Candy Dish Blog

In the last few U.S. administrations the First Ladies all have had serious agendas.  As a former librarian Laura Bush was known for her efforts to encourage children’s literacy.  First Lady Hilary Clinton ’s tag line was “It takes a village” as she encouraged public private partnerships as part of a “global village” concept of assistance to underdeveloped regions of the world.  She has continued that interest as U.S. Secretary of State.

Many of us in the Washington area have been wondering when First Lady Michelle Obama was going to declare her agenda.  A  hospital administrator before becoming our current First Lady, she’s also a devoted mom to two young children. Her background in health administration and her personal role as a mom has helped define her agenda which has been rolled out over the last few weeks.  Mrs. Obama is joining forces with two respected health care leaders, Health and Human Services Secretary Kathleen Sebelius and U.S. Surgeon General Regina Benjamin to “help Americans lead healthier lives through better nutrition, regular physical activity and by encouraging communities to support healthy choices.”   The First Lady says she will launch a major initiative on childhood obesity in the next few weeks stating “today’s epidemic of childhood obesity is unacceptable.”   She notes that the prevalence of obesity has tripled among children and adolescents from 1980 to 2004.

Along with the U.S.  Surgeon General the First Lady would like to see changes in community, home, child care settings and schools to allow individuals to make healthy choices.  According to a news release , likely  practical applications of this initiative include “the limitation of advertisements of less healthy foods and  beverages” ; reducing  consumption of products with added sugars and appealing healthy food and beverage options in child care and school settings.  The First Lady carefully refers to childhood obesity as an “epidemic” threatening America’s “quality and years of healthy life.”

NCA takes seriously the First Lady’s interest in healthy children. We hope the emphasis will be on positive incentives to create healthy lifestyles including encouraging physical activity, wonderful  inspiring incentives  to encourage increased consumption of  tasty fruits and vegetables and initiatives to discourage overconsumption of foods and beverages.

We also hope that the First Lady and other food policy leaders will continue to acknowledge  that there is a place for small pleasures, like candy, in the lives of children and adults. As most  diet programs  acknowledge it’s the little pleasures that help us achieve lasting change and good health.

If you’re reading this blog I’m going to assume you are a candy lover.  I’m also going to assume you have an interest in food.  What’s your food agenda?  What do you do to keep yourself fit and healthy?

Michelle Obama by Story Accents.

Manipulatives are visual, tactile devices that are meant to be handled and are especially useful for teaching abstract topics like fractions and percentages. I pointed out earlier that one math teacher in Glendale, CA Chamlian Armenian School uses Hershey’s bars as a visual aid to teach math concepts.

The chocolate bars are divided into four rows of three squares each, totaling 12 squares in all. If a student breaks the four rows apart, it is easy and delicious to teach concepts like half and quarters. If you break the bar other ways, you can teach thirds and even twelfths. Other brands that are scored in different ways can help teach other fraction concepts. Let’s look at a simple math problem using a Hershey bar:

What is one-fourth of 12? Break the chocolate bar into squares. Next, divide the squares into four equal groupings. Each grouping has three pieces, so one-fourth of 12 is three.

As the students progress with the math, they can get to more advanced concepts like remainders. How many times does five go into 12? To solve this, start with 12 squares and make as many piles of five squares as possible. You end up with two piles of five squares with two squares leftover, so the answer is two remainder two.

This is not difficult math for most of us but getting kids to see a concrete visualization like this can be a big key in getting them to think abstractly.

Those of us who have been in the classroom know that there are different types of intelligence and different learning styles. As educators, we have a golden opportunity to be creative and implement some approaches we did not have ourselves so we can communicate ideas to young minds. To me that was where both the frustration and joy of teaching came from, changing from one to the next and ending in success for the kids I worked with.

Back then I never thought of using chocolate as a manipulative but I salute the teacher who thought of this. It’s a sweet ending to math class – a course often feared and dreaded.

Chocolate Squares by Siona Watson.

One question we always get is how candy is made. Since it is the right time of year, I thought this candy cane video would be fun to share.

This is a great video. I had never seen the whole candy cane manufacturing process mechanized before. Previously I had seen people rolling candy canes by hand, or else getting the peppermint sticks from a roller and crooking them by hand. It’s neat to see how all this is done by machine.

