How I teach Properties of Real Numbers

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

1.2 – Properties of Real Numbers

Properties of real numbers. What a snooze fest, am I right? WRONG!

This set of notes turns that notion upside down and gets students involved in creating their own examples to demonstrate each property to make a lively and memorable lesson.

You might wonder, “why would I want to teach properties of real numbers?” It’s a simple way to help students start thinking algebraically and flexibly, especially after having a long summer off from math. These properties demonstrate nice rules for manipulating and moving numbers and variables around in expressions and will help them understand why certain moves are “legal” when we start solving equations. Helping students think flexibly and understand the structure of an expression is a huge step in their journey toward mathematical fluency.

To really increase student engagement during this lesson, I often ask students if they can help figure out what the rest of the property should be. “Okay, so if we have a+b, what is that the same as?” Oh, b+a. Sweet, we just figured out the commutative property of addition. Then I start asking students to help me make our own example by volunteering their own favorite numbers. Students LOVE sharing their favorite numbers and just making up random numbers to use in our own class examples. It seems so small, but it makes a HUGE difference for boosting engagement.

I repeat this process throughout the rest of the properties in this foldable having students see if they can guess what completes the property and then generating examples by picking their own favorite or random numbers.

The next day – we start class off with a recap warm-up to review the properties and to encourage the habit of referring back to their notes. Students can share their answers and can use their properties to defend how they know they are right.

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.

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

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!

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

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!

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

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