Teaching approximating irrational numbers is probably my favorite topic that I teach all year. It’s the second thing that we teach in the fall, and I get pretty stoked for it. I’m not quite sure why I like it so much. It’s probably the cool pattern that it makes. Also, the idea that numbers are irrational and that they actually don’t have a place on a number line makes me giddy (and yes, I know how math nerdy that sounds!). To help you find engaging ways to practice approximating irrational numbers, I’ve compiled a list of some of the activities and resources that I like to use. They get students just as excited about approximating irrational numbers as I am!
Here’s the list:
- Task Cards
- Approximating Irrationals Mazes
- Number line in INB
- Two Truths and a Lie
- Class Activity on a Number Line
- Targeted Feedback
- Number Talk Anticipatory Set
- Visual Representation Video
Approximating Imperfect Square Roots Task Cards
Task cards are a staple in my classroom. They have so many uses. They can be used individually, with partners, in small group games, and with the whole class.
For this particular topic I used the Approximating Imperfect Square Roots Taks Cards with the whole class to practice together. I showed individual task cards on the overhead projector and students worked to solve one at a time. This practice came directly after the lesson, so it worked as the “we do” part of the learning sequence.
I especially love these task cards because the student work page has number lines on it for them to record their answers and get lots of practice approximating on a number line. These task cards make a great low prep, high impact activity.
Approximating Irrational Numbers Mazes
Once students are ready for independent practice, mazes are a great way for them to see if they’re on the right path (hah, see what I did there?!) I use these 3 approximating irrational numbers mazes for bellwork later in the unit to not only start the class off with practice, but to also give me a quick formative to see how my students are doing. I can see the path students are following and quickly see who is still struggling and which types of questions are throwing students off.
The first maze asks students to approximate a square root to the nearest tenth and the second asks them to approximate cube roots. The third maze asks students to find between which two whole numbers the approximation of a square or cube root would fall.
Often I don’t get to all three mazes during the unit, so I’ll use one later for cyclical review. I’ve found that I can even bring back a maze again after a few months as a review. 
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Number line Activity in Interactive Notebook (FREEBIE)
I created this number line that I print on 11 X 17 paper for activities like approximating irrational numbers. The fact that it’s over-sized makes it more interesting to students. They fold it up and save it in their interactive notebook or it can be glued in the back. At any point students can pull their number line out to do a class activity or to use as a math tool when problem solving.
I have my students write the perfect square roots onto their number line. So, below the 2 they’d write √4, etc. This gives the students a handy reference when finding imperfect square roots. I also encourage them to make their own smaller number line when they don’t have one available (like when they’re taking a test, etc.).
Two Truths and a Lie
I found this little gem when I needed something for my “I got this” group to work on. This Two Truths and a Lie game gave students an irrational number and three representations of that number. Then, they had to decide whether each representation is true, or whether it’s a lie. Finally, they justified their answers.
This activity worked great for my fast finishers. They could work on it on their own and they loved the idea that there were lies (wrong answers) on it. I especially liked that they had the opportunity to make their own truths and lies at the end.
Number Line Game for Approximating Irrational Numbers
This number line game can be played in small groups or with the whole class. Questions are presented on task cards, but students take chips/markers to show their answers and their confidence levels. This game really pushes students to not just answer questions, but to evaluate their answers.
To play, each player has a certain amount of triangles (game markers) with point values on them. These act as a way for students to wager on how confident they are on their answer (like chips). A question is presented to the group and students place the little triangle where they think the square root goes on the number line.
If they’re correct, they get the points listed on their triangle. If they’re incorrect they don’t get any points. Having students wager on their own answers is a simple way to add a little fun to practicing this topic.
This game can be played as a whole class review game, or in math centers as a partner/small group activity.
Targeted Feedback with SmartPals
A couple of years ago my co-teacher and I started doing this targeted feedback activity as a way of making sure that students were getting feedback as they were learning. It can be a little unwieldy in a big class with only one teacher. But if you have about 30 students it works well. Basically, students show how they got their answer on a SmartPal and they have to get it checked by a teacher. They have a stamp sheet with them and get a stamp when they get the question correct. To get even more feedback for students, I like to have fast finishers help with the stamping as well.
Number Talk Anticipatory Set (Quick Discovery Activity)
This number talk activity extends students’ understanding of approximating irrational numbers. It’s perfect for an anticipatory set or quick introduction to this topic. While we’re focusing a lot on imperfect square roots, we can extend that by looking at imperfect cube roots and by pushing kids to make the connection.
For this activity I use these 1-inch cubes. I give each partnership a random number of cubes between 1 and 30. They have to build a representation of their numbers’ cube root. It is really fun to see them work together to come to a conclusion. Some of the groups get perfect cube numbers and they kind of get a kick out of that.
Visual Representation Video from PBS Learning
This video is a short way of showing how imperfect square roots work. It’s easy to follow and works great as an anticipatory set or a flipped classroom assignment. This guides students to work through the problem solving process in a step by step manner. It comes with lesson plans to turn this activity into a full class length activity.
Taking it to the Classroom
With eight great ideas and resources, I hope you’ve found at least one new activity for your unit on approximating irrational numbers. Whether you need additional practice or an engaging hook, these activities bring this topic to life. Plus, students love the effort we make with engagement strategies. A bit of novelty goes a long way to help students get, and remember, what you’re teaching.
With so many fun ways to practice approximating irrational numbers, I encourage you add something new to your unit and make learning this concept a bit more magical.
Thanks so much for reading. Until next time.