Candy Math Monday is all about demystifying math for the benefit of all, especially our young friends who struggle with math in school or while preparing for the SAT or a similar test. It’s a pain, to be sure, but that’s why we are working with candy – to make math a bit sweeter for you.

Today we will look at probabilities. Notice that the Mike and Ike candies in the photo have about twice as many green pieces than red. Let’s assume that is the exact proportion: two green to one red. If you have a bag of these you are sharing with a friend and you randomly pick one out, what is the probability that it will be a red one?

Break it down
First, what is probability? It is a term used quite a bit, so let’s come to an understood agreement. Basically put, probability is the quantifiable likelihood of something happening. In other words, it is the possibility of a particular outcome over the entire set of outcomes. Simple? I thought so.

How it all works
If we have two green candies for each red one, that is a ratio of 2:1. Add those numbers together and you have three candies total (2 green + 1 red = 3), or some multiple of three, assuming you have a big bag of them. One way to think of this is to imagine what you are trying to find (a red one) out of the total in the bag (including green and red).

One out of three of the candies is red, so you have a one-third chance of getting a red one. Simple answer, right? Well, this is an entry-level problem. Let’s kick it up a notch. If you have the same ratio and five red candies, what is the probability of getting two red ones in a row?

The first thing you have to do is calculate how many candies you have. If the ratio is 2:1 (G:R) and you know you have five reds, then you have ten green ones, right? That means your expanded ratio is 10:5.

The Answer
The first part is easy. We already did that. Five red candies, ten green ones means a 5 out of 15 (5/15) or one-third chance.

The second part is tricky. You have already eaten one red one, or maybe shared it with your friend, so how many are left? You have four left. This changes the ratio, so you have to do some more math. Your new ratio is 10:4. The new probability of getting a red one is 4 out of 14. 4/14 can be reduced to 2/7. It’s easier to work with smaller numbers, so let’s go with that.

So now we have the answers to the first and second parts of the problem. Now we have to bring them together. When dealing with probabilities like this, you have to multiply them to get the final answer.

1/3 * 2/7 = 2/21

So you have a 2/21 chance of getting two red candies in a row. Simple? I thought so.

The key to solving complicated math problems is to break them down into manageable, simpler problems. In addition, putting some candy in the mix adds some fun to the process.

Can you name the key ingredient in lollipops? Marshmallows? Caramel? Pez? Rock candy? Those pleasantly chalky textured mints that restaurants always put in bowls but you never really see anywhere else (and they seem kinda stale but are actually tastier that way)? If you answered “awesomeness,” you are only partially correct. All of these delicious treats (and many more) are composed primarily of sugar. The versatility of sugar’s repertoire results from its fabulously unique chemical properties.

Now that I have spouted promises of interesting explanations of sugar’s underlying scientific principles, you’re wondering, “what are these fabulously unique chemical properties that make sugar the all-star of the confection squad?” Table sugar, or sucrose, consists of two very simple molecules not unlike those that compose the backbone of our DNA. The bulkiness of the fused product of these two small monosaccharide (single sugar unit) molecules, fructose and glucose, promotes crystallization, which as I will explain below is a desirable property of some confections.

For other types of candy, this propensity for sugar crystals to crystallize out of solution is frowned upon. Thankfully, some smart candy scientists discovered that addition of acids or other ingredients to the candy mix can cleave our favorite disaccharide into fructose and glucose, freeing them from their crystal structure and allowing them to more easily dissolve into a liquid and assume a smooth transparent state. Another bonus of cleaving sucrose into its two smaller subcomponents is the wicked sweetness boost that comes from these sweet little molecules!

Sucrose
Sugar structures of confections can be generally categorized as either crystalline or the exceedingly explicit category noncrystalline. Crystalline candies, such as rock candy or Pez, are made up of individual sugar crystals that are held together by a small amount of amorphous sugar syrup (it’s not as scary as it sounds, its just basically like a really delicious sugar glue). In crystalline structures, sugars crystallize out of solution and align themselves into nice neat organized arrangements. The surest way to tell if a candy is crystalline is to hold it to your tongue. The individual crystals will be anxious to escape their strict organizational structure (everything in the universe always flows towards disorder or at least that is what I have been telling myself to explain my life’s penchant for chaos) and you will feel the candy dissolve quickly.

