I love teaching students about irrational numbers. In 8th grade math we focus on identifying irrational numbers and approximating them on a number line. This concept is so fun for me to teach because it blows their minds. They’ve never considered that a number could be approximate and have no exact location on the number line. Some of my students get it and believe it right away. Other students resist and don’t want to believe it. Luckily, by teaching them this concept you can blow their minds without crumbling their world view- seriously, so fun! Another great thing about identifying irrational numbers and approximating them, is that this topic is very gettable. It can be a real win for struggling students. That’s what makes it one of my favorite to teach. In this post I’ll walk you through our entire interactive notebook unit that goes from identifying what irrational numbers are to approximating irrational numbers.
Teaching Irrational Numbers with Interactive Notes
I’ve used interactive notebooks for about 5 years and each year I try to improve my practices. I’ve come up with 5 components that each unit contains in order to make my notes more cohesive and easy for students to follow and use. Each notebook unit looks a little different with each topic that I teach, but there’s an overall flow to the madness. Students use their notes for different reasons (from initial instruction to reference for review), and this structure gives students many opportunities to interact with their notes.
I Can Statements
We start each unit off with our I can statements, which gives us a chance to establish the learning objectives for the unit. This year I’ve been having students circle the verb, underline the main idea, and put a squiggle under the key words to help them really understand what they’re expected to learn and do.
I have two sets of I can statements for this topic. The first one is distinguishing between rational and irrational numbers. This topic is basic, but it’s a necessary building block for approximating irrational numbers. When students focus on the verbs they’re performing, they can more easily understand if they’re getting the material or not.
The other set of I can statements is for approximating irrational numbers. In 8th grade math the only irrational numbers that students work with are pi, imperfect square roots and imperfect cube roots. So, that’s what they’ll be approximating on the number line.
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Activating Prior Knowledge
Students are already somewhat familiar with pi when they start this unit, so there’s a base for them to build on. I like to have a background building exercise that ignites some of their prior knowledge. This true or false activity gets kids thinking, and they use these simple true and false cards to choose a side. Not only is this a fun way to practice, it also gives me as a teacher a good sense of where they’re starting. After we’ve complete the true and false activity, then students write a summary of their understanding. This gives them a small base to connect the new learning for the day to.
They can keep the true and false signs in the pocket in the back of their notebooks and we can use them again for another activity. This gives students a way to interact with the material and it forces them to take a stance on what they think. When using these cards, I have students hold their signs on the desk first so no one else can see, and then I have all of them raise the signs at the same time.
Using Graphic Organizers in the INB
After introducing the topic and building background, now it’s time to give students the input that they need to learn the topic and support them during practice. We use a variety of graphic organizers to help students keep track of steps and processes. Graphic organizers are a great way for students to see that there is order in what they’re doing. Some students need a tremendous amount of support and scaffolding and these kinds of notes give all students an entry point to understanding the input of the lesson.
Rational vs. Irrational Chart
This is a simple t-chart where students can organize the characteristics of rational numbers and irrational numbers. I start by having students write the characteristics that they remember from the rational and irrational introductory presentation. Then, they share with their partner and get additional ideas. In the end we share with the class and students finish up their lists.
Approximating Imperfect Square Roots to the Tenths Place
I created a way for students to approximate imperfect square roots with fractions. They just have to figure out how many numbers are between the two perfect square roots and that becomes the denominator. Next, they figure out how far the imperfect square root is from the perfect square root just before it. This number becomes the numerator. If they convert this to a decimal then they will have an approximation. If students need a reference for this process, they can use this foldable graphic organizer.
Practicing approximating irrational numbers
I like to include some practice in the interactive notebook. We follow the I Do, We Do, You Do method and I model some of the problems for the students. This really is based on how well they’re getting it. The other day when I was doing this in class, I could tell that my students were ready to try them on their own. In that case, I let them give it a try. Sometimes, I give some students a head start and then those who need more modeling follow me. There are always kids who like to speed ahead of me and this approach gives them permission to do that.
Cut and Paste Activity
Another activity that I like to put in the interactive notebook is this cut and paste activity. Students have to place the approximations of the square roots onto a number line. This activity is very interactive and kids like to have the hands-on experience. With this activity there’s enough room left on the page that you can have students summarize their learning or list the steps that they follow to approximate. This gives them a chance to process their learning.
Cheat Sheet
Another resource that we add to the interactive notebook is a cheat sheet. Some people call it an anchor chart. I life for it to have some parts that students add and other parts that are printed for them. On this one students have a number line where they can record the perfect square roots. They can reference this when they do their practice and they save themselves time. Also, they have a quick examples to look at for approximating to the tenths place. I love this for an anticipatory set because you can get them process information from recent lessons.
Putting it all together
I hope that you and your students benefit from these ideas. Remember that you don’t have to include every part in your interactive notebook. You just need to figure out what works best for you. I don’t always get to everything, and I find that different classes need different support. What’s most important is that students are seeing the concept in different ways and that they get lots of meaning repetition. Good luck on your INB journey!
You can use these notes as inspiration for your classroom, or grab the whole set ready to print and go here. For activities and ideas for practicing approximating irrational numbers, check out the post “8 Activities to Make Approximating Square Roots Magical.”
Thanks so much for reading. Until next time.
