In Montessori classrooms, children begin learning about equations and algebra as soon as 4th grade. In turn with the interactive views Montessori is based on, they are exposed to the forces behind life and how their world works as soon as they start school. As they grow, they are enveloped in an environment where they learn how different subjects and areas revolve around each other. As a 10 year Montessori student myself, I can easily relate to what our 8th-grade math and science standards are teaching us. In daily life, math and science are an interlocking system. One of the most similar pairings is chemical and linear equations. Both have closely related aspects and uses. This paper will discuss solving multi-step equations, parts of a chemical equation, and how they compare and contrast.
Solving a linear equation is a matter of going through a series of mathematical operations. Depending on the number of steps required to complete an equation, you might first combine like terms or skip straight to isolating the variable. Whatever you begin with, the equation must always be balanced. For example, 2(x-5)=x+5 would be x=15. The steps that would proceed the answer would start with multiplying the numbers inside the bracket by 2. You would get 2x-10=x+5. Then you want to isolate the variable, so you take 1x away. The reason you do this is to cancel out the x on the right side of the equation. After doing this, you have x-10=5. Now we need to get rid of the 10, so we add 10 to both sides. Now we have x=15. Since a variable with no coefficients always equals 1, we know that we have found the answer. To check our answer, we can plug it in and find the value of both sides and see if they are equal. In this case, it was. In a few steps we have solved a linear equation. The basic idea for solving a linear equation also applies to chemical equations.
In fact, chemical equations are quite similar. I’ll go over the nitty-gritty details in a few moments. But the steps in a chemical equation are different. One obvious detail is there is not an equal sign, but a yield. To balance a chemical equation and therefore solve it, you must balance the reactants and the product(s). I’ll use _NaCl + _F?->_NaF + _Cl? as an example. To start, we must look to see if we can find any clues. In this case, I see that Cl has two atoms in the product. I know that I must have at least 2 atoms of Cl in the reactant, and to do that I must make two molecules of NaCl. So now our equation looks like this: 2NaCl + _F?->_NaF + Cl?. Now we see that we have an extra atom of Na. And as a fortunate coincidence, we also possess two atoms of F. This balances out equally if we make 2 molecules of NaF. When we plug those numbers in, we discover the finished chemical equation 2NaCl + F?->2NaF + Cl?. In a few steps, we have solved a seemingly complicated chemical equation. However, you might be wondering to yourself about how they are the same. Let’s find out.
For the simple reason that they are both equations, they have a lot in common. When we compare the two, we find that both use similar symbols to represent operations and values. They also must stay balanced; in other words both sides on either must contain the same number value or number of atoms and molecules. In contrast, linear equations are an abstract idea while a chemical equation represents an actual submicroscopic phenomenon. Linear functions possess unknown variables that may be solved with a set of all real numbers. Chemical equations have one simplified yield, or answer. In linear equations, you might also combine like terms. In chemical equations, the reactant and product must stay the same with the exclusion of coefficients. Summing their traits up, both have a few almost identical traits, but they also have substantial differences.
In conclusion, multi-step equations and chemical equations have a lot both in common and unique to themselves. Linear functions are an abstract algebraic representation of numbers with which use a variety of mathematical operations to solve them. On the other hand, chemical equations are an actual physical change that is represented by numbers and letters to learn more about chemical transformations. Whichever equation is being solved, it is sure to be fun and a wealth of knowledge. Why not go try out a few now?
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