organization…it was a truly successful morning of learning!

House Reno and Geometry

My husband and I have been renovating our house (HGTV/DIYnetwork style, sadly without the help of Chip and Jo from Fixer Upper or Yard Crashers) and I realized it was the perfect opportunity for some real world geometry. The inside is almost completely done with a new kitchen and new flooring, so next we will move on to the outside. I put together an assignment for my students to help us calculate how much our renovations would cost using area and perimeter of polygons and presented them the idea of helping us be sure our calculations were correct as well as deciding a best option for an additional dog run area we have been designing. My kids totally bought into it the relevance of this assignment and the meaning behind it as I could tell they truly wanted to help us make our house the best it could be. After class, I even had a student tell me they were building a new house and asked if we could make a math problem out of her house plans! 


Side note: Our patio and deck plans are not actually a rhombus and a perfect parallelogram, but it made for more challenging and relevant math. Everything else was real data, decisions we are trying to make, and plans we want to do! 

Thoughts from the Semester

As the first semester winds down, there are several things I have been reflecting on in my mind. I spent one class period of semester exams organizing a drawer full of manipulatives I created this year and it feels great to be clutter-free…so, I think organizing my thoughts about this semester in a post will double that feeling. Before my mind goes to winter break, here’s what I’ve been thinking…

  1. SBG Grading: I have continued to do a lot of research on this topic as I find my right path in standards based grading and I have a lot I feel confident about but also still have a lot of growing to do in this area. 
    • Disaggregating Quizzes: The main thing I am proud of that has worked really well is disaggregating my quizzes. Each quiz I give might be on one standard or it might be on multiple. Instead of giving one grade on the multiple standard quizzes, I give a grade for each standard. This has helped students (and myself) pinpoint exactly what students are mastering and what they still need to work on. Students come in to correct and retake only that portion and are using the language of the standard when they need to retake.
    • Self-Evaluation: I also like having students reflect on how they think they did on each quiz. I made this much simpler than my original plans (1. because it took up too much space, and 2. it saved time). At the bottom of each quiz is a simple question, how well do you think you mastered the standard ____________ of of a 1, 2, 3, 3.5, 4. Then there is a space for any comments for me to read and respond to. This adds an extra piece for them to re-read the standard, self evaluate, and provides a communication tool between me and the student.
    • Two areas of growth that I need to continue to work on are disaggregating tests and possibly being more standardized with my grading. I reverted back to 0-100 because it was easier for me and easier for students, but I still have thoughts about using a 4 point scale.
  2. I want to make reviewing for the Algebra 1 STAAR engaging and worthwhile for students. Sometimes when reviewing for several days (like for semester exams), I must admit, there are days where I feel like some students work and some students just waste time. I know if I don’t do a good job of planning the days, it will not be beneficial for students. I don’t want this to happen with STAAR review next semester. I have some stations I can use, I know I want to do a test taking strategies mini-lesson, and students need to continue to see past tested problems..but, in what ways can I make this enticing to students?! So…any ideas for standardized test prep is more than welcome here…leave a comment!
  3. I want to explore the Desmos activity builder more (https://teacher.desmos.com/). I saw this parabola activity on Twitter the other day and it looked really fun! It could be a great intro to quadratics for my Algebra 1 kids…or a follow up…I need to look into it more.
  4. I had an idea the other day while I was working with students on word problems and I realized students were reading from the middle of the sentence, jumping around to find key words, and then trying to answer the problem. As warm ups next semester, I need to include more lengthy problems and focus on reading strategies. I thought about starting out by covering up random parts of the sentences like they do in their minds and asking them to solve the problem…nearly impossible! Then with that hook, we can talk about more reading strategies to solve math problems throughout the following weeks…perhaps I can collaborate with our English teacher on the team.
  5. I planned a Julia Robinson Math Festival to be held at a local university for students at our school and a feeder middle school, but unfortunately we had to cancel it because of a huge flood back in October. We are rescheduling for February, but it is still not solidified and I just hope it can work out and be something extra for students to become more interested in math.
  6. I got accepted to present two sessions at CAMT, but soon after applying, I found out I was pregnant!! 🙂 🙂 With my due date only a couple weeks before the conference, I decided it was best to turn down the opportunity to present. I hope I can make it to the conference at least for a couple sessions in between baby time to continue learning this summer.
  7. Lastly, I want to continue to help my students become nicer and more thoughtful citizens. With bullying and hate so prevalent in this world, I as their teacher, want to instill a sense of kindness in my students that goes against high school stereotypes and promotes inclusiveness and compassion for others.

If you’ve gotten all the way to the end of this post, thanks for reading and I hope you have a wonderful holiday!!  


