What is Algebra?
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The second and the third videos explain algebra by giving an example of an equation that is classified as algebra. Both start off with a basic equation and go on to point out that the blank space in their equations can be filled by a letter, or a variable. Both also explain that the difference between arithmetic and algebra is that algebra uses variables as placeholders for missing numbers. They also go on to show that by working the problem backwards, starting with the overall answer you can use simple measures to find the missing number that was substituted by a variable. However the third video explains that if you have one problem with two numbers with the same variables can be combined (3x+4x-2 can be re-written as 7x-2).
Contrast
The first video defines algebra as "generalized or abstract arithmetic which uses symbols such as X and Y to represent numbers". They go on to say that algebra is important because it has real world applications and that by learning algebra we discover various ways to solve one problem. The second video however starts off by giving an example of arithmetic and substitutes a number for a variable to change it to an example of algebra instead of giving a direct definition. They then go on to make a T chart to show that in algebra the variables, or numbers, are really just placeholders for the actual numbers. The second video gives an example of how you would work a problem backwards to find what the variable would equal. They also explain different things that are commonly included in learning algebra. They show examples of liner, quadratic and system equations and he also explains what functions are along with radical and rational expressions.
The second and the third videos explain algebra by giving an example of an equation that is classified as algebra. Both start off with a basic equation and go on to point out that the blank space in their equations can be filled by a letter, or a variable. Both also explain that the difference between arithmetic and algebra is that algebra uses variables as placeholders for missing numbers. They also go on to show that by working the problem backwards, starting with the overall answer you can use simple measures to find the missing number that was substituted by a variable. However the third video explains that if you have one problem with two numbers with the same variables can be combined (3x+4x-2 can be re-written as 7x-2).
Contrast
The first video defines algebra as "generalized or abstract arithmetic which uses symbols such as X and Y to represent numbers". They go on to say that algebra is important because it has real world applications and that by learning algebra we discover various ways to solve one problem. The second video however starts off by giving an example of arithmetic and substitutes a number for a variable to change it to an example of algebra instead of giving a direct definition. They then go on to make a T chart to show that in algebra the variables, or numbers, are really just placeholders for the actual numbers. The second video gives an example of how you would work a problem backwards to find what the variable would equal. They also explain different things that are commonly included in learning algebra. They show examples of liner, quadratic and system equations and he also explains what functions are along with radical and rational expressions.