## 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

## How do I set up an interactive notebook?

If you need suggestions about what to put on the first few pages, check out this post.

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

Classifying real numbers is so much more important that we often give it credit. Math is very much a foreign language class as much it is a class about patterns, persevering, and problem solving. Without knowing the language of the land, math class can be so much more difficult than it needs to be and needlessly can lose students who are otherwise capable.

I like to start by explicitly teaching vocabulary and helping students look at distinguishing the similarities and differences between sets of numbers. This also embeds several opportunities to review representations of numbers from middle school.

I’m all about making my notebooks highly visual for students, so including flowcharts are a MUST. I often put them before the notes for a topic as a visual introduction and reference sheet for students. You can get this classifying real numbers flowchart here.

I always start the next class with a recap warm-up of the prior day’s lesson. I use this as an opportunity to encourage students to start using their notes to refer back to, and I can use it as an opportunity to catch misconceptions and iron out any lingering questions students might have from the day before.

## 1.2 – Properties of Real Numbers

Properties of real numbers may seem like a bit of a snooze fest for notes, but I have this foldable set up where students can help build examples to demonstrate each property which makes it much more lively. This is a great way to help students start thinking mathematically after being on vacation for the summer. Again, the next day we do a recap warm-up where students apply their learning from the day before and are encouraged to use their notes. This helps to start building the notion that their notebook is meant to be used and referred back to, over and over, day after day.

It’s one thing to say that students should use their notebook as a tool. It’s another to explicitly teach it and integrate it into our daily class routine. Studying and referring back to notes actually needs to be explicitly taught, and Turing it into a daily warm-up habit goes a long way.

## 1.3 – Order of Operations

PEMDAS, GEMDAS, GEMS, BEDMAS…whatever you call it, I offer this order of operations “tips for success” page with that acronym. This is a quick reminder for students that emphasizes the different grouping symbols and the need to work from left to right.

The notes include common mistakes students could make as well as an opportunity to write some “notes to self” after completing each problem that had a potential common mistake in it.

## 1.4 – Evaluating Algebraic Expressions

Evaluating algebraic expressions is a great topic to include in the first unit of the year. Not only does it reinforce order of operations, but the substitution property that students will need to use countless times. As always, we start the next day’s class with a recap warm-up to encourage students to refer back to their notes, and to allow me to iron out any misconceptions that may have developed.

## 1.5 – Combining Like Terms

Combining like terms can seem like such a simple concept to us math teachers, but it is actually pretty tricky for students. This set of notes encourages students to think about what it is that they are doing, and forces them to face some common misconceptions along the way! Application problems like finding an expression for the perimeter of a shape are included!

## 1.6 – The Distributive Property

This set of notes on the distributive property is sure to touch on common mistakes students might make…like having a 4+3(x+2) and students wanting to make it a 7(x+2) or what to do when there’s just a negative sign in front of parentheses like -(5x-4). These all trip students up, so we intentionally practice them to make it less scary.

## 1.7 – Translating Algebraic Expressions, Equations & Inequalities

Color code. Color code. Color code. Please just read this post where I go into my method for teaching translating expressions, but, trust me, when I say: color-coding is ESSENTIAL.

I start off this topic by going over key words and phrases, and then our notes focus on applying our color-coding strategy to translate written expressions into algebraic expressions, equations, and inequalities. This is such an important lesson to start off the year, because I like to incorporate equation writing into each unit.

## 1.8 – Solving 1-Step & 2-Step Equations

Before we start solving equations, it’s of the utmost important that students know what a solution actually is. How can they check their work if they don’t even know what it is that they did?

We start by looking at the definition of a solution, which is any value that makes an equation true. We use replacement sets to help locate the solution(s) to two equations. One of them is even quadratic! It’s as simple as substituting and evaluating the expression (see how that skill always comes back!).

We then move onto actually solving 1-step and 2-step equations. Lots of common stuck-points are included and students are encouraged to check their solutions on every 2-step equation. It takes quite a bit of practice for students to be comfortable checking their work, so constantly relating it back to that definition of a solution being a value that makes an equation true is a must!

## 1.9 – Solving 2-Step Inequalities

For our last lesson of the unit, we do solving 2-step inequalities. Before doing any solving, we do a sign-flipping investigation that is meant to really build up the understanding of why it is necessary to flip the inequality symbol after multiplying or dividing both sides of an inequality by a negative number.

We then move onto a foldable that covers the different types of endpoints, includes a reminder about flipping the sign, and lots of practice of solving, graphing, and writing the solution set.

## 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.