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.

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.

prog 1prog 2
prog 3
prog 4

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.

rubric pic

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!

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).

IMG_7139I 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.

 

Introduction to 3-D with Polyhedron Nets and Islamic Design

A couple weeks ago, I was planning for our last unit in geometry which is 3 dimensional solids, and as I was measuring nets and counting vertices, edges, and faces, I suddenly realized I was really bored. If I was bored, my students definitely would be! I knew I needed to amp up my curriculum to still teach nets, relationships between 2-D and 3-D, and constructions (TEKS G.6B and G.2A), but somehow make it more engaging.  What eventually fell out of my plans was a new connection between math and World History.

I started thinking that students could choose a 2-D net, decorate it, and then fold it into the 3-D polyhedron. However, this was not very exciting and required little critical thinking. Also, I knew I wanted students to decorate their models, but I didn’t want them to just draw flowers or smiley faces or simplistic designs with no reason behind it. So, I asked the World History teacher if there were any connections he thought I could make between our two classes. He told me they were about to start Islamic culture and history which was perfect because Islamic art incorporates a lot of geometric design. We talked about some questions to prompt some thinking for his class. By asking students to pre-think, my geometry students were able to be the experts the next day in World History.

Here’s the basic outline of the lesson plan.

1. Pass out the Islamic Art and Polyhedron student worksheet and talk with the students about the fact that we are going to make a connection between World History and geometry…yet again!! 🙂

2. Show this video (or any other video you find) and ask students to jot down anything they see that answers #1 (What patterns do you see in Islamic art?).

3. After the video, have students pair up and talk about what they saw. Then call on students to share out whole class. (Think, Pair, Share model)

4. Then, we went on to the questions #2-4 which talks about the history of the region and asks students to compare Islamic design to Chinese, Eurasian, and African Art, but you can add or take out any other questions that would be relevant to their World History class.

5. Show students the net templates they can choose from. Some chose simple nets like cubes, rectangular prisms, while others chose more complex such as octahedrons and stellated dodecahedrons. (There are many templates online…I decided to use this website. Warning: Some models are very tricky, but I think if students get to pick, they will have the buy in and motivation to complete it.)

6. After they have chosen their template, found the number of vertices, edges, and faces, we used the rest of the class to design their Islamic artwork. Remind students that they must use rules and compasses when drawing lines, circles, and arcs, because Islamic art focuses on very precise designs.

7. The next day, we came back and started class by having a chalk talk with this question: “What is the main focus of Islamic art…what does it include/not include?”

8. Then after a 3-5 minute chalk talk, I let them work on their design and fold their 3-D nets.

Overall, students enjoyed this hands on activity. One change I would make is to print out the larger nets rather than the single page nets, especially for the more complex types (anything larger than an octahedron) because folding and taping those got quite tricky! My plan is to hang these up with fishing wire between my room and the World History room as a visual connection between the two classes. Thanks, Mr. Sprott, for helping me dream up this mini-project!

polyhedron2polyhedron 1polyhedron 3

MatHistory Part 2

This post has taken me a while to write with several revisions because I just haven’t known how to write it in a way that gives justice to everything I have loved about this assessment. Every time I sit down to write it, a new way to introduce the post races through my head. However, I think the best way to start out is simply thanking the AP World History teachers who had the vision and the enthusiasm for working with me to create this complex, unique, and highly successful interdisciplinary assessment. So, thank you, Mr. Freeman and Mr. Sprott! I hope this leads to many more mathistory and mathenglishistry (math-English-history-chemistry) ideas!

