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This is an essay written by one of my students. The full essay is here.
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Plus, receive a "Live Demonstration Inside Our Unique 1 On 1 Online Classroom." Mathematics Problem Solving Skills Tip #1- Understand the Problem
Most students have difficulty with a math problem because they do not know how to start it. In order to begin the process of solving a math problem you need to understand the problem. By understanding the problem, you know what the problem is asking for.
Mathematics Problem Solving Skills Tip #2- Identify the Knowns and Unknowns
All math problems give you information and ask you to find the unknown information. The first thing you need to write down is what you know in the problem. Then you need to write down what you do not know. This is the information you will be solving for.
Mathematics Problem Solving Skills Tip #3- Translate the Problem to Mathematical Language
Now that you have identified the knowns and unknowns in the problem, you can translate this information from English to Math. You can develop a relationship between the known information and unknown information by writing an equation with appropriate variables.
Mathematics Problem Solving Skills Tip #4- Solve the Problem
Your equation is already set up from the previous step. Now you can solve the equation by using the correct mathematical operations. Make sure that your unknown variable is by itself and that you include the right units in your final answer.
Mathematics Problem Solving Skills Tip #5- Check your Answer
You can check the validity of your answer by plugging it back into the original equation. If both sides are equal then you have solved the problem. Otherwise, you need to refer back to the previous steps to check for any errors in mathematical calculations, translation, and your overall understanding of the problem.
Remember that in order to start a math problem, you need to understand what the problem is asking for. Ask yourself: “What do I need to solve for?” Then you can identify what is given and not given. Make a table with two columns: 1. Known Variables and 2. Unknown Variables. After identifying the known and unknown variables, write your problem in the form of an equation. Once your equation has been established, you can solve the problem. Perform the correct mathematical operations. Finally, check your answer for clarity. Does my solution make sense when I plug my answer back into the original equation?
Here’s an example: Gary is driving in his car at a rate of 50 miles per hour. Two hours later, Sharon leaves Gary’s house and hops on her motorcycle at a rate of 70 miles per hour. How long does it take Sharon to catch up to Gary?
Step 1: Understand the problem
What is the problem asking for? Reading the last sentence, we see that the problem wants us to know how long it takes for Sharon to catch up to Gary.
Step 2: Identify the knowns and unknowns
We know that Gary's rate is 50 miles per hour and we also know that Sharon’s rate is 70 miles per hour. We also know that Sharon left two hours later than Gary. What we do not know is the time for Sharon to catch up to Gary.
Step 3: Translate the known and unknown information to mathematical language
We know that Distance is rate times the time, so D = RT. We can use subscripts like G for Gary and S for Sharon. Since Sharon is catching up to Gary, we know that the distances are equal. So, D(S) = D(G). Then we have R(S)T(S) = R(G)T(G). From Step 2: we see that R(S) = 70, and R(G) = 50. Since Sharon left two hours later than Gary, we can write Sharon’s time in terms of Gary’s time, which is T(S) = T(G) – 2. So, our equation is
70(T(G) – 2) = 50T(G).
Step 4: Solve the problem
We can now solve for the equation from Step 3 by using the distributive property. We have 70T(G) – 140 = 50T(G). Subtracting 70T(G) to both sides, we have -140 = -20T(G). Our last step is to divide both sides by -20 to get T(G) = 7. This is Gary’s time. But Sharon started two hours later than Gary, so we plug in T(G) = 7 into Sharon’s time to get T(S) = 5 hours. Therefore, it takes Sharon five hours to catch up to Gary.
Step 5: Check your answer by plugging it into the original equation
Using T(G) = 7, we have 70(7 – 2) = 50(7). 70(5) = 50(7) = 350, so our equation is true.
By following these five simple and proven steps you’ll quickly improve your mathematics problem solving skills.
The conscious input to the Inferential System also explains the conscious control of attention. If you attend to red -- consciously think about red -- your Inferential System produces perceptions and other thoughts consistent with red. Put simply, the perception of a black dog is not consistent with "red". Similarly, if you consciously attend to a location, your Inferential System is constrained to producing perceptions about that location. Conclusion This essay made two important points about the Inferential System. First, the Inferential System can be very powerful and creative. It is the source of most major scientific and mathematical breakthroughs. Second, consciousness can also input information into the Inferential System. This gives consciousness some control over the Inferential System. This is important control, but it also means that consciousness can impair functioning of the Inferential System if it doesn't know what it is doing.