Fractional number lines can help develop number sense and estimation ability by illustrating the relative size (scale or magnitude) of numbers. This happens in second grade with the use of number lines to visualize addition and subtraction of 2-digit numbers. Good clear fractional number lines can do the same in 4th and 5th grade.
Part of the problