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YOU are better than YOU think. Show yourself how:
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-/[]\- Logic chapters 1 to 5 re- appear not in sequence, as is or longer, in Volume 1A, Pattern Based Reason, Bon Appetite. Logic
Mastery Logic mastery makes the hard, easier. Logic mastery leads to better, stronger and richer comprehension. Logic mastery improves reading and writing. Logic mastery ease learning difficulties. Logic mastery gives a headstart. In sum, logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck. After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving liinear Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6;
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-/[]\- What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts. Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice. |
Talking about numbers, amounts and quantities, and letters representing them
In mathematics crib sheets or dictionaries, we may see that a letter used in mathematics is a variable, or vice-versa, a letter that appears in an equation is a variable? Now the Greek letter q appears in trigonometry. It is a letter, so that it must be a variable according to above. On the other, what if I said that the letter represents a the measurement of a constant angle - an angle that will not change. Is q then a constant as well? The Greek letter p appears in formulas for perimeters and areas of circles, and in formulas for the volume and surface area of a sphere. Is this letter p to be called a variable? Now the modern mathematics curriculum may say or define a variable as an element of of a set of numbers or a variable as a function of time or a function defined on a set, discrete or not, continuous or not, in one or more directions. The first definition assumes an understanding of sets and may come after the shorthand use of letters or variables in the development of mathematics. The second approach also comes after the concept of function (computation rules) and so may come after the shorthand use of letters and sets in the explanation of mathematics. Both views represent a mathematical codification of what is a variable in a context too complicated for novices to immediately grasp. A simpler comprehension may be put first. But before the use of letters and symbols in mathematics - in the statement of formulas and/or the statement or description of properties of real numbers (eg associated law for addition), we can understand the everyday usage of what is a variable. We can talk about the height of a bird or the number of centimeters or meters in the height of its beak above the ground. That height may be constant or unchanging. That height may be increasing or decreasing while the bird is flying or falling. And while the height is changing, we will say it is variable. Here variation is over time, a variation that may later be viewed as a function. However, in the first instance, the common person in the street TCPITs may understand the notion of height varying as the bird moves. If we also talk about two different birds, each will have a beak height above the ground. So height may change or vary between birds. That introduces another sense of what it means for a number or quantity to vary. Variation may give us a set of values over time and position (or bird selection) I favour the following notion of variable, a notion that can be understood before the use of letters and symbols in mathematics, and a notion that requires no knowledge of sets nor functions to understand and explain. Namely, a number, amount or quantity is a variable in a situation when its values may vary (vary from one situation or moment to another if you wish). This view is precise enough in the first instance to introduce the concept. Beyond this a letter or number that denotes a number, quantity or amount is said to be a variable, constant, known, unknown, given when the value of the number, quantity or amount is respectively variable, constant, known unknown or given. This first concept may be codified or described later in terms of sets and functions, if need-be.
Chapter subsections: Next: Algebra 10 Describing & Changing Calculations (the second and third skill for algebra)
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www.whyslopes.com
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