Common Core

The fourth grade worksheet above where students are given a table to fill in corresponds to the common core standard A.2. This standard accounts for comparing two fractions with different numerators and denominators and recording whether the fractions compared are <, >, or = one another.

• The first, second and fourth problems have the same numerator but different denominators, based off of the students response the teacher would be able to see if the student understands that smaller denominators account for a larger portion shaded when the two fractions compared have the same numerator. With these problems students may believe the larger denominator covers a larger portion due to it being a higher number. A good method to aid students confusion would be a visual.
• The third problem has different numerators and denominators. This problem is a good problem to use to see if the student understands the concept of 1/2 and how to tell if a fraction is higher than 1/2 or lower than 1/2. A good method to aid students would be to write out a number line and put 1/2 on that number line and then have them write where 4/5 would fall on that number line in comparison.
• The fifth problem is a little trickier. It has both different numerators and denominators. This problem is a good problem to really gauge how in-depth the student understands fractions in comparison to one another. With this type of problem students may once again choose the fraction with the higher numbers to represent the larger fraction.
• Proficiency on this worksheet would be demonstrated by the students showing their understanding of size comparison when it comes to fractions. This would be demonstrated by students correctly identifying which sign <, >, or = belonged to the pairs of fractions listed in the table.

The fifth grade worksheet above where students are given addition and subtraction problems with fractions with deifferent denominators corresponds to the common core standard A.2. This standard accounts for adding and subtracting fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equal sum or difference of fractions with a common denominator.

• Problems one, three and four represent addition and subtraction problems with different denominators. These problems would test students understanding on getting a common denominator to add or subtract the fractions. A common mistake found among students when initially learning how to add and subtract fractions is that they add or subtract the numerators and denominators by eachother straight across horizontally. A method to aid students confusion is to line up the fractions vertically and to really highlight the importance of finding a common denominator when teaching students about adding and subtracting fractions.
• Problems two and five heighten the difficulty of adding and subtracting fractions by throwing in a mixed number. A common problem with mixed numbers is that students will either disregard the whole number to the left completely or just carry it down once solving for the addition or subtraction problems of the two fractional parts. It is essential to teach students that the whole number can easily be written as an improper fraction to make the addition/subtraction easier for the student once finding a common denominator. A way that they can find the numerator is by a little chant, "bottom times the side add the top, woo!"
• Proficiency on this worksheet would be demonstrated by students showing their understanding that a common denominator must be produced between the two fractions in order for addition or subtraction to be carried out.