Reflection of Fractions

Although fractions can appear scary to many at first glance, there is no need to fear! Although there are many common mistakes made when it comes to fractions, numerous methods have been found by teacher to aid students who are having a difficult time.

• The first area of common error we discussed is one that is very easily fixed, especially once students have a better understanding of fractional parts and how to add and multiply fractions. Students are very comfortable with fractions like 1/4, 1/3, 1/2, 2/3 and 3/4, but once they begin to see areas which do not appear to represent any of those fractions, they often begin to panic and have no idea where to begin. As a teacher, the method I would use with my students would be to first identify any fractional part that represents one of our commonly used fractions. Typically students are able to at least see where 1/2 should be. Once figuring out at least one base fractional part of the figure, the teacher can then explain how to solve for say 4 squares that should be equivalent to 1/4 like in Figure 5.1 from our workbook. Once students understand the concept of finding a denominator that will add up to what the whole of that segment is supposed to be (ex: 1/16 + 1/16 + 1/16 + 1/16 = 4/16 = 1/4), students have a much better idea of where to go from there and are able to work with much more clear direction.

*Although we are often times much more comfortable with common fractions, it is important not to panic when we see a fraction like 1/6 or 1/16.

• This may be one of the most common difficulties and errors made among students- claiming that equal parts are not equal simply because they are not the same shape. Although it is much easier to tell pieces are equivalent when they are the same shape, just because they are different shapes does not automatically rule out that they are equivalent. One of the methods I would use as a teacher would be by setting up a visual like Figure 1.1 to the left. Students are much more likely to accept that parts of a whole are equal if those parts are all the same shape. By placing a visual of equivalent pieces made up of the same shape next to another visual where pieces are still equivalent but the shapes are different may allow students to visually understand that, although the shapes differ, the portion each shape fills is actually equivalent.

*Another great method used by teachers to help students when they get confused with different shapes and what each shape is equivalent to within a whole is pattern blocks. Teacher Fran Dickinson in the video "What Fraction of this Shape is Red?" explains how he uses pattern blocks to help students visually see what fractional part each color represents within a whole drawing. By having students color in triangles with different colors, students are able to count the total amount of triangles and then, for example, the total amount of blue colored triangles and write that number over the total number or triangles to get to their fractional whole- one.

*This method also aids students in seeing that different shapes can represent equal parts within the whole. For example, in the flower image above, students can visually see that one hexagon is made up of six triangles. Therefore, six triangles is equal to a single hexagon.

• Comparing two fractions or arranging a set of fractions into order from least to greatest is a common concept students struggle with. There are many ways to aid students though when they are unsure of whether or not 3/7 is bigger or 5/9. Many students may look at the denominators at first and simply choose the denominator with the bigger number to represent the larger fraction or they may look at the numerator and pick whichever number is bigger. When dealing with fractions however it is extremely important to look at both the numerator and the denominator, students must understand that the fraction works together and both the numerator and denominator account for the fraction in its entirety.

*Method One- Use a common numerator and visually draw out the images. Students will see that the fraction with the smaller bottom actually is larger because those pieces are cut larger than the fraction with a larger denominator.

*Method Two- Take the two fractions and place them on a number line in comparison to 1/2, the fraction that is closest to or past 1/2 is the larger fraction.

*Method Three- Convert the fractions to decimals and compare the decimals.

*Method Four- Simply compare the fractions to one and see which fraction is closer to one, that fraction will be larger.

• The final problem is one which has been addressed throughout each of the problems listed above. When it comes to fractions our minds often are not able to completely visualize 1/24 or 4/6 in comparison to 3/5 which is why when it comes to fractions it is imperative that teachers teach through the use of many visuals for this concept. By allowing students to visualize what each fractional part looks like in comparison to other fractional parts, students will be able to understand the concept of fractions much better.