# 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).

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!! 🙂

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. 🙂

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

# Conditional Statements in Geometry and Computer Programming

While planning for the logic unit in geometry a few weeks ago, I wanted to increase the rigor and apply a more meaningful experience to the topic than I had in previous years. In the past, I have had kids do a project in which they found ads in magazines that used (or could be rewritten to use) conditional if-then statements. Then they rewrote the ads to include the converse, inverse, and contrapositive statements. I think this is a fun activity and it is a really great way to have students recognize if-then statements in the real world, however, I began to think that this experience might not be project worthy. I found that asking students to rewrite the statements did not have a lot of meaning to them and some of the mathematical logic got lost when they simply repeated a statement about shampoo or men’s deodorant.

So this year instead, I planned to use the ads as just a warm up by showing students an Allstate commercial and asking them to identify the if-then statements. Then, I started thinking about what else in our world uses conditional statements and how I could make a more meaningful and rigorous project. I realized computer science uses if statements for a program to do something if a condition is met. Several years ago I worked for a company where I used coding, but I knew I needed to brush up on my understanding before I could teach it to kids. In my search to make this project of relating conditional statements in geometry to computer programming, I stumbled upon two helpful resources: Pearson and Khan Academy.

In our Pearson textbook, there are enrichment activities and coincidentally, the textbook had a similar idea to mine for the logic unit. They gave students some code and asked them to identify the hypothesis and conclusion in it. However, they used GOTO which is a bit outdated and not used a lot anymore. So, I held on to their idea about dissecting code and rewriting the hypothesis and conclusion, but searched around for a more relevant platform.

In my mind I wanted students to actually write code, manipulate it, and see it work with this project. I soon found Khan Academy’s tutorials on if statements and as I was working through them, I found that it was the perfect match to what I wanted. The tutorials teach students how to edit code with different scenarios and then students do a similar challenge to try to master the code. In the first challenge that I had students do, they were shown a ball that drops off the screen and they had to use if statements to make it go back the other way, displaying a bouncy ball effect on the screen.

For the project, I created a worksheet for students to use while they watched the tutorials, practiced the code, and performed challenges to see that their code actually worked. It asks the student to rewrite the if statements as a hypothesis and conclusion (similar to Pearson), decide if there is a biconditional phrase, and then also use the inverse code to manipulate it again. (The worksheet is below and a Googledoc is linked here). Then after completing their code, I planned to have them reflect on their work by writing a blog post with two key aspects in mind: Connections: The student can recognize, explain and use connections among mathematical ideas and Problem Solving: The student can apply mathematical algorithms (series of steps), tools, and/or representations to accurately solve problems.

Finally, I showed my ideas to one of the deans at our school who is much more knowledgeable in computer programming than me to get some of his insights on the activity. He helped me create a short piece after students finish the challenges that helped them pre-write before their blog post. It also helped me create a rubric (below) to guide students as to how I would grade them including accuracy of conditional statements, problem solving throughout the activity, and the written expression of their blog post.

Overall this project went great…it has now become one of my new favorites!! Every student was engaged in the tutorials and the challenges; I saw them have a sense of ownership in their learning because they could self direct and work at their own pace. When students got the code, several of them got so excited and called me over showing off their successes. I also had a lot of really interesting conversations during and after the project…one student said they can now imagine how complex creating a video game would be with all the coding involved. Several students said they understood why their program needed both the if and the then components to make it work and really liked seeing their work actually do something. I am excited to read their blog posts soon (they’re due on Tuesday) and hear how they summarize the project and learning objectives!

# Back to School Night: Two of My Favorite Things To Do

We just had back to school night last night with the parents and I wanted to share two of my favorite things that I always enjoy doing. It’s always quick night having to rush through so much information such as briefly explaining about myself as a teacher, the class, expectations, class trips, and so much more, all in about 8 minutes! But no matter what, I will always make time for these two things.

