How I teach The Real Number System, Classifying Real Numbers, and Closure

This is part of my Unit 1 Interactive Notebook for Algebra 1. You can view the rest of it here.

1.1 – The Real Number System, Classifying Real Numbers & Closure

There’s nothing trickier than picking the very first topic to cover in all of Algebra 1. So many options, so what goes first?

To start the very first unit of Algebra 1 off, I begin by talking about the real number system and how we classify numbers.

Why oh why, is this where I start, you might ask?

Instilling this vocabulary is very important in helping students be able to hold fluent conversations about math. I can’t tell you how many students I’ve had in Algebra 2 (or Pre-Calc!) over the years that have asked “what’s an integer?” and they are unable to complete a problem that they otherwise would know how to do solely because they lack the basic vocabulary and don’t understand what the question is asking.

This is silly, and I want to prevent these things from happening as much as possible. Math really is its own language, and helping students learn it will allow them to be more confident and much more successful in the long run.

Next, I introduced my first flowchart of the year. I want to instill in students that their notebook is really a great reference, and that there are tools in there that are really meant to help them. We quickly filled out 3 flowchart examples, to show students how they can use this if they get stuck on their homework. (Note: flowcharts are included in a separate bundle and are not part of the Unit 1 interactive notebook kit, which contains notes and warm-ups).

To finish off the class, I used the warm-up on Closure from my set of Unit 1 Warm-Ups as an exit slip. I don’t always have a special, topic-specific, pre-printed exit slip for my lessons because I often use these exit slip templates that I print off in mass quantities at the beginning of the year. That said, it’s really nice to have a formal exit slip for the first few experiences of the year.

Next day – I like to begin each day with a recap warm-up over the prior day’s lesson. Students work on the warm-up during the first 3-5 minutes of class and then students present solutions. Like the notes, this gets glued into their interactive notebook (INB) for quick reference. I love including the warm-ups because it is like the summary of the entire unit and students can quickly see examples.

This lesson is part of my Unit 1 Interactive Notebook for Algebra 1. You can view the rest of the unit here.

Like what you see? Grab the entire download-and-done unit!

What do all those symbols mean?

Pages marked with the “understanding” symbol provide special opportunities to slow down a topic and build conceptual understanding so you can speed up later and in the long run. These will be essential in developing your students’ understanding of what it is that they are doing and why.

Pages marked with the “flowchart” symbol are the perfect companion differentiation tool to help ensure that all students can find success. They are great study tools that students can refer back to over and over again and to turn to when they need help getting “un-stuck.” Use them to introduce a topic!

Pages marked with the “bonus file” symbol provide extra utility to the interactive notebook. Starting an interactive notebook can feel really daunting, but it doesn’t need to be. These pages are those “extras” that make an interactive notebook function all the better, and make your life easier, too!

These understanding builders are included in all Algebra 1 interactive notebook kits.

Flowcharts are not included in notebook kits and are sold separately here.

Bonus files are special to the mega bundle of all Algebra 1 notebook kits, sold here.

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