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A fraction is a mathematical expression with a numerator and a denominator, and is a disconnected piece or a small part of a whole. An example of a fraction in mathematical terms is 1/3, and written out as one-third.

The verbal and real life equivalency and expression would be translated as so: Jamie, Joan, and Julie all wanted a piece of the same whole cookie. The cookie was split between the equally, into three different section, each section the same size, for each girl.

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In this lesson, you will be learning the basics of fractions. This includes learning how to define, identify, and creation fractions. By the end of the lesson, you should be able to identify and divide items presented to you in halves completely. Elements of thirds will be presented to you, but you will not be expected to be proficient in them by them end of this lesson.

The common core state standards met by this activity are: 1.G.A.3 and 2.G.A.3

Materials Needed:
-Paper cut out circles (2 per student), divided into halves and thirds
-Miscellaneous colored crayons (2 different colors, minimum)
-At least three people
-A positive, ready to learn attitude!

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. The root word "fraction" comes from the Latin word "fractio" which means "to break". To briefly summarize the history of fractions, they are fairly new when considering how long other math operations have been in place. Fractions, as we use them today, were not applicable until the 17th Century. The concept of fractions was not always an easy one to grasp, and it was passed down for centuries, information being gathered by newer empires, learning from what the people before them had left behind. Everyone from the Babylonians, to the Arabs, to the Europeans reconstructed formula, fixed the way it was used and finally discovered how to accurately depict pieces of a whole that are no longer united, but separated.

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Every fraction has two parts, a numerator and a denominator. The number on top is the numerator and the number on the bottom is the denominator. The numerator represents the amount given, and the denominator represents how many pieces the whole is divided in to. For example, if you had a pizza with five slices in it, and you ate two pieces, the fraction to represent how many pieces of pizza you have eaten compared to how many you had to begin with would be two-fifths, or 2/5

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The fact of the matter is, fractions are going to be something you use almost every day throughout your normal life, whether you realize it or not. Everyday tasks such as cooking, getting gas, telling time, paying bills, and splitting things. Fractions are very helpful in helping people determine how to share and split items such as food. For example, if you have a large uncut pizza and 3 friends to share it with, and every person wanted two slices, how many pieces of pizza total would you cut? The simple way to do that, using fractions, would be to cut six slices in the pizza.
2 slices per person = 2 slices x 3 people
=  6 slices total
The fraction representing how many slices each person gets is 2/6, because each person gets 2 out of the 6 pieces. Fractions make the process of dividing everything evenly much easier and more efficient!

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In order to understand fractions, you must see them in real life first, not just read about them! In order to do this activity, you must each get into groups of three people. After you have gotten into your groups, you will have your materials for the activity given to you. The materials you will also be given for this activity are two pieces of paper cut into circles ; One of the circles will be divided into halves, and the other into thirds. For the activity's sake, the circle representing 1/2 is divided top to bottom, while the circle representing 1/3 is divided like a peace sing with the missing middle line that intersects the third portion. Lastly, you will need two colored crayons, and two colors that you want, just make sure the they are each distinct and different.

Examples of the way the circle representing the fraction 1/2 should be represented and divided (with liberty to shade whichever side you please) below

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The example provided for how the circle representing the fraction 2/3 will be divided is also shown here, and once again, you may shade any combination of the two slices, as long as the fraction equals 2/3

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On the first circle that has two different pieces, color in one of the halves of the circle. Once you have finished, move on to the next piece of paper. This should be the piece of paper that is divided into thirds. Next, with your different color, shade any two of the pieces out of the three, giving you a fraction of two thirds, or 2/3. Once you have finished, raise your hand and wait until all of your other classmates also have their hands raised.

Now that everyone has completed it is time to see which portion of the fractions everyone has colored in. First, look at the fraction representing 1/2. if you colored in the top half of the fraction representing 1/2, raise your hand. Now look at the people in your group, how many people in your group raised your hand? If only one did, then 1/3 of your group colored the top portion of the circle, and the other 2 people remaining did not, meaning 2/3 people colored the bottom shaded portion.

Once you have done the assessment with the paper circle representing 1/2, take out your paper circle representing 1/3. Raise your hand if you have the left and right side colored in, write down how many people colored in the right and left side. Next, raise your had if you colored in the left and bottom portions. Write you number down again. Lastly, raise your hand if you filled in the right and bottom segments. Write the number own. Determine which fractions of people in your group colored in the fractions using the left and right, bottom and right, and bottom and left. Determine which method the most people in your group used, if there is a dominant method. After you have completed this group activity, go to your desk to work on a worksheet that will help you identify what a 1/2 fraction is by using visual representations.

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Before we begin the activity, take a look at the example below one more time.
The total amount of pizza slices, 2 is represented in the denominator. The total amount of pizza slices that are being highlighted and stand out, the part of the whole, is 1.

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After learning what you have about fractions, try to identify which shapes have 1/2 of them colored in. Things to keep in mind are: the fraction 1/2 will be split into two equal sections. Remember that fractions are always equal parts of a whole. The correctly shaded fractions that represent 1/2 should be equal to that parts that are not shaded in. Take your time, and the answers will be down below so that you can check your work. No peeking!

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The shapes are corrected filled and represent the fraction 1/2 are:
-The green square
-The blue rectangle
-The orange circle
-The purple hexagon

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Now that you understand what the fraction 1/2 is supposed to look like, why not try it by yourself? On the worksheet below, first begin by again identifying the shapes that make up 1/2. Once you have completed the assignment move on and begin working on the second part, which is to color in one part of the shape to make 1/2. Once you have completed, check below for the answers to which shapes are filled in correctly, and have an adult or teacher check to make sure you filled in the half correctly.

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The shapes that are correctly filled in and represent 1/2 are:
-The purple circle
-The blue rectangle
-The orange/yellow diamond.

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In the activity, you have learned how to define, create, and identify fractions. The fraction you have become proficient in is 1/2, but this is only the beginning. With the foundation of knowledge you now have that teaches you how to identify when 1/2 is shaded, shade in 1/2, and determine fractions based on people in a group, just like our hands on activity showed, you may hopefully continue to grow you education.

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Education.com. “Fractions of a Whole: Lesson Plan: Education.com: Lesson          Plan.” Lesson Plan | Education.com | Lesson Plan | Education.com, 25 Apr.            2019, www.education.com/lesson-plan/i-want-a-fraction-of-that-pie/
Education.com. “Identifying the Fraction 1/3: Worksheet.” Worksheet                    Education.com, 23 Dec. 2008, www.education.com/worksheet/article/id-      fractions-one-third/

Education.com. “Identifying the Fraction 1/2: Worksheet.” Worksheet                   Education.com, 23 Dec. 2008, www.education.com/worksheet/article/id-      fractions-half/
1.G.A.3 Worksheets, Workbooks, Lesson Plans, and Games,                                          www.education.com/common-
core/CCSS.MATH.CONTENT.1.G.A.3/.
“History of Fractions.” NRICH, nrich.maths.org/2515.