1. Good News Post Cards: I started this last year and thanks to our bookkeeper, she helped design and print the post cards for me. The picture to the left is the front…yes, our mascot is a globe :)…and on the back is our school’s return address and a space for parents to write their name and address. As parents walk into my class on back to school night, I have them write their name and address on the postcards. Then, before presenting my class information, I explain that I think parents don’t hear enough good things about their students. So, throughout the year we, as a team, will be hand writing them little post cards when their student does something great. I love doing this because I think we all get caught up in some of the craziness of the year, but taking a moment to reflect on the good our students are doing really helps refocus our energy. We plan to write one each during team meetings and sign them from all the teachers.
2. Parent Note Cards: At the end of my presentation, I pass out note cards and ask parents to write one thing about their student that I might not know, or that they want me to know. I love reading the proud things parents say, the insightful comments they say about their child as a learner, and the interesting facts they share about their kids. In a night of speedy conversations and lots of information, it helps to give parents a voice.

# World Geometry

While planning for geometry last week I began thinking about how I could amp up midpoint and distance formulas. After learning the formulas, my students practiced with very abstract points. However, I knew I wanted them to see examples that had meaning. With the help of the English and World Geography teacher, I developed my students first interdisciplinary activity of the year which they named their World Geo-metry assignment.

In WorldEng (their combined World Geography and English class) my students had been learning about Burma. So, I gave them a map of the region with questions where they had to find coordinate points of key locations they had been studying such as Dhaka, Naypyidaw, Bangkok, and Yangon (I learned a lot just from the start of this!!) After finding the coordinates, I asked them to find the midpoint and distance between these locations and draw conclusions based on the map. To make it more complex and meaningful, I added some questions about the scale in miles for students to understand the actual distance it would be to travel from one place to another. The final question asked students to compare the size of the border of Burma and Thailand to other borders of Burma and justify why refugees might be immigrating along this region (something they had been discussing in WorldEng).

I really liked the discussion I heard between students as they worked through the activity. I decided to give each student a worksheet, but make each pair share a map and I think this helped students talk through the locations, make connections, and agree upon their answers. I also really liked how the answers for distance were not exact integer answers. They had to work with tricky numbers and understand if their answers really made sense. Finally, I knew this activity was successful after students commented on how they were combining three classes to do their calculations.

# First Week Highlights

I just finished the first week of school and looking back, it was one of my favorite starts to the year. Normally I’m not satisfied with my first day of school activities and either feel that they’re too cheesy or too boring. This year, however, I finally feel really happy with how the first day went because I had a high level of engagement from my students and the rest of the week followed in the same way. So, to recap the week, here are a few highlights, including many protocols for certain activities that can be used throughout the year and not just the first days of school!

Monday (first day of school part 2): After completing our quizzes, I explained our last activity: 31-derful. I found this activity from another favorite blogger: “Everybody is a Genius.” I displayed the same instructions she did and then let them go for it in groups. I loved seeing and hearing their thought processes with their groups. It gave me an insight into their problem solving and communication skills. Every class had 1-2 groups complete the puzzle and the other group were super close! Just like the activity above I knew this one was successful because on Tuesday (and Wednesday) several kids came into class asking if they could play the game again saying it was so fun!

Tuesday (part 1): I saved setting rules and going over the syllabus for the second day because I didn’t want to rush through either one and I knew the first day class times would be shortened. Normally, when going over my own rules and setting classroom norms I have done a chalk talk. I like chalk talks, but students don’t understand the value of silence during this activity, and it’s hard for me to facilitate without saying to stay quiet every 5 seconds when they are hyped up from the first days of school. So, I thought I’d save introducing chalk talks for later in the year…or maybe one of my fabulous colleagues will do one before me and be better at keeping them quiet :). Instead, I did a four corners activity to facilitate setting classroom norms. I loved how this went for several reasons: It got students up and moving, but in a structured way. Also, as we discussed agreements and disagreements, students were standing, which at first I thought might be a little chaotic, but in every class, they actually listened really well while standing…somehow it made them more self aware to who was talking and what they were saying. I also liked hearing students voice their opinions about how they learn best. I think students felt safe sharing how they felt because they often had someone else beside them that felt a similar way.

