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.

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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.

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Algebra 1 Unit 1 Interactive Notebook Pages – The Foundations of Algebra

Starting the year off right is SO important for any class, but especially in Algebra 1, in particular. Everything that is done in the first unit lays the foundation for everything to come throughout the rest of the year, so there is is a lot riding on starting the year strong.

Here’s what to include in your first unit of Algebra 1 to start the year off right…

Students NEED to have a strong foundation, or else they’ll be fighting an uphill battle all year, which is no good. I’ve spent a lot of time thinking about what topics are most important for students to know (from vocabulary to skills), so that each following unit has a strong foundation. Here are all of the notes I used with my students during the 1st unit of Algebra 1.

If you want to look inside any of the pages included in this unit, you can take a look at these topic-specific posts for a more detailed look!

  • 1.0 – Notebook Setup
  • 1.1 – The Real Number System, Classifying Real Numbers, & Closure
  • 1.2 – Properties of Real Numbers
  • 1.3 – Order of Operations
  • 1.4 – Evaluating Algebraic Expressions
  • 1.5 – Combining Like Terms
  • 1.6 – The Distributive Property
  • 1.7 – Translating Algebraic Expressions, Equations & Inequalities
  • 1.8 – Solving 1-Step & 2-Step Equations
  • 1.9 – Solving 2-Step Inequalities
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How to Set up an Interactive Notebook for Algebra 1

Getting started with interactive notebooks? Here’s what to do!

The logistics of starting an interactive notebook is one of the most dauting barriers for math teachers. Here’s a set of simple 3 steps to take to get started!

1. Number the pages (If nothing else, do this!)

You will want to be on the same page as your students, quite literally, when using interactive notebooks. Being on the same page allows you so many opportunities to promote study skills and refer students back to a particular topic to help them get “un-stuck.” Promoting study skills is one of the biggest benefits of interactive notebooks so don’t skip this step.

WORD OF CAUTION: Make sure to number the pages as the very first thing that you do! Interactive notebooks get very thick over the course of a semester, and it will be difficult to write in the corners by the time the notebook is almost complete.

If you want more tips on choosing a notebook, read this post about What notebook should I use for an Algebra 1 Interactive Notebook?

2. Make a Plan

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What notebook should I use for an Algebra 1 interactive notebook?

If you’re just getting started with using interactive notebooks with your Algebra 1 class, you might have a few questions about what type of notebook you should use, how many pages, and how to make sure all of your students have one to use. In this post, I’ll try to address them all. If I leave something out, leave me a comment so I can answer your question!

What type of notebook should I use for interactive notebooks?

As a die-hard spiral-notebook lover, it even surprised myself when I first realized that composition books are the best choice for interactive notebooks. They had never been my first, second, or even third choice for my own personal note-writing over my life, so I was a bit resistant to trying them for the first time. Here’s what I found:

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How I teach factoring + Factoring Investigation

If you’ve followed me for a while, you might already know that I’ve taught just about every factoring method under the sun over the years.

Through many trials and errors (along with teaching progressively more advanced classes such as pre-calculus), I have come to the conclusion that factoring by grouping is the best and most flexible method for students to learn.

Not only is it easy to catch onto and has a built-in check halfway through the process, but it’s flexible enough to keep being used in any future math course (something that is certainly not true for all factoring methods).

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Made for Math Freebie: A Daily Pear Deck Template to Boost Student Engagement & Get Authentic Formative Assessment in Distance Learning

Whoo boy, that was a mouthful of a title, but it’s spot on! I’m now back in the thick of distance learning, once again, and this time it’s quite different than what I experienced in the Spring. In the Spring there were a lot of pre-recorded class sessions and we only met for 30 minutes 2x a week to do quick check-ins and a super fast mini-lesson. I also already knew all of my students so getting them to engage really wasn’t difficult at all.

This time around, it’s really different. Classes are 90 minutes each, 4x a week, and we’re doing a whole year of content in a semester. I also know only a small handful of my students because they’ve either been in my Advisory class for the last two years, or I had them last year and they have the total pleasure (mild sarcasm) of learning with me again. I’m grateful for all of the pictures of their faces on our online gradebook, because that’s the only way I know what any of them look like.

There are lots of blank screens and the chat box can be pretty quiet, but don’t let that intimidate you! I’m so excited to report that, amongst all the negative noise this year has brought, I’ve got something really good going on. I’ve found that Pear Deck has been a GAME CHANGER for student engagement and getting formative assessment feedback that is even better than what I get in the classroom in a normal year!

