As promised last week, here are some exit tickets that you can use with a Similarity Unit in Geometry. Just a reminder of how I use these. I give feedback on each submission and have students work on them until they are correct. I love doing this with the comment feature in Google Slides. In Canvas, I am using the Google Assignments LTI so it looks just like Google Classroom.
Now, you might not want my Bitmoji on your slides. I mean, she’s cute, but I get it! You can go to view-master and change the Bitmoji there. I changed my jacket color for each day. One student told me he was excited each day during the lesson to see what color the jacket would be but slightly less excited about the math. 😂 Whatever gets them there!
I wanted to share with you a quick update to Road Kill Kafe that I use in my Geometry class to discover congruent triangles. It was shared with me by my friend Craig Klement (@CraigKlement) and you can read about all of my Triangle Congruence activities here.
We are hybrid this year and it usually takes 2 days to complete the activity. That’s 4 class days with both classes and we simply didn’t have the time to do that.
So… I turned it into a digital activity. It worked out ok. I did model some skills for them regarding the drawing tools in Google Slides and that made things go more smoothly. I also pasted a reference segment so we could make sure our side lengths were what they should be.
Here are some images of our completed triangles.
If this is your original activity, let me know! I would love to give proper credit. If you want to try Road Kill Kafe goes Remote, just click on the links below. The first one is the activity to send to students. Make a copy for EACH student. The second one is the collaborative slide with the reference segments for students to paste their completed triangles. Make sure you set it so EVERYONE has access to the same slide.
Installment three of the area, surface area, and volume application problems. I know some of you have been using these and I hope they are working out well.
Area application can be found here. Surface area application can be found here.
In this post I have included volume application problems and application for surface area and volume of spheres.
I also provide students with candy in boxes and have them calculate the wasted or empty space in the box. This gives them hands-on application and allows them to use their tools. And, student LOVE to eat candy!
The Life Savers box is an amazing find! It’s a trapezoidal prism and we calculate the Life Savers as cylinders with a cylinder removed in the middle. The Mike and Ike’s are also fun because we calculate them as a cylinder with hemispheres at each end. The Kisses container is a triangular prism and we use the cone formula to estimate the volume of each Kiss. Gobstoppers are less fun, just spheres inside a rectangular prism, and the Tootsie Roll container is the least challenging of all with cylinders inside of a cylinder. I have each group work these problems on poster paper and then present them to the class. Giving students the opportunity to share in front of the class is something I try to work into each unit. Please make sure you have a culture of trust and respect in your classroom before you do this with students. It can be damaging to their fragile egos if they are ridiculed or made fun of. And if you chuckled at fragile ego, remember back to high school. What others thought of you mattered at lot!
Here are the application activities I promised. Please let me know if you find them useful. It makes me happy when others can benefit!
I love taking boring problems from the book and turning them into fun learning experiences. A boring word problem was the beginning of this task.
The actual prompt (which I can’t seem to find anymore) gave two popcorn containers, one a cylinder and one a cone, and asked the relationship between the volumes.
I saw an opportunity to construct three-dimensional figures AND eat popcorn. Oh yeah, we could discover the formula for the volume of a cone and have some great mathematical conversations too.
I’ve been doing this project for quite a few years. I originally posted it on my Infinitely Teaching blog. I have updated the Google Slide I give to students and I now encourage them to begin with the cone and move to the cylinder. This simplifies the process significantly.
Here are some pictures of our recent process. My favorite comment overheard by a student was “This is so much fun!” I want math to be fun so this is a success.
Here is a link to the Google Slide I give students with instructions and a scoring guide. If you use this, please let me know about it. It makes my day when others find my contributions useful!
I posted some area application problems last week. You can find that post here. I also promised some surface area problems, so here you go. One page is many different problems that you could use as an assignment, assessment, or problem of the day. The second one is one problem broken up into 5 days, perfect for a daily warm-up. This idea of taking one prompt and using it all 5 days, called Focus on the Question, comes from Sue O’Connell in her Putting Practice Into Action book. It’s written more for elementary but the idea can be used with high school. I’ve found this strategy to work better with struggling learners. They have conversation time and it breaks the task down into smaller parts. I always call on a table, and not a person, to allow them to share what they discussed, discovered, and concluded.
