Saturday, December 22, 2018

Student Guest Blog Post: Sweet Treats in Deceit - Problem Solving Project

Here is second post by a different student in my Honors Problem-Solving Seminar; not every student had to do something that involved pure math. This student chose to use problem solving to figure out how to make cookies that she could eat...and the results were delicious!!


For the remaining blog posts, go to sasproblemsolving.blogspot.com


My name is Jamie and I wanted to solve the problem of substituting healthy options for unhealthy ingredients in a variety of desserts. Solving these problems are interesting to me because I love to bake, but I am gluten-free and mostly sugar-free, so I am unable to bake as much as I used to. Due to this, I am now able to bake, but with ingredients that stick to my diet. Although there are many recipes that were made to be healthy that I have tried in the past, I have never enjoyed them. Because of this project, I have created new recipes that hopefully I, as well as other people in the same situation, will always be able to enjoy in the future.


                                          


First, in order to correctly replace traditional dessert ingredients with healthy ones, I had to study the chemical reactions in baking to reproduce the same reactions, but with healthier ingredients. For example, the melting of butter in the oven causes cookies to spread out and flatten. It creates smaller air pockets, resulting in the product becoming much chewier. Coconut oil can be substituted for butter, but be careful not to use too much because then the cookies will taste like coconut.



                                    


Sugars contribute to the taste of your product, as well as caramelization and the Maillard reaction. The Maillard reaction is the combination of proteins and sugars, at 310˚, which creates rings and the brown color seen in most cookies. Also, as the sugars continue to break down, at 356˚, they turn into a brown, flavorful liquid, which is a process called caramelization. White sugar is mostly sucrose, so only dark sugars such as brown sugar are used for to create the Maillard reaction. This is why most cookie recipes call for both granulated and brown sugars because the white sugar is used for one process, while the brown is used for the other. To make up for sugar’s major part in the taste of the cookie, honey, dates, and banana can be used, or other natural sugars.


                                   


Additionally, the thickness of a cookie depends on the amount of flour used. If a thicker cookie is wanted, additional flour should be added to your product. Some substitutions for all-purpose flour consist of either almond, oat, potato, or gluten-free flour. For my project, I used almond and oat flour, but it depends on personal preference.


                              


The final ingredient I will eliminate from dessert recipes is chocolate, which for most people, is the most important part. A couple of months ago, I substituted milk chocolate for dark chocolate, precisely 86% cacao. Most people would call it disgusting because it is extremely bitter, but to me, it is my favorite type of chocolate. Because I have become accustomed to eating it, I no longer enjoy eating milk chocolate. Due to this, in my recipes, I have use 86% cacao, which is actually extremely beneficial because of all the antioxidants, as well as lowering risks of diseases. Here are my two cookie recipes. I hope you enjoy them as much as I do!


                                 
Zucchini Chocolate Chip Cookies:


3/4 cup oat flour

3/4 cups shredded zucchini

1 teaspoon baking soda

1 tablespoon almond butter

1/2 cup almond flour

1 teaspoon cinnamon

1/2 teaspoon salt

1 teaspoon coconut oil

1 tablespoon honey

1 1/2 teaspoon vanilla

2 eggs

1/4 banana


Preheat oven to 325˚. Whisk eggs and combine with almond butter, banana, zucchini, honey, vanilla, and coconut oil. Add in salt, cinnamon, baking soda, almond flour, and oat flour. Bake for 25-30 minutes.

                                 


Banana Chocolate Chip Cookies


1 banana

2 eggs

1 teaspoon baking soda

8 dates

2 1/2 teaspoon vanilla

1 ½ cup oat flour

2 tablespoon honey

1/2 teaspoon coconut oil

1/4 teaspoon salt

86% cacao chocolate

Preheat oven to 325˚. Remove the seeds from the dates and blend them until they are no longer solid. Add in the eggs, honey, coconut oil, vanilla, and a mashed banana. Mix thoroughly. Combine the remaining dry ingredients with the wet mixture. Place tablespoons of the cookie dough onto a pan with parchment paper and flatten each of them. Bake for 25-30 minutes.