So, here’s how the project unfolded…

Last Tuesday, the World History teacher presented our students with the idea of a power scale timeline and explained how to create one. Each group of four students were given 16+ maps of various European empires that showed the time at which each empire owned land. After identifying the region, they transferred the area onto a larger scaled timeline. Then, when all the empires were on one map, students used their mathematical knowledge to identify key points and explain why they are important relevant to time and land area (we presented this part on the second day). At this point you may be thinking whhhat theee hecckkk is this lady talking about…don’t worry, our students were also a bit perplexed by the task at the beginning and in first period, we did have a brief time when we felt as if our students might revolt against us. However, after encouraging our students to just try it out, much to their surprise with a little patient problem solving (as referenced by Dan Meyer) they excelled at the task. After they got the hang of it, I asked one student to explain the process and here is his recording. I liked getting to be in the history classroom this day because I was a second person who could help facilitate and answer questions as students created their timelines. They also started to make the connection with me being in the room that this might have some math involved in it.

On the second day, as the students were finishing their timelines, we presented them with the math portion. As they identified key points historically, we heard them using mathematical language and vocabulary terms as they talked about undecagons, parallel slopes, parabolas, intersecting lines, exponential growth, etc. It was really cool to see students make connections and hypothesize using their knowledge from both classes. We encouraged students to work together because the questions we gave them ranged in topics from both Algebra II and geometry. Each group had students from both classes and therefore they were able to be experts in the subject they were taking. Walking around helping students work through the assignment, I overheard two students talking about interdisciplinary learning and caught the end of their conversation on tape. Hearing them voice their appreciation for interdisciplinary learning really made it all worth it!

Yesterday I finished grading the math portion of the timelines and was sitting with the English teacher during our monthly Saturday school when she asked me, “so, would you do it again?” My immediate answer was, “YES!!” I think that asking students to use mathematical evidence in their explanations of what was happening historically made them think deeper. I also think they were able to synthesize better by using logical mathematical thinking. Additionally the featured image at the top of this post is one that we were very impressed by. She spent time finding key images and icons from each empire and finished her timeline with detailed watercolors. It made us think of the possibilities…perhaps students could design a timeline based on different aspects of each empire (religion, architecture, art, etc.) I think there is so much more we can do and definitely lots to think about. Over the next few weeks students will continue to learn in their World History classes about each empire and add to their timelines in order to create a large final timeline in groups…so more to come!!

IMG_5221

Here is the link to the math student materials: MatHistory

MatHistory

Featured imageI’m getting really excited for a new idea the world history teacher and I have been brainstorming for a few weeks. We are working to intertwine some math content when he teaches Eurasian Empire power scale timelines. He came to me with this thought that math could somehow be modeled in the drawings and as soon as I saw the previous year’s final products, my math brain started running! We started drafting the actual questions today and we are going to continue to formulate our ideas until we present it to our students next week (I’m sure there will be revisions even as we are presenting it to the students…forever in reflection of our craft). Here is the link to our questions and above is the image of our thought process…but stay tuned for the final student materials and some finished products!

Nuclear Culture

We just finished a 3 week long interdisciplinary unit on nuclear energy. I am very grateful to have the opportunity to work with the same core sophomore teachers for the past three years. We have grown together personally which I think in turn has had a positive effect on our students learning (supported by The Washington Post here), and we have also accomplished a lot professionally together. We started out three years ago trying to become more unified in our teaching approaches with simple ideas like wearing the same t-shirt on the same day. Needless to say, that wasn’t quite an authentic learning opportunity for students. Our approach evolved into us using the same vocabulary word somewhere in our dialogue throughout the week in hopes that our students would catch on and use it for their “personal dictionary” assignment in English. I definitely learned a lot of new words, but again, this was such a simple daily act and we knew we could do more!

Featured imageWith the help of our Trinity University interns a couple years ago, our most unified approach was created- a UbD unit centered around nuclear chemistry with lesson plans in English, world history, geometry, and Algebra II. (I have to plug an incredible master’s program here that prepares student teachers with a high level of understanding about teaching pedagogy and practice). This unit has gone through three years of revision and I have to say, the way in which everything came together this year, I think it was the our best year yet!