I’m currently working on some volume application, which sneaks in some surface area. I will have another one including spheres. Stay tuned.
In Geometry, we teach area as a quick review before surface area and volume. This year, I wanted this topic to be more of a life skill than just a review. I taught students how to use Google cards to find the area of common shapes. A quick search will pull up the following card for almost any shape.
The more important skill I wanted to help my students with was using area. In life, if we can find the information we need and know how to use it, we can solve almost any problem we have. I created some tasks, some based on actual activities I’ve done, to help them use area. I’m sharing them here so you can use them too. Teachers have limited time and sometimes finding a good activity that you don’t have to create is just what you need.
If you use these activities, please share with me on Twitter. It makes my day when someone finds value in what I’ve created. Happy mathing!
Click on the image to view the template.
Stay tuned for surface area and volume application.
I’ve always had my students draw in the lines and explore the interior and exterior angles of a polygon, but they struggle with drawing the lines. Many students try to draw lines from every angle to every other angle and you end up with a spiderweb mess. We also spend so much time on the lines that we lose focus of the pattern that develops. During a PD when we were talking about students questions and exploration, a colleague suggested letting student cut out the angles on the exterior of a polygon and put them together. Well, if you’ve been around my blog long enough you know I am NOT a fan of cutting paper. So I created the exterior angle exploration during our session. It allowed the same exploration as the paper, but was possibly even more visual. Our team LOVED it. I went on to create the interior angles exploration also. The purpose of this one is to spend time on exploring the pattern and not on the drawing of the actual lines.
If you use this exploration, please let me know. Make sure you put in in Google Classroom with make a copy for each student.
I love to create in the math classroom. It’s a great way to connect with students who may not LOVE math but love to create. However, I want the projects we create to enhance their understanding of math, and not just end up an art lesson.
This project, with the addition of a critical thinking discussion, does both. I hold up a few of these pieces of art and walk around the room so students can look at them. They automatically start talking at their tables about what they see.
Then I ask the question, “What type of transformation is represented in this art? Discuss at your table, but be able to support your answer.” I immediately hear “rotation, it’s a rotation!” But as they start to justify to each other they hit a road block. It does’t fit what they know about rotations. Eventually they decide it’s a reflection and provide the necessary justification to support their idea. I love the rich conversations that happen.
Now, I could stop there and my students would have learned, but what fun is that? They want to create one of these art pieces. I already have triangles cut out and ready to go and we discuss a plan to make one of our own. As they are creating, we “remember” that this is a reflection, not a rotation, and discuss how we can achieve this. Students are engaged, they are helping each other, and they are having fun in math.
Here are some pics of the process and some of my kiddos work. It is always a success!
I’ve also included a slide show of some of the art created.
What do you do at the end of the year when students have already turned in their laptops? Tessellations.
This was a great review of transformations and students were able to show their creativity. We learned how to make tessellations that translate, rotate, and reflect and then students could choose which 2 of the 3 they wanted to make pictures with. I loved the A-HA moments when students created their tessellation realizing that the transformation used to create the template was the same transformation they were trying to make.
I created some stop motion animations to help make each type of tessellation.
Some were simple, some were fancy. All of them were very fun.
Keeping students involved and excited about math at the end of the year with finals and impending summer break is very important. I want students to love math more when they leave my classroom than when they entered. I don’t want to lose them at the end.
I have been doing this activity LONG before computers were a staple in the classroom. (We won’t talk about how many years that’s been!) I love this project now as much as I did when I started.
I used to have a Far Side by Gary Larson desk calendar and each year I would keep the images and use it for this project. I don’t buy the desk calendar anymore, but you can find Larson’s comic’s online.
I take the comics and cut them equally into 3-4 congruent parts (depending on my groups). Students must work in groups of 3-4 to decide on a grid size for their original and a scaled paper size and grid size. Once they’ve worked together to draw this in, they start sketching their drawing box-by-box. We spend about 4 -50 minute class periods on this project.
The students have a lot of fun with this and are proud of their product when finished. It also reinforces teamwork. When one person doesn’t complete their part, a picture is hung up for viewing incomplete. So sad.
Here is the planning guide I use for this project. If you use it, post about about it on Twitter, and tag me @MandiTolenEDU.