Tuesday (part 2): After we set norms and before we went over the syllabus, we jumped into a discussion of our summer assignment (a reflection about their own math understanding after reading the freshmen assigned book, Bamboo People). With the suggestion from a fabulous colleague, I used a Microlab protocol to facilitate discussion. This went well because it gave all students a chance to speak while keeping the conversation flowing in a productive manner.

Wednesday: We started the day with a WODB warm up that I’m going to do this every Wednesday…I love this activity! With it, students had a chance to communicate their thinking while producing some really interesting debates. In geometry, I used “shape 5” which gave students some new language and facts that they will be using later in geometry such as a dodecagon, polygon requirements, and composite figure. In algebra, I used “number 1” and a couple students gave an argument for something I didn’t even see…9 didn’t belong because all the others made 7 when you added together their digits. After the warm up, geometry played TGT to review algebraic concepts before moving on to geometry (I’ve posted about this game before). All students were engaged in this game because it was competitive, but safe. I think having students choose their comfort level with the material helped them feel at ease and confident in their competition teams. In Algebra we completed a KWL chart with a preview to their first quiz. I think this helped set the tone for why they need to know what they will be learning the next few weeks. Then, we reviewed patterns by doing this lesson. It was a great, low prep activity that helped students review patterns and formulate their own thinking without me directly telling them the sequence. The next couple days we did some book work from our Springboard textbook. I am really liking the reading required from the textbook, but I realized I need to work on my facilitation of teaching from a textbook (this is my first year directly using one). I’m not going to use it every single day, but definitely more than I ever have in the past because I think it is a really good resource for STAAR type of materials.

Friday: After taking some notes and doing practice on Thursday about points, lines, and planes, geometry played this sketch game. It was great to hear students communicate their learning again to each other. Many were saying the process was so hard, but kept at it and saw that the more specific they were, the more accurate their partner’s drawing would be. Algebra had their first “standards check” before moving on to non linear patterns. Geometry will have one Monday. I think the format of the SBG checks are going to be really good for myself and students. I especially love having students know exactly what their learning goal is and having them self assess their learning.

One last highlight: So far, students are doing really well with my grading breakdown of homework/classwork counting for 0%. I know it’s only been one week of school, but students seem less concerned about what counts for a grade and whenever I assign a task to complete, they all jump into it knowing it’s for them to practice their learning…hopefully the rest of the year follows the same way!!

I’m so thankful for all the great resources I’ve found through other blogs and am ready to take on the second week with a little finalizing of plans tomorrow…for now, time to relax! 🙂

# Chicago Trip and Math

My husband and I just got back from a great trip in Chicago to celebrate our first year anniversary. I loved every part of our trip from the delicious food, enjoying a no-hitter game at Wrigley Field, walking the city, seeing iconic sights, and so much more. Even though we were there for absolutely nothing to do with work, I couldn’t help but become inspired by the math of the city. I decided to jot down my notes here so I don’t forget!

1. Chicago Architectural Tour: This was one of my favorite things we did. It was a 90 minute guided boat tour that took us along the Chicago River as we learned about the history of the city through the architecture. I definitely want to show my geometry students pictures from this and hopefully convince them through photos that math is truly used in professions, appreciated in everyday life, and highly sought after for beauty and meaning in a city. It was incredible to stand and look up at the enormous buildings as I visualized what it would be like to build one. I also found the history behind each structure to be really interesting from a math mindset. One of the first things our tour guide reminded us about was the Egyptians were very influenced by geometry in their early architecture. As we went along the river, we saw the transformation from early styles such as Gothic, Renaissance, and Neoclassical, to modern day styles. Some key buildings are below. The first building is the John Hancock building which I found really interesting because we learned that the X’s were intentionally structured on the outside of the building as a way to provide the building stability, allowing it to have no poles throughout the inside, and thus giving it a completely open concept.The second was a very iconic apartment and multi-functioning building used in several movies (I still need to find out what movies…but I know there was one where a car crashes out of the building and falls into the river). The circular shape meant a lot to the architect, Goldberg, with it’s aerodynamic features, lack of any corner rooms (often thought of as reserved for high society), and enabled all rooms to be centrally located to the center. Next, was a triangular shaped building which was again, designed intentionally, to allow residents to have more lakefront views than a square or rectangular shaped building.Then, there was one that was built right over a train and so the builders were tasked with how to safely design such a building. They designed it narrow enough at the base such that the train could pass by it, but then it will become wider as it goes up with the use of triangular frames.

