There are several shifts in the way fractions are presented in grades three through six, in the new Common Core Standards. Recently, Education Weekhas published several articles about these changes; however, as long ago as August of 2011 other sources, such as Hung-Hsi Wu, have published related information. Here is a brief overview of the changes that we can expect to see in how students are introduced to and expected to understand fractions and their relationships to each other.
We used to jump right in with adding fractions using a traditional algorithm in the third grade. The new standards turn our focus to a conceptual understanding of fractions that extends beyond the traditional rectangle or pizza representations. Now, we hold off on applying operations to fractions in lieu of developing a deeper understanding of fractions as numbers. While we will still represent fractions related to whole in the forms of rectangles or circles, and parts of a set, we will also represent fractions as numbers on a number line. This focus on the number line extends throughout the rest of our work with fractions.
This new focus on representing fractional parts on a number line is intended to give students a more solid understanding of fractions related to a whole. On a number line, students can see whether a fraction is closer to zero or one, closer to one-half or one, and so on. We can also use the number line to more reliably compare fractions—it’s easier to draw two equivalent number lines than it is to draw two perfect circles and divide them equally into different fractional parts. I frequently see students attempt to compare fractions with different denominators using hand-drawn circles, and the results are not only inaccurate but frustrating and misleading as well.
Students will use number lines, as well as tried-and-true circle or rod manipulatives, to identify equivalent fractions as well. If you look at a common ruler it is easy to see how this is not only convenient and accurate, but applicable to practical endeavors. Think of the additional benefit that exercises with a number line imply for measurement and conversion activities. We can easily connect students’ previous learning about the relationship between centimeters and millimeters, to current explorations of equivalent fractions on a number line.
Students will use number lines to compare and find equivalent fractions, decimals, and percentages. By the time students approach these types of challenges in fourth grade, they will already be familiar and comfortable with fractions on a number line. Similarly, mixed numbers are just an extension, literally, of the number line students are already using. Also in fourth grade, students will compare fractions that have different denominators, add and subtract mixed numbers, and multiply fractions by whole numbers.
In fifth grade, students will be expected to reach facility with adding and subtracting all kinds of fractions and mixed numbers. However, the new standards move away from finding common denominators as a matter of course using least common multiples, and the focus is now on using them when we need to compare fractions or find equivalent fractions. Simplifying fractions is not considered essential as it was in the past. Correct answers are correct, even if not simplified. And, after all, some fractions are more easily understood and compared before they are simplified. Think of how much simpler it may be for a child to understand the comparison of 75 cents () to one dollar, compared to three-fourths of a dollar. Finally in fifth grade, students will understand the relationship between fractions and division, and they will multiply and divide fractions. The intention of the standards is that by this time, students will have a conceptual understanding of fractions that leads them naturally to understand the processes of multiplication and division, rather than just memorizing the steps of an algorithm.
Although the bulk of instruction in fractions occurs in grades three through five, students will still be introduced to fractions as early as kindergarten, dealing with simple fractions and developing a firm foundation that focuses on unit fractions (with one as the numerator) as the basic unit of our work with fractions. And their understanding of fractions and what they mean will extend to sixth grade, where they will interpret quotients of fractions. Of course, as is the intention across the math standards, students will be expected to express their ideas using grade-level appropriate math vocabulary in each grade. With fractions, decimals and percentages so ingrained in our lives and society, it is easy to see why a solid understanding of these concepts is not only academically advantageous, but also useful in daily life.
For more information about the new math standards for fractions see these resources: