Dear Parents, Students and Teachers,
In my monthly, five-minute STEM Skill Step Up Letter, I give hints like the following on improving critical cognitive and technical skills for young adults. I will also respond to questions that you submit. To do so, subscribe to the newsletter by emailing me. I will respond to questions on the Play-Ed Corporation Facebook page when appropriate.
The Write Way to Learn STEM
Observing my nephew do his physics homework, I noticed his dangerous habit of skipping steps to save time. Though solving math, physics, and other STEM-area problems often involves performing calculations, they should follow careful preparation that includes writing and even drawing a picture. The problem-solving process I taught to my nephew and other students appears below. Students who have used it repeatedly remark how valuable it is not only for helping them determine how to solve a problem, but also in reducing mistakes in computing the final answer.
- Draw a picture of illustrating the problem, labeling the picture with the information on the different numbers and variables provided.
- Write down what you need to find for the problem or solve it.
- Thinking about the theories and principles you know related to the problem and the information you have, attempt to set up an equation in general terms that includes the quantity you need to determine.
- Then, fill in the information that you have from your diagram. Be sure that all units are the same. For example, if one quantity is stated in feet and the others in meters, you will either have to convert the latter to the former or vice versa.
- Think about whether you can solve directly for the solution in one step or whether you need to perform several intermediate steps like substitutions in the process. In the latter case, write out the substitutions you need to make.
- Solve for the answer.
- Check your answer by using it in the equation with all of the other given information. If the answer is correct, both sides of the equation will be equal. If they are not, you should repeat the entire process to find your mistake. Confirm the logic of your answer.
The example below illustrates how to use this process to solve a real STEM problem.
Problem: A 10 meter tree casts a shadow the (horizontal) length of which is 10 feet. What is the length of the hypotenuse, that is the distance from the top of the tree to the end of the shadow?
Solution:
2. I need to find the length of the hypotenuse.
3. The tree and my distance from it form a right angle. The Pythagorean Theorem tells me that the sum of the squares of the lengths of the two sides forming the right angle equal the square of the hypotenuse. If I solve for the hypotenuse, that will be the length of the shadow. The equation for this relationship is as follows:
(Height of tree )2 + (Horizontal length of shadow)2 = (shadow)2
4. Filling in the information, I can write the following equation:
(10 meters)2 + (10 feet)2 = (shadow)2
Now, I need to convert meters to feet. I know that 1 meter = 3.28 feet. This means, 10 meters = 3.28 feet / meter x 10 meters = 32.8 feet.
Rewriting the equation completely in feet yields:
(32.8 feet)2 + (10 feet)2 = (shadow)2
5. I can solve directly for the shadow length because it is by itself on one side of equation. I do not have to make any prior substitutions.
6. I will solve the equation.
(32.8 feet)2 + (10 feet)2 = (shadow)2
1075.84 feet + 100 feet = (shadow)2
1175.84 feet = (shadow)2
shadow = 34.29 feet
7. Check the numbers.
(32.8 feet)2 + (10 feet)2 = (34.29 feet)2
1075.84 feet + 100 feet = 1175.84 feet
1175.84 feet = 1175.84 feet
The logic is correct, too. The hypotenuse, which should be the longest side of the triangle, is in fact longer than the two other sides.
Joseph Gabriella, Ph.D., MBA
Founder and CEO, Play-Ed Corporation
(10 meters)2 + (10 feet)2 = (shadow)2
Now, I need to convert meters to feet. I know that 1 meter = 3.28 feet. This means, 10 meters = 3.28 feet / meter x 10 meters = 32.8 feet.
Rewriting the equation completely in feet yields:
(32.8 feet)2 + (10 feet)2 = (shadow)2
5. I can solve directly for the shadow length because it is by itself on one side of equation. I do not have to make any prior substitutions.
6. I will solve the equation.
(32.8 feet)2 + (10 feet)2 = (shadow)2
1075.84 feet + 100 feet = (shadow)2
1175.84 feet = (shadow)2
shadow = 34.29 feet
7. Check the numbers.
(32.8 feet)2 + (10 feet)2 = (34.29 feet)2
1075.84 feet + 100 feet = 1175.84 feet
1175.84 feet = 1175.84 feet
The logic is correct, too. The hypotenuse, which should be the longest side of the triangle, is in fact longer than the two other sides.
Joseph Gabriella, Ph.D., MBA
Founder and CEO, Play-Ed Corporation
Dr. Gabriella is an accomplished scholar and businessman. Ivy-league educated, he has served as a lecturer or professor at universities in the U.S., Japan, and China. Currently, he resides in Japan, where he is a senior manager and active consultant. A former high-school math teacher, Joseph is passionate about teaching critical STEM skills to future generations through his company, Play-Ed Corporation.
jgabriella.played@gmail.com
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