Most types of candies are noncrystalline, or at least partially noncrystalline, in nature meaning they are made up of sugar crystals that are dissolved into liquid. The properties of these mixtures of sugar and water are largely dependent on their moisture content and the coolest thing about these candies is that they are actually liquid. Bet you didn’t know that lollipops were technically liquid and so are caramels, marshmallow and taffy. These candies are fluid in that the sugar molecules run randomly all over the place but these liquids have a very high viscosity, meaning these liquids are thicker than the tension between the Packers and the Vikings this season.

If you still believe me, and I know sugar’s rockin’ chemistry is unbelievable, I bet you want to know the difference between hard candies and their softer counterparts like taffy and marshmallow. Hard candies have undergone a phase shift from an amorphous liquid to a glass. Now don’t get me wrong, candies in the glassy state are still liquid, since the molecules are just as random as Susan’s hatred of pandas or Carl’s love of circus peanuts, but these liquids are so freaking viscous they are basically immobilized. Candies with higher moisture content will become glass at lower temperatures than those with lower moisture, increasing the likelihood that they will not be in the glassy state at room temperature (watch out for these cause they also tend to be less stable than low moisture candy).

Next week we will look at corn syrup and how it differs from sugar.

To continue the candy math series, today we will look at problems dealing with sets and overlapping sets. If you are studying for the PSAT or SAT, you should become very familiar with this concept. Let’s start by looking at a typical problem:

After school, kids gather to trade gum (unchewed, of course). If 25 students have bubble gum, 19 have chewing gum, 12 have both and 5 have neither (poor gumless kids), how many kids are there?

This type of problem requires more than simple adding because some kids fall into more than one category. There are two basic ways to solve this problem. One is to use an equation. For overlapping sets, you can always use this equation:

Total = Set 1 + Set 2 + Neither – Both

So to plug in these numbers you get:

x = 25 + 19 + 5 -12

and thus:

x = 37 kids

There is another way to solve this problem. Some people do just fine with this equation but some people think more visually and need to see things graphically. I am that type of person. Did I mention that I am a photographer? That’s part of me being a visual person. The second method of solving this requires Venn diagrams, which give a visual representation of the problem.

The problem lots of people have with these problems has to do with the overlap. One way to use the Venn diagram is just as a visual cue to remind yourself to subtract the overlap. Another is to help you determine precise numbers of how many of these wonderful young people have only chewing gum or only bubble gum.

So you can see that when adding these numbers together, you have to subtract out the 12 students who overlap. 13 students have only bubblegum, seven have only chewing gum, 12 have both and five have neither. 13 + 7 + 12 + 5 = 37.

The moral of the story is that math is fun and tastes like candy.

Candy Math Mondays are a biweekly feature here and will be around for as long as I can stretch this theme out. Are you a teacher wanting to incorporate candy into the classroom to get kids more interested in math? Let us know what problems you would like to see tackled with a candy twist. We will do our best to help.

Last week we looked at one type of combination problem, figuring out how many different possibilities of candy you can have mixed into your ice cream. This week we will look at a different combination problem, really a permutation problem – how many ways can you do something? Let’s look back at Sera’s photo of gummi bears from a couple weeks ago:

Ten different flavors of gummi bears are represented here. Yes, I know the two red ones look the same. Let’s assume one is cherry and the other is raspberry or some other red flavor. I want to eat them, one at a time, and want to know how many different possible ways I can do it if I have no order preference, choosing them randomly one at a time. This is another typical SAT problem with a simple solution. In fact, it is even easier than last week’s problem.

I choose my first gummi bear. How many options do I have? Ten. Then I have nine left so I can choose one out of nine. Then eight, seven, etc., all the way to when we have only one gummi bear left and thus have only one option. So we have worked out the logic of this problem, but how do we find the answer? The solution is to multiply these different possibilities together:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800

Simple, right? You probably had no idea that ten little gummi bears offered such a huge number of possibilities for your life! So what do you think? Is math more fun with candy or without?

Gummi Bears by princess_of_llyr.
Candy Math Mondays are a new feature here and will be around for as long as I can stretch this theme out. Are you a teacher wanting to incorporate candy into the classroom to get kids more interested in learning? Let us know what problems you would like to see tackled witha a candy twist. We will do our best to help.