Tiered Lesson Plan

A few weeks ago, our administrative team presented ideas on devolved writing and tiered lessons to benefit student learning in our classes. They encouraged us to try one of them out and reflect on the strategy. I decided a tiered lesson would fit really well in my Algebra 1 classes because the these students have such a varying background knowledge and the new material of parameter changes would enable students to build off of their previous knowledge and/or help students start from a baseline understanding to develop the necessary skills.

My lesson began with a pre-assessment I created on Desmos (https://www.desmos.com/calculator/pn26rqzsje) which allowed students to visually see parameter changes of a function (I love Desmos…see this post for more Desmos!) I showed students a parent quadratic function and then used the sliders to manipulate the function with horizontal and vertical changes. Then, I asked a series of questions about the effects h and k had on the function. After answering independently, students self-assessed their answers and based on their accuracy I put them into tiered groups to work on the parameter changes assignment. In the assignment they investigated the h and k effects on both linear and quadratic functions, graphed the parameter changes, and wrote sentences summarizing the effects. The higher level tier gave fewer examples and required students to infer the information more quickly. Furthermore, this tier also asked students to summarize their learning in an open response format rather than with sentence stems and a vocabulary bank that the lower level tiered group had.

Several things went well in this lesson:

  1. Students felt a sense of ownership with their group. I was worried students might feel that they were put in the lower “dumb” group and feel defeated, but my lower level group was actually the hardest working group and they really bonded together wanting to .  improve upon their knowledge.
  2. Students relied on each other more than normal instead of myself to learn the material. I think this grouping process allowed for more transparency to students and they felt a sense of purpose in why they were with other students.

Revisions I made from class period to class period which helped:

  1. In the first class I did this lesson with, I was pretty lenient on the specificity of the answers from the pre-assessment, which made more students be in a higher tiered group when they really were not prepared with the language and understanding I wanted them to have. So, in the next classes, I was more particular on if students got their answers correct with vocabulary, language, and detail. For example if a student said the k made the graph move along the y-axis. That wasn’t fully correct for several reasons. I wanted students to verbalize that the graph moves up or down depending on adding or subtracting from the function and not always on the y-axis.  When I was more specific with student’s responses and language, it made students be in a more appropriate tier where they could learn and use the higher level vocabulary of parameter changes.
  2. Finally, with the appropriate grouping, the struggling students were able to use more sentence stems and vocabulary banks to write their summaries. The upper level tiered students then had the background knowledge and were able to write more open ended responses with their more advanced language.

Mental Math Monday 

I must first dedicate this post to my mom. She first introduced me to mental math when I was in elementary school. As I tell my students, I used to have to do a series of mental math before I was allowed to eat dinner every night…I’m not sure that’s a true story, but it’s what I like to remember (and I like to tell my kids so they get a glimpse into my math loving family). So, in celebration of my mom, Monday warm ups in my class are dedicated to mental math. In fact, last year, my mom and I had a competition between my students and hers…unfortunately Skype didn’t work the day we planned for, so we did the competition separately…I think we should try again this year, what do you say, mom?! Rematch, 2016?? 

Anyways, I love doing mental math as a warm up and my students actually do, too. Ironically, when first introducing the idea to my students, there was a whole lot of whining…”Awww no calculators…no, I can’t do math in my head…but, it’s Monday.” So, after a little convincing that everything is going to be okay, my kids soon realized that they loved mental math more than they ever thought! As it creates a little friendly competition amongst each other and themselves, it also reinforces concepts like square roots and any other operations students have been studying, helps students grow their quick thinking algebraic skills, and reinforces their listening skills. 

Here’s how it works…ask students to clear off their desks…it’s all done in their heads and the less distractions the better. Tell students not to talk, not to say things like “wait, wait” or “ahh I lost it” (they will do that), because it’s all about listening and processing. Tell students when you are done, and only then, to raise their hands if they got the answer (mine tend to just blurt it out at the end which is okay sometimes, too, if you can’t control the excitement!) Call out a series of operations starting with a single number. I just make it up as I go and calculate in my head as I say it, but you can create the series if you want before and read it off. 

Example: take the number 25, add 5, divide by 3, double it, divide by 4, add 2, square it, add 3, subtract 10, divide by 2, subtract 1. 

You can get more or less complicated…throw in fractions, negatives, triple digits, ect. Today, I had my kids make up their own problems, ensuring they had operations that could be calculated in their heads and nothing ended  with something like 157 divided by 17. Then, I read a few of them out, and in some classes, several students volunteered to try calling the ones they created out to the class.

If you try it, have fun with it…kids get really into it as they race to get them all correct! 

