We start our school year out with teaching perfect square roots and cube roots. It’s a perfect topic to start with because it’s relatively easy and the students already have some background with it. This means kids have success early on and you can build on that as you go. Also, square roots and cube roots will be used again during the year when we approximate irrational numbers and solve with the Pythagorean Theorem. Let’s look at how we can teach perfect square roots and cube roots using an interactive notebook.
Using an interactive notebook to teach square roots and cube roots
I’ve been using interactive notebooks with my students for about 5 years. Every year I try to *up* my game a little bit. Over the past 6 months, I’ve worked hard to up my game a lot. I felt like something was missing in my use of INBs so I sat down and identified the components that I would love to have for every unit (you can read a general overview of all 5 components in this post). Now, let’s look at what these 5 components look like when teaching square roots and cube roots.
I can statements
Teacher guilt is real. I used to feel guilty that I didn’t really incorporate the kid friendly version of the standards. They sat there on the board and taunted me all day long. Students hardly even glanced at them. Now, I use it in our INB and we refer to it often.
Each unit starts with a page of I Can Statements like the one above. This breaks down the specific concepts and skills we’ll focus on while learning the perfect square roots and cube roots. The three main learning goals are:
- I know all the perfect squares and perfect cubes between 1 and 12.
- I know all the perfect square roots and perfect cube roots that equal 1 to 10.
- and I can solve for x in a problem like x²= 64.
I figure that even though students can use a calculator, there are some basic calculations that students should be able to do in their heads. The first two learning goals focus on fact fluency, memorizing perfects squares and square roots and cubes and cube roots. Based on the 8th grade standard, students also need to be able to solve for x using square rooting and cube rooting.
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Word Splash
The second piece that goes into students’ interactive notebooks is basically an anticipatory set for the whole unit. Anticipatory sets really help kids to activate their prior knowledge about a topic. I think of it as jump starting the learning. This word splash activity can be seen as a game. First, students read the directions. Next, I give them 3 minutes to individually write down everything they know about square roots and cube roots. Then, we share our answers with a partner and then with the class. It serves as an activity with a low barrier to entry, so all students can experience success, and we get our minds focused on the topic at hand.
Square roots and cube roots foldable notes and graphic organizers
The graphic organizer that I use for teaching this topic is a place where students record the perfect square roots and cube roots. We use these as a way to practice. Students can challenge each other or work together to quiz each other (similar to how you would with flashcards). Also, it’s a place where students can reference these numbers. I can’t really explain why, but this is one of my favorite foldables. It’s simple and straightforward, but it’s very effective.
Students use this foldable graphic organizer a lot. I only include the perfect square roots and cube roots from 1 to 10, but this year I’m going to have my advanced class memorize up to 20. That should be fun.
Practice makes perfect
The next part of our INB unit is practicing solving using square roots and cube roots. I find this to be mostly intuitive for kids, but it does take them a few repetitions to really grasp what is happening. We work through the problems together and I make sure that students have a chance to discuss their work. This is a great way to model the thinking process students will use when solving, and it provides an easy to use reference for students when practicing later
Not only do these worked problems help students work with square roots and cube roots, it’s also the first time that students see equations in my class. And as you know, equations is a common theme throughout the rest of the year.
This step is basically the “We Do” part in the “I Do, We Do, You Do” lesson sequence. For these problems, you can use them as somewhat of a discovery activity. Let students try a problem on their own before you tell them how to do it. One of my big areas of emphasis is to encourage students to attack unknown problems. This will serve them well on tests, as well as in life. They need lots of chances to get out of their comfort zone and try things on their own. Of course, since this is the modeling portion, I have students talk about their process and answers in small groups and then as a whole class.
Cheat sheets and reminders
I don’t have a classic cheat sheet or anchor chart for this topic (again, you can read more about each component in our INBs here). Instead of one half page cheat sheet like I have for most topics, we use a couple of smaller references to help students remember key ideas related to this topic. One of them is a reminder of what each part of a radical is called. It’s a simple vocabulary boost.
The other part of the cheat sheet gives students repetition with expressing the square roots and cube roots with variable notation. Later on this serves as a place where students can review how to solve for x when radicals are involved.
I’ve found that not all cheat sheet have to look the same across topics. Instead, these are final reminders and tips for students as they begin their independent practice. I’m sure that as I use them more they’ll continue to evolve. That will give me something to add to our notes for next year :).
That’s a wrap
I hope that this has given you some ideas on how to teach square roots and cube roots to your students. Remember, there’s no one right way. You have to do what works best for you as a teacher and for your set of students.
You’ve got this. Students get so much more out of thoughtful, interactive notes. You can use these ideas as your own jumping off point, or grab all the notes I use in this notes pack. Thanks so much for reading. Until next time!