Finally, the last one was really aesthetically pleasing and it wasn’t until our tour guide explained that it was designed as a map of the river with the red feature symbolizing a “you are here” spot, that I really appreciated the creativity and brilliance behind the design.

2. The Ferris wheel at Navy Pier: While waiting in line for the Ferris wheel, I couldn’t help but notice the geometry behind the huge structure. I will definitely show these pictures to my students, and hopefully I can think of some cool project and/or investigation we can do with circles, arc length, area of a sector, etc. and Ferris wheels.

3. The Bean (Cloud Gate): This is one of the most well known areas of Chicago and I’d love to learn more about the shape and structure of it. When I show this to my students, I’m curious to hear the words they would use to describe its shape. I think there are also some interesting reflective properties my students and I could talk about. For example, when you walk in the middle of the structure you can see the same reflection 4 times (I tried to capture this in the picture below.) My husband and I had fun finding ourselves in the mirrors and then I suddenly realized we could be using words like translated and reflected…I think this would be a cool example to show students when we discuss these terms. I think proportions and similarity could also be referenced with this structure when you think about how your image changes depending on where you stand in relation to it.

Thanks, Chicago, for an awesome trip and lots of learning!!

# SBG Plans

I’ve spent A LOT of time thinking about grading this summer. As summer winds down, I have put focus on getting some solid planning done and after lots of coffee, sketches on scratch paper, and chats with colleagues and friends, I think I’ve finally found a happy place where I feel comfortable and confident with my plans. This is going to be my first year trying out SBG, so I want to keep it simple as to not confuse myself or my students. Here’s what I’m thinking:

In both Algebra I and Geometry, I am going to be diligent about maintaining short, frequent assessments on one standard at a time. These will happen every couple of days after we learn a standard. After reading the math=love blog, I loved her idea (I pretty much love everything she does) of having students write the skill and learning goal on their paper. I think this could reinforce the topic we are learning, and overtime, I think having students write “I can” statements will increase their confidence in their understanding. For example, when we learn solving linear equations, this will fall under the skill, “linear equations,” and the learning goal for the students would be “I can use algebraic methods to solve a linear equation.” Both of these will be posted on the board along with the 2-3 problems they will be solving. Hopefully by just writing the problems on the board, it will save me time typing up problems and making copies since they will happen frequently (again, keeping it simple will be my SBG motto this year). But, I will need to be specific in helping students understand how to write the problem and show their work in a neat and organized manner. I am also pretty sure I’m going to use a 1, 2, 3, 3.5, 4 scale and require students who make less than a 3.5 (88%) to retake. Below is the example of the SBG quiz template I revised from the math=love blog. This also takes place of the red, yellow, green systems I talked about in a previous SBG post.

These SBG checks that will happen about twice a week will comprise 60% of a student’s grade. Projects and larger Quizzes that comprise multiple standards will count for 30% and then there will be one cumulative nine weeks test that will be 10%. Students may retake any SBG check or larger quiz if it is below a 3.5.

I think by having frequent checks, followed by more comprehensive projects/quizzes, will help kids retain their knowledge beyond just for one day, one check. Then, having one final test at the end of each nine weeks, my Algebra 1 students will have the feel of a larger spiraling test like the STAAR test, and my geometry students will also keep retaining their spiraling knowledge.

Feel free to comment with any thoughts or ideas as I start to move forward into the new year!

# Summer Thoughts and Goals

Next year I am transitioning to a new prep at my school and will be teaching freshmen Algebra I and Geometry. For the past five years, plus a year as an intern during my master’s program, I have been teaching sophomore Algebra II and Geometry. So, after knowing I was going to move to a new team, a new prep, and a new age of students, I was honestly a bit nervous. One main reason I was nervous was because I knew taking on Algebra I meant taking on the STAAR test. I knew that added pressure on both me and my students would make this year a lot different, and while I don’t want my students to feel pressured, the test is inevitable and I want to help them be successful in the best way I can. Thoughts have raced through my mind this summer about the new prep, but after this weekend I am more excited than ever.