Friday, December 21, 2018

Student Guest Blog Post: Drawing Mandalas with Compasses and Protractors! Geometry Art!

Here is the first guest post from my student Morgan! Morgan was in my Honors Problem-Solving Seminar class, and her final project was to learn how to draw a mandala using math! Enjoy! For the rest of the posts, visit: sasproblemsolving.blogspot.com


Hi! My name is Morgan, and because of my love for yoga, I decided to learn how to draw a mandala!

Mandalas represent an imaginary place that one's mind travels too when he or she meditates. Each object one observes in that place has significance, embodying an aspect of wisdom or reminding the meditator of a guiding principle. The mandala's purpose is to help transform ordinary minds into enlightened ones and to assist with healing just as yoga has for me with anxiety. The different movements and yoga positions leave me feeling relaxed and allow me to clear my mind. I felt a similar feeling of relaxation when I drew my mandala.

Having never drawn a mandala before, I had predicted it to be a long, complicated process that would be draining. However, I felt calm and stress-free as I allowed my mind to unravel and draw my mandala. At first, it was a little challenging to know what shapes and lines to draw after I had created the skeleton of the mandala, but by the end, I didn't even have to think much. I went with my intuition and let my mind do what it felt in the moment.

Here is a video of my first mandala drawing, showing the whole process and what goes into creating a mandala.





My first mandala completed


A close up shot of my mandala

Materials needed to draw a mandala:
  • Compass
  • Protractor 
  • Ruler 
  • Pencil
  • Black pen with felt tip (thin sharpies will do)
  • Blank notebook or 8.5 by 11 sheet paper

Procedure:
  1. Draw “skeleton” in pencil.
    • As I showed in my video, use your compass to draw a small circle in the center of the paper then continue outward drawing circles until you reach near the end of the piece of paper. 
    • TIP: rotate the paper while using the compass as shown in this video. 

    • Once your circles are complete, use your ruler to draw straight lines to divide the circle up into several different sections. 
      • 22.5 cm trick shown above
      • In addition, although I didn't show it in my video, you can use a protractor and make markings at every 22.5 cm then use a ruler to draw lines so that your mandala is more precise.
      • Also, the circles do not need to be exactly the same amount apart from each other. It actually comes out better if you organically draw some circles close together and and some further apart. 
  2. Then begin using your black felt tip pen (or Sharpie) to draw the mandala. 
    • Some commons designs and shapes include:
      • Petals 
        • Longer and thinner
        • Shorter and rounder
      • Triangles
      • Various line lengths 
      • Circles with dots 
      • Squares 
      • Symbols such as: 
    • Tip: Begin with drawing simpler shapes then use dots and smaller designs to fill in shapes and the areas surrounding them!
  3. After you finish drawing and designing with the black felt tip pen, erase the pencil marks underneath and admire your mandala! 
    • You can also add color to your mandala to brighten it up if you want!
    After learning how to draw a mandala, I shared the process with some students who are part of Saint Andrew's Mu Alpha Theta, which is a math club at my high school. Here below are some photos of them and their mandalas.

    Designing the mandala

    Beginning the design after creating the skeleton

    Working on the first step with compasses

    A colorful mandala!

    A finished mandala with a unique design: a different design for each half

    Another finished mandala

    I hope my blog inspires you and teaches you about mandalas! I have linked some mandala designers and tutorials that I found helpful below as resources for you. :) 

    Here are some accounts that I found inspiring when creating my mandala!
    @courtneybetts was super helpful in getting me started with my mandala and giving me tips. She has a super cool art Instagram story on her page that features beautiful mandalas. I came across @mandalabybhagya 's Instagram page when looking for inspiration for designs for my mandala. She has lots of intricate colorful mandalas, too! 


    One of @mandalabybhagya's colorful mandalas

    Another one of @mandalabybhagya's beautiful creations


    Lastly, here are some tutorials that I recommend to help you on your mandala journey!
    https://www.youtube.com/watch?v=OiSzGBguPm0
    https://www.youtube.com/watch?v=QcHDIK0E5KY&t=573s

    Thanks for reading! :)