Wouldn’t it be wonderful to shrink your math teacher, pop her in your backpack, and take her to your house for homework help? Yes, but only if she remained the same, only smaller; her brain may be filled with math content, but her head should still stay proportionate!
The process by which we transform a proper-sized professor – adorable dress and all - into a magical mini math teacher, is called dilation. We use dilations to reduce or enlarge an object, proportionally. Most commonly, you may hear this term used in a doctor’s office. When the doctor dilates your eyes, they are widening the pupils of the eyes in order to allow more light to reach the retina. In this image, the life-size teacher is the preimage, and the resulting petite instructor is the dilation image.
Sometimes small children see an architect’s model and think it’s a dollhouse, though it’s really a scaled down – yet proportional – representation of an actual development. (Please don’t rearrange the landscaping or you may have a tree growing out of your pool! 😊)
The tiny townhomes (shrunken skyscrapers and miniscule malls – complete with pint-sized people and pets) architects use to represent new communities are created using scale factor. To find the scale factor of an actual hotel to the model, the architect divides the length of each of the corresponding sides (length, width, and height) by the same number. Architects often use scales as crazy as 1:2400!
Math modeling is another great way to figure out real-world problems using the language of mathematics! Let’s say we want to figure out which Eva Mendez dress on the New York & Company site is the cutest; we’ve already completed the first step by determining what we want to know!
Next, make some assumptions; in this case, what is cute? Length? Cut? Pattern? By assigning value, you begin to define consistent factors that impact outcome. Now it’s time to figure out what you really know and what you don’t. After researching and gathering data on hashtags, social media posts, customer reviews and fashion blogs, you define your variables and figure out a solution!
Now it’s time to analyze and asses your model. Does it make sense? Has it solved the problem? Is the answer reasonable? Prove it by validating the model. Now that your creation is complete, report the results - you know which dress is the cutest – shout it from the ceiling, sister!
Your findings should summarize the problem, methods, and results in addition to explaining why you chose this problem along with your approach. (Because fierce fashionistas need to know!) Be sure to lay out your entire process, cite sources and explain your conclusion.
See, math is always in style! 😊
Photographer: @jaxonphotogroup http://www.jaxonphotogroup.com