Up until this point, students have had very limited exposure to fractions. Now they will work with numbers that exist between two whole numbers. Students learn that a fraction is not only a "part of a whole", but also a point on the number line. This is significant because students often think of fractions (such as 3/8) as objects in a completely separate category from whole numbers. Locating the fraction 3/8 on a number line shows that a fraction can be thought of as between two whole numbers.
Understanding the Standard:
- Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. For example, a fraction such as 1/3 will partition the number line between 0 and 1 into 3 equal parts, the same number of parts as the denominator of 1/3.
- Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. For example, if the interval from 0 to 1 is divided into eight equal lengths, each of the lengths is 1/8; 5 of he eight lengths can be marked off on a number line starting at 0. This would produce marks at 1/8, 2/8, 3/8, 4/8, and 5/8. 5/8 is not only the distance from 0 to the end of the fifth part; it is the number that identifies the location of that last mark. The result of the distance from 0 to the last mark will be 5/8.
- Students need practice identifying fractions with their appropriate word name and picture representation.
- Work with a number line, manipulatives, technologies and even rulers are useful tools that will provide a variety of learning experiences for students. One idea for a manipulative is to have students put number lines on paper and then fold them to create four equal parts. Students then label the endpoints of the parts 0/4, 1/4, 2/4, 3/4, and 4/4.
Questions to Focus Learning:
- Can students match a fraction with its word name and picture representation (matching a fraction to its location on a number line)?
- Are students able to name fractions on a number line?
- Are students able to mark the location of a fraction on a number line?
- Can students break intervals on the number line into 2, 3, 4, 6, and 8 equal parts, attending to precision?
Students have had limited practice with partitioning a circle or rectangle into equal parts and have described those parts using appropriate vocabulary. Furthermore, they have had practice representing whole numbers on a number line, and with representing addition and subtraction on a number line.
At Grade Level:
Students will identify a point between two whole numbers on a number line as a fraction . Additionally, they will plot a fractional number on its correct location between two numbers on a number line.
Beyond Grade Level:
The ability to conceptualize fractions on a number line has a direct carry over into measurement and the later study of decimals.