The first year we did the project we were not able to incorporate math because it did not fit with the scope and sequence. I still remember hearing one student mumble, “you know, we’re studying nuclear energy n every subject except math.” My heart sank and I knew I was going to find a way to make it happen! The next year, I decided to switch the sequence of our curriculum and teach exponents at the beginning of the spring semester when the nuclear culture unit started. Working with my Trinity intern that year, we created investigative lesson plans where students discovered how radioactive elements decay. Understanding asymptotes also helped students see that nuclear waste will never reach 0. We then discussed the implications for using nuclear energy based on exponential growth and decay and exponential properties. This year, I added the geometry component and solidified the inclusion of math in the unit. After my students learned about proving congruent triangles, I went into the English/World History combined classes and introduced their persuasive essay by asking students to write an outline in a mathematical proof format (I was lucky to have another intern this year and she taught a great lesson on truss strength involving triangle properties this day while I was teaching in the other room…I’ll save that post for another day). I loved how the proof writing gave my geometry students the chance to be experts on the topic they just learned and were able to refresh the Algebra II students how to write proofs. Also, the English teacher loved the way they provided evidence for their essays and did some formulaic pre-writing before jumping on a computer to type their essays. Finally, after the culminating day of the project (a “town council meeting” to debate whether we should pursue nuclear energy in San Antonio), the World History teacher created a graph where the x-axis was labeled as a continuum from “San Antonio should not pursue nuclear energy” to “San Antonio should pursue nuclear energy” and the y-axis was a continuum with “the US should not pursue nuclear energy” to “the US should pursue nuclear energy”. Students then plotted their personal opinion as a visual representation for further dialogue.

My heart is full after this unit and I loved hearing quotes like this: “I like the way every class was included in this unit because we understood all perspectives.”Featured image

One of My Favorite Projects

Featured imageI am starting off blogging by sharing one of my favorite projects that I created with my dean a few years ago. After attending a conference at Southwest Research Institute, I got inspired to do a project that would help students connect their learning of quadratics to the real world. I decided to make it about projectiles. I dreamed of getting to launch projectiles across the math classroom, but had no idea how to make this possible. After talking with my dean who is essentially a physics guru, he helped my dream become a reality. Below you will find the process and some reflections on the project.

First, we modeled a projectile using LoggerPro software and found the quadratic equation. This equation became the central focus for our students to manipulate. We asked them to find the vertex form, x-intercepts, y-intercept, and the domain and range. The fun part came on the second day of the project. We hung tennis balls in the back of the room and gave each group (groups of 3-4 students) a different height at which they would set their equation to. Using the quadratic formula, they solved their equation for the x-distance at which to launch the projectile. If their calculations were correct, they would successfully hit the tennis ball. With safety goggles on, measuring sticks in hand, and genuinely excited emotions, each group stepped up to the projectile launcher to try out their solutions. Some chose to set the launcher at the farthest distance for more fun, and some chose to go the safe route and try the closer distance. Several groups hit the target on the first try which was so fun to to watch the teamwork of their groups as they high-fived and congratulated each other. The groups that didn’t hit the target on the first try realized they needed to watch for the human error of lining the projectile launcher up straight. By the end of each class period, each group had successfully hit the target and proved their math calculations correct.

I love this project because it’s an authentic way to check their work. Also, my first couple years of doing this, I connected it to space science by having a hook that the students were trying to blast a near earth object out of our orbit (Armageddon style). Two years ago, my sophomore team and I designed a full interdisciplinary unit on Nuclear Culture. So to connect it to this, I changed the theme up a bit and had students watch a video about NATO’s ballistic missile defense program and then act as if they were helping NATO use projectiles to intercept incoming harmful missiles. Students were able to communicate their reasoning behind advantages and disadvantages of using technology like this and what might happen if we were successful or unsuccessful in hitting their target. I loved that students made connections, communicated coherently, problem solved, and found reasoning and proof (all performance outcomes that the math department at my school tries to achieve) in one single project!

Here’s the link to the student materials: Saving the World with Math