Algebraic Proof Written as Expressions
Algebraic Proof statements can be written as expressions usually using the letter "n". In the graphic below there are 6 statements that can written as an expression of n.
Algebraic Proof Example Question
The algebraic proof example below asks students to prove that the difference between 812 and 127 is a multiple of 4. To answer this question first show that 812 is the same as 81 x 811 which is the same as (4 x 2 x 811). Next show that 127 is the same as 121 x 126 which is the same as (4 x 3 x 126). As an extension to this problem students could show that the diference between 8a and 12b necessarily equals 4n.
Consider the conjecture below. Use proof by mathematical induction to come up with a solution.
Algebraic Proof Key Words
Terminology is important when applying algebraic proof. You'll want to have a good grasp of all the key words.
When proving a statement algebraically you will use expressions usually in the form of the letters n or x. For example, to prove that a number is even we show that n is divisible by 2, or that n is a multiple of 2.
The graphic above asks students to explain the difference between a 'conjecture' and a 'proof'. A conjecture presents an idea which is yet to be proven. To learn more about the Poincare Conjecture see the article Grigori Perelman - The Mathematician Who Proved the Poincare Conjecture.