1-2: The Field Axioms
Platform: Video + Textbook
Why are you allowed to regroup numbers, change their order, or add zero without changing an answer? These familiar algebra moves are supported by a collection of rules called the Field Axioms.
You have been using many of these rules for years—often without realizing it. In this lesson, you will give those rules names and learn how they justify the steps we use when simplifying expressions and solving equations.
Do not worry about memorizing all eleven axioms at once. Focus on recognizing the pattern each axiom describes and connecting it to a familiar mathematical move.
Explore
Warm-Up — Do These Quickly
Complete Lesson 1-2’s Do These Quickly: Q1–Q10 in your notebook. Spend no more than five minutes. If you get stuck, skip the problem and check the solution afterward.
Watch the lesson video below with your notebook open. Pause whenever you need to take notes, work through examples, and try problems on your own before continuing.
Treat the video as an active exploration, not a lecture to watch passively. The more you pause, think, and work alongside me, the more you will gain from the lesson.
Notebook Check
Before beginning the textbook work, make sure your notes:
- include all eleven Field Axioms;
- contain an example that helps you understand each unfamiliar axiom; and
- clearly mark any axioms that you still find confusing.
You may use a Field Axioms reference page on the Chapter 1 test. The goal is not simply to copy the list—it is to organize the information so you can recognize and apply the correct axiom.
Practice
Find Lesson 1-2 in your textbook and complete the two sets of work below.
- Problems: #1, 2, 4, 6–10
Show enough work to support each answer.
Check and Correct
As you did in Lesson 1, check your answers using the solutions manual after attempting all the assigned work. Do not erase incorrect work. Mark corrections in a different color and make sure you understand what caused each mistake rather than simply copying the correct answer.