Desmos and Functions

In Algebra, we just finished our unit on functions and a colleague of mine had been talking about Desmos, so I decided to explore it a bit and see if they had any resources on functions. I discovered Function Carnival and thought it would be a perfect mini project for applications of functions. The activity has students watch three videos simulating different carnival activities (a cannon man, bumper cars, and a Ferris wheel) and then asks students to draw the scenarios as functions. After each scenario, the students are also prompted to help find errors in a provided graph and explain how to fix it. Before creating their own scenarios, I wanted to be sure students fully understood the situations they had been practicing on Desmos. I thought it might take some students more tries than others to get their graphs correct (and it did), so I also added to the project by asking students to redraw their graphs on graph paper after they completed the Desmos portion. With their hand drawn graphs, they then had to correctly label the independent and dependent axis with names and units, and then find several key features of the graph such as domain, range, y-intercept, and extremas. That way, the concepts were reinforced and they were able to analyze correct graphs before creating their own. (Below are student examples of graphs).

cannon bumperferris

I am so happy with how this project turned out for several reasons:

  1. Every student was engaged in the Desmos activity. Giving students real world scenarios to physically see and digitally manipulate peaked students interest. The technology was easy for students to understand, but the scenarios were complex enough to capture their interest. Furthermore, students had the ability to self check their answers and when they weren’t exactly right, they wanted to go back and fix their mistakes to get the simulation to work precisely. It was tricky for some to understand why their path wasn’t matching, but I liked letting them have some time of productive struggle. They often called me over when they got their graphs perfect and wanted me to see their accuracy…I loved that!!
  2. Desmos incorporated a writing component for students to synthesize their learning. I really liked seeing how students interpreted the given scenarios and how they explained the errors that they were asked to correct. It gave students a chance to write in their own words about the mathematics of the situation. Telling students that I can also see this portion on my teacher view in Desmos perked them up to write in more complete sentences and will give me a chance to evaluate their grammar and mathematical vocabulary. Below are some examples:
    1. “The graph says that cannon man will have no suspension period in the air and that he will fall at the same speed going down without deploying his parachute. He should try adding a still period at the apex of cannons man jump and then making him fall fast. Afterwards he should slow him down before he hits the ground.”
    2. “The bumper car would end up going backwards because its going back towards the start. she needs to make it into a straight line.”
    3. “The graph says the bumper car goes back in both time and distance. To help her, I tell her to measure how far along the road the car´s traveled, NOT draw the car´s path.”
  3. The additional portion I added required students to create their own units for the graph and reflect on what was happening in the scenario. When students had to create their own axis, they had to logically think about what would make sense…some started to write that their cannon only shot up to 5 or 6 feet tall…that wouldn’t make for a very fun carnival event!! After understanding this, they fixed it and were able to justify more appropriate units. They also realized without units, they could not accurately state their domain and range.
  4. Vocabulary from our unit was reinforced at several points throughout the project. Several students quickly noticed when they drew extra lines in the Desmos window it would make more cannon men or bumper cars appear…which was quite fun :)…but beyond that, they explained to me that it was no longer a function because their graphs did not pass the vertical line test and there were too many outputs for one input. We also talked about the slope of the lines when the cannon man’s parachute deployed, when the bumper car crashed and stopped, and when the Ferris wheel ride had a constant speed. It brought meaning to the lines and why they were less steep, flat, or constant.
  5. Lastly, I got to use this super cool half graph and half lined notebook I requested for our math department!! 🙂 notebook

I’m looking forward to more Desmos projects! If you’re interested in the additional pieces I added to the project, Desmos Carnival Project.

Lions, Tigers, Math, Biology, World Geography, English, and DIM, oh my!

Okay, I know that title is cheesy…

We took our freshmen students to the zoo last week for their first class field trip and I loved how it wasn’t just a field trip related to one content area, but in our planning we managed to relate it to every class. Here is the link to the assignment: Zoo Student Handout and the explanation is below…just in case you’re going to the zoo anytime soon with students and want to do a similar activity. 🙂

To begin the zoo experience, the biology teacher asked students to research one animal that is at our local zoo and find out how much land area and resources the animal needs to live a healthy life (they have been studying health and wellness recently in biology). Then, in math I had students do this Estimation 180 as a warm up to review how we could estimate lengths and sizes. I explained that at the zoo, they will be using their estimation skills and area calculations to confirm or deny that their chosen animal has enough space. When we got to the zoo, students split up into groups to explore the zoo with the land and resources in mind. The math part of the assignment at the zoo also had students draw the enclosure using points, lines, planes, rays, and line segments if they were in geometry, and write/solve a linear equation about their day at the zoo if they were in Algebra. For the WorldEng (World Geography and English) portion, students were asked to reflect about borders and responsibility of the zoo to protect animal’s habitats. When we returned to school, students read an article about the city’s limitations of our zoo and the historical implications of the area. The next day in their Digital Interactive Media class (DIM), students wrote a blog post about their experience. They were asked to summarize the experience, discuss the area calculations and findings, and respond to some challenging questions about the zoo which forced them to consider multiple perspectives.

I’m looking forward to more opportunities that we can create interdisciplinary learning for students.