# Exterior Angle Sum Theorem

I 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!

# 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! 🙂

# 3D Solids Lesson Using Jigsaw Cooperative Learning

Here is a quick lesson I put together using the Jigsaw Cooperative Learning technique for 3D solids. We learned the surface area and volume formulas for prisms in a direct instruction model and because we have such little time left in the year with testing and such, I decided Jigsaw-ing these concepts would be the best way. Overall, it went well…I did have to model how to have students teach each other and not simply copy, but after doing that, I was very pleased with how they communicated their understanding to each other.

I gave each expert group some cards of one of the solids I found here: http://math.about.com/od/formulas/ss/surfaceareavol_2.htm. With these cards, they had to talk through what the variables meant, what the lateral vs. total areas were, and how to use the volume formula. After each group finished completing their row of one assigned solid (writing the formulas, defining variables in their own words, solving a given example, and creating their own example), I mixed up the groups to have one solid represented in each new group. Then each expert taught the others how the formulas work and what they learned.

Here is front and back of the student worksheet I created, the rest can be found here: .

# 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!!

Here is the link to the math student materials: MatHistory

# Teams-Games-Tournament

I am always looking for new review games to use before a quiz or a test. This year, we have played Team-Games-Tournament (TGT) several times and have had great success with student mastery and engagement. This game is a cooperative learning strategy that is discussed further in “The Strategic Teacher” by Silver, Strong, and Perini. In their book, they explain the reasons why this strategy works with the number one reason being that “TGT incorporates the best of cooperation and competition.” Furthermore, it “highlights interdependence among group members, holds students individually accountable…promotes positive face-to-face interaction, builds small-group skills such as communication and conflict resolution, and encourages group processing so that students use their reflections to become better team members.” There is a bit of prep work on the teacher before hand to possibly reformat your review, create the playing cards, and make color-coded copies (my interns wonderful suggestion) for each role, but it proves very worthwhile. As compared to other review games that require the teacher to reteach or be the leader, this game is student centered and the teacher can now simply be a facilitator while students take ownership in playing, coaching, and teaching each other.

I typically give students a review sheet for the test the day before we are going to play the tournament. I give them some class time and/or assign the evens for homework. By only doing half, students are familiar with the material, but still need to review more the next day. The following day during the tournament, they will complete all the review questions. When they draw one they have already done they are instructed to do it again on a whiteboard (or a scratch piece of paper), whereas when they draw an odd question they should do it on the actual review. This gives them repetition of review and complete mastery of the content. The first time using this strategy, students will need the directions read to them and seen posted on the board. However, after a few rounds, the game becomes very clear and natural. I have loved watching students coach each other through the work while also competing with positive interactions.

Here are some directions that you can display for students as well as teacher notes to further clarify. Let me know if you play and what you thought!

Teams Games Tournament

Reference: Silver, Harvey F., Richard W. Strong, and Matthew J. Perini. The Strategic Teacher. Alexandria: ASCD, 2007. Print.