So, this weekend a few of my friends and I traveled to Dallas for a girl’s weekend. On Friday night as we were just sitting around talking, one of my friends posed the following simple, yet very thought provoking, question: if we were to all gather back together in one year, what do we hope to have accomplished? After I shared some of my hopes in my personal life, I said that I hoped I could say that 100% of my Algebra I students passed STAAR. After saying it out loud, that previously mentioned nervous feeling tried to sneak in…I started thinking is that too lofty of a goal, what if it doesn’t happen, was the passing standard even going to be the same this year, should I take it back and say I hope most of my students pass, etc.?! But, I didn’t take it back and I didn’t change my goal. I continued on with it to my friends as I said, why would I hope for something like 95% or 98% passing?! How could I look at my class and hope “Johnny” passed but not “Kelly”?! How could I give up on the kid who claims they are bad at math, or the student who is too shy to ask questions in class, or the one who passed with a 70 every year before, the one who struggles, the one who comes to tutoring, or the one who doesn’t? I can’t and won’t give up on any of them. As I was telling my friends this, I knew my students were the ones that should hear it. I want my future students to know we are in it together and my goal should not be a secret to them. I want them to know my goal leaves no student out. I want them to know that I will celebrate successes with them and help them learn from the mistakes. I want them to know that I will never give up on them and in turn, I hope that they never give up on themselves. I want them to be confident in their growth as mathematicians rather than judge themselves on their initial understanding. I want them to know that although their scores on state testing does not define them as mathematical scholars, I will be working every day to help each of them pass with 100% of my effort. I can’t wait to tell them this on the first day of school!

I am excited for next year, for new challenges, new adventures, and to start the year off with a goal that encompasses every student, every day. Although I will miss my sophomore team, my sophomore students, and my sophomore content, I am excited for freshmen students, an inspiring freshmen team, and the confidence that my thoughts of nervousness have been replaced by pure excitement.

# Open Middle

After joining the Twitter Open Middle conversation last week by Michael Fenton, I was intrigued to try out some Open Middle problems in the last few weeks of school. To kick off our review for the final exam, I posed one problem to Algebra II and one to Geometry. My students reactions were great, starting with one kid saying, “nope, Mrs. Taplin, it’s impossible.” After explaining the concept of “Open Middle” and encouraging them to have some grit and resilience with the problems, my students really got into it. Some proudly held up their whiteboards for me to check when they got their answer, many requested just a bit more time so they could finish it, one excitedly jumped out of his seat when he got the answer, and another claimed, “this is my greatest accomplishment!” I would say that means Open Middle was a success!

Here are the problems I used and if you haven’t checked out Open Middle, it’s a great resource…here is the site for even more information on these types of problems: http://www.openmiddle.com/.

Algebra II: Create three equations that produce the exact same parabola by filling in the blanks with whole number 0 through 9, using each number at most once.

Geometry: What is the longest chord in a circle that has an area of 25pi square units?

What I like most about these problems is the conversation that unfolds with students. For the Algebra II problem, I started with vertex form, but several students started with factored and/or standard form. One student said she went from standard to vertex, but another argued that she did both factored and standard, then graphed to get vertex (something I didn’t even think of doing, but what a great well rounded way to review this concept). In geometry, I thought this problem might be too easy, but with the different way of thinking from more straight forward problems it created a challenge to students. I loved the conversation focused around vocabulary, the “good mistakes” (as I like to say) students made, and the corrections they did. Several students got 5 units for their answer, but forgot that the question was asking for a chord, not a radius. It forced students to reevaluate their answer and not stop too early.

I like to do Mental Math Monday’s (I got this idea from my mom…the teacher verbally says a string of arithmetic problems and students try to quickly get to the correct answer in their heads) for warm ups into class on Monday’s, so maybe I can add this to the week rotation next year and try Open Middle Wednesday’s (since it’s the middle of the week). Thanks again, Michael Fenton, for some great ideas!