<p>This lesson introduces you, the student, to the Cartesian coordinate plane. The goal is that you understand Cartesian coordinates well, and that you are able to master using them to describe points in the Cartesian plane.</p> <p>First, you will explore the idea of using pairs of numbers to describe intersections of roads that are arranged in a grid pattern. You will use the insights you gain there to learn how to describe points in the Cartesian plane using pairs of numbers called coordinates. You will also learn how to locate a point with given coordinates.</p>

<p>The aim of this unit plan is to introduce students to the addition, subtraction, multiplication and division of integers, where negative integers are involved.</p> <p>The goal is that students become proficient in the following:</p> <ul> <li>adding and subtracting integers using models;</li> <li>adding and subtracting integers using paper and pencil;</li> <li>multiplying and dividing integers using paper and pencil.</li> </ul> <p>The plan consists of 4 lessons, which can be taught in 4-6 lesson-hours.</p> <p>First, students are presented with a counter model of the addition of integers. The patterns they observe are used to present the most important, and basic, rules of addition of integers, including:<br /> “adding integer <em>-b</em> is the same as subtracting its ‘opposite’ <em>b</em>”.<br /> The rules are presents both in words and symbolically.</p> <p>Students are then presented with a counter model of the subtraction of integers. The patterns they observe are use to present the basic rules of subtracting of integers, especially:<br /> “subtracting integer <em>-b</em> is the same as adding its ‘opposite’ <em>b</em>”.</p> <p>Finally, students are introduced to the rules for products and quotients of integers. The connection between the latter rules and those for addition are highlighted.</p>

<p>The aim of the plan is to introduce students to the concepts of the Cartesian plane and Cartesian coordinates. First, students are introduced to the the idea of identifying road intersections in a square grid (of roads) using ordered pairs of numbers. They then translate these ideas into the concept of Cartesian coordinates and develop proficiencies in the following:</p> <ul> <li>writing coordinates of given points on a graph as ordered pairs of numbers;</li> <li>plotting ordered pairs of numbers on the Cartesian plane;</li> <li>reading and identifying points in the Cartesian plane;</li> <li>connecting points in the Cartesian plane to make lines and shapes.</li> </ul>

<p>The article is meant to present to middle and high school students the principles underlying the rules of arithmetic of the integers and the rational numbers. The aim is to demystify and simplify those rules so that the student can master the arithmetic without the usual amounts of confusion.</p> <p>A model of the addition and subtraction of integers is provided via a GeoGebra applet. The student will have the opportunity to use the applet to investigate the addition and subtraction of integers.</p> <p>The student should see that, in the case of addition and subtraction of integers, there really is just one main rule to remember, and the rule follows a pattern that the student should find not too hard to remember!</p> <p>Exercises are provided throughout.</p>

<p>The article comprises some lecture notes for a university course in Basic Introductory Mathematics that I taught in 2004. The notes pertain to the topics ‘Limits’ and ‘Continuity’.</p> <p>I am aware that there are many errata. In time, provided I find the LaTeX original, I will make the corrections.</p>

<p>This short article aims to describe what variables are for the high school mathematics students, and what one can do with them.</p>