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!

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**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