If you’re not familiar with Pear Deck, I would HIGHLY recommend it. I have found it to be the closest way to recreate a typical classroom environment.

I use Pear Deck in conjunction with writing my notes under a document camera that I am screen-sharing through Google Meets. Students log in at the beginning of class every day, and it has quickly become a routine. I have more students engaging through Pear Deck than I have experienced over past years in the typical, in-person classroom setting that we’re all used to. If I have 26 students logged in on Pear Deck, I get 23 responses! That might not be a 100% success rate, but how many times in a traditional, in-person class do you get EVERYONE responding to every one of your questions?

At first, I was trying to be so fancy…Let’s make a new Pear Deck for every class every day, she said, only to later find out how unlikely of a routine that would be to maintain. So, here’s what I did–I made myself a Pear Deck Google Slides template that I can use with any of my math classes (this year, I have Algebra 1/Algebra Support, Pre-Calculus, and Statistics) and reuse every single day. All I have to do is launch the Pear Deck at the beginning of each class and generate a fresh code for my students and we’re in business! If you want to be extra fancy, you can log in early and grab a link for students to join with (so they don’t have to use a code) and post it to Google Classroom for a super painless way to join the Pear Deck every day.

So much of formative assessment are things that come up on the fly, and this template allows the flexibility to recreate it beautifully in a virtual setting. When I was pre-planning everything into Pear Deck, this didn’t allow me that same flexibility to ask questions if I didn’t think of adding them ahead of time. DISCLAIMER: You can add slides on the fly once a Pear Deck has been started, but I haven’t found a way to add custom slides that really fit my math-class needs.

I have created a Pear Deck Google Slides template that has multiple copies of the slides I like to use with my students for formative assessment so that there’s always a fresh slide of that type available if I decide that’s the type of check-in I need to do in that moment. When I use the Pear Deck, I always turn it to instructor-paced, which allows me to change slides as needed, and students have no idea that there may be 7 identical prompts in a row that all say “Ask me a question!” If there’s a need for me to show another one of those slides later on, I can swap to a fresh slide so they can start typing again. If I don’t, no harm, no foul.

When the moment arises, I verbally direct students to swap over to their Pear Deck tab to respond to the question/prompt I just gave them. At this time, I turn my screen into split-screen mode where half of it is showing the Pear Deck slide in question (on projector mode) and the other half is still showing my document camera. Again, this duo has made student engagement in the lessons so much higher than simply relying on them to type into the chat box or asking them to unmute themselves and actually speak (I do both of those, but none of them come even close to the same level of student participation that I get with Pear Deck).

I hope you try incorporating this into your daily classroom routine! It has really been fantastic for me and I hope it does the same for you!

Everything You Ever Wanted To Know about Using Exit Tickets in your Math Classroom

Although the idea of exit tickets is well known, figuring out how to master using them in your middle & high school math classes is a different story. From finding time to create them, remembering to actually give them, and teaching your students how to do them, this 5-part blogging series covers it all. At the end, there’s even a bonus installment that’s all about how to turn your exit tickets digital!

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How to Make a Digital Exit Ticket: Turn Your Exit Tickets DIGITAL!

This is a bonus installment in the Everything You Ever Wanted To Know about Using Exit Tickets in your Math Classroom blogging series to show you how to take an exit ticket template that you use and love, and turn it into a digital format for your students to complete. As we grapple with hybrid schedules and the possibility of distance learning, this is more important than ever!

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Implementing Exit Tickets in Middle & High School Math – Why I Failed Before & How I Fixed It

This is the fifth installment in the Everything You Ever Wanted To Know about Using Exit Tickets in your Math Classroom blogging series. If you haven’t already, check out the first four posts and then keep reading!

Read Post 1 here – 5 Reasons you Should be Using Exit Tickets in Your Middle & High School Math Class. This post covers what an exit ticket is and why you would want to use one in your math class.

Read Post 2 here – How often should I use an exit ticket? A secondary math teacher explains all. This post discusses how often you should be giving an exit ticket, and ways to save time in creating them so you can actually keep up and make it routine.

Read Post 3 here – How to Implement Exit Tickets like a Math Teacher Pro. This post discusses how to introduce them to your students and tips for actually remembering to give them each day!

Read Post 4 here – What do I do now? What to do with the exit tickets after your students hand them in. Reviewing, feedback, grading, and more! This post goves over all of the logistics and teacher-decisions behind what to do after your students actually complete an exit ticket. This one is jam-packed with easy-to-implement ideas!

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