The triangle inequality theorem is not one of the most glamorous topics in middle school math. It seems to get swept under the rug and no one talks a lot about it. Like most geometry concepts, this topic has a proof that can be learned through discovery. It’s pretty cool when students realize that they can actually figure out if 3 given lines will make a triangle. I love teaching this concept to 7th graders, and I like that it’s not super complicated. Most of my students can get this idea pretty quickly and they enjoy it. I’m excited to share with you 11 activities that will help students get, and remember, the triangle inequality theorem.
I’ve collected a variety of activities to helps students learn and practice the triangle inequality theorem. I’m confident you’ll find something that you can add to your class and make learning this concept even more engaging. Because this is such a visual topic, you’ll definitely want to try a hands-on activity so that students can see how it works.
The List of Triangle Inequality Theorem Activities:
Let’s jump right in
Within this group of activities you will find a variety of activity types. Students can practice online or with paper. Also, some of the activities work for partners or for the whole class. So, take a few minutes and explore these activities. There’s definitely something for just about every situation on this list.
This match and paste activity gives students a simple way to practice with the triangle inequality theorem. They get to cut out some squares with possible side length combinations. Then, they have to sort them into “makes a triangle” or “doesn’t make a triangle”. I find that students don’t realize how much they are thinking when they do a match and paste activity. Also, you hear a lot of math talk if you have students complete this in partners. It includes some blank squares so that fast finishers can make their own examples and challenge each other.
The thing about gallery walks is that they get students up and walking around. Also, when I do a gallery walk I like to make sure that students do a lot of thinking. Typically, problems in gallery walks consist of more than multiple choice questions. This triangle inequality theorem gallery walk is no exception. It gives students the opportunity to look at a variety of side lengths and then they have to identify which combinations make or don’t make a triangle.
Usually, when students work on a gallery walk I sit at a specific table and have them check their work with me as they go. By doing this I really get to see who is getting it and who isn’t. It’s a perfect opportunity for feedback.
Mini task cards give students the chance to get a lot of practice quickly. They don’t have a very complicated question on them. In fact, they see the same question on every card, “Can a triangle be constructed with the following conditions?” Then, they have to determine if those conditions could create a triangle with the different options given. As always, students can check their answers on the back if you copy them that way.
These cards work great for playing scoot. You just place one card on each desk. Then, you give students a set amount of time to finish the problem, and then they scoot to the next desk’s problem. They really get into it and this game holds them accountable to get working, because they know they’ll have to move soon. Scoot works well with these tasks cards because they are all at the same level and each problem takes about the same amount of time to finish.
I love this manipulative from Geogebra. Students can try to build all sorts of triangles using this online tool. Best of all, it’s ready to use. It’s so simple, but students can use it as a work mat to try different combinations for making a triangle. You could have them use this tool when they’re working on the mini task cards or the gallery walk.
Also, you could do a discovery activity with students using this tool. Before teaching students the triangle inequality theorem you would give students different combinations of side lengths to put into the triangle sides possibilities tool. As they work through different scenarios, you would challenge students to see if they could figure the rule for the triangle inequality theorem.
Math Giraffe has a great way to practice the triangle inequality theorem… with paper plates! You have to scroll down the page a little bit to see the activity. It is made with three clear plastic plates. What this does is give students random sets of 3 side lengths and they have to figure out if they make a triangle or not. I like this because it brings some novelty to the classroom, and students can work with it independently. I would definitely have students write a reflection at the end of this activity to make sure everything is working well. You don’t want to assume that they get it just because they keep busy.
Often you come across worksheets that you can use, especially if you mix it up. We rarely use a worksheet just as a worksheet in my class. I like to spice things up because usually that means that students are more engaged in the activity. I found some these worksheets from Geometry Coach in one place, and I found a class game in another place. So, I put these two ideas together make solving problems on a worksheet more fun for students.
The game is a football game for the whole class. I love football, and most students have a favorite football team too. You can make this game as fancy as you want. You can create a cool bulletin board for this game like the one in this post, or you can draw a simple one on the board. I drew one on the board and used two colored magnets I already had because that was what worked best for me.
I like the visual approach of the explanations from Kate’s Math Lessons. She has a very understandable way of explaining how the triangle inequality theorem works. Students could read through this webpage as a way of reinforcing or reviewing what they have learned.
Also, there is a simple and easy quiz that students can complete. The website has three tabs and the third tab is practice. Students click on the quiz and they have 5 questions to complete. One thing that I love about this practice is that it is no prep for me! It gives students a different look at things, and sometimes that makes all the difference for a students who struggles to grasp the concept.
When you search for activities for triangle inequality theorem, you’ll find a lot of discovery-like activities. I’ve created my own activity because I like to have background building and reflection built into my discovery labs. I use strips of paper for students to use as they discover what the rules are for making triangles. When you look on Pinterest you see people using all sorts of things to make triangles like spaghetti and straws. It doesn’t really matter what you use for the triangle sides. The point is to let the students figure out the rule before you tell them.
When students finish with the discovery lab, I have them add an example and non-example to their interactive notebook. They use the same the triangle sides we just used in the activity, but now they’re a permanent reference for students as well.
One of my favorite sites is Illustrative Mathematics. They have an amazing collection of performance tasks for Common Core math concepts. These tasks get students to go further than the simple mechanics of working through a problem. When students work on performance tasks they are forced to think more.
This task brings a real-life application to the triangle inequality theorem, using walking lady bugs to illustrate the theorem. Now I just need to make sure that my colleague knows about this task before she teaches this concept next month. She has about 1000 ladybug things that decorate her room. She will be so stoked to know about this task and her students will get a cool math challenge!
Sometimes kids need challenge problems that make them get frustrated. This video presents a problem that works great for that. I have a lot of students who give up really fast when the problem is “too hard.” Really, they’ve just never seen a problem like this one and they don’t want to look bad in front of others. I like to make sure that students have opportunities to show their growth mindset and learn that making mistakes isn’t a bad thing- it’s how we learn. If they don’t have a growth mindset yet, then we work on getting one through challenging problems like this one.
This video shows one problem and how to solve it. You can pause the video and let students try to figure it out. Then, restart the video and they show how to solve the problem mathematically. It will really challenge your students.
If you’re looking for some additional practice for the triangle inequality theorem, Khan Academy has a few problems to practice with. Sometimes when students are absent, I have them watch the Khan Academy video and complete the 4 problems. Also, this could be used as homework or for fast finishers.
Try one thing
In my class we only have a few days to teach this topic, so we don’t really have enough time to complete all of these activities. If you’re in the same boat, then you’ll just have to choose those activities that will work best with your students and your teaching style. I hope you try one of these activities and that it brings a bit of fun to your class. Thanks so much for reading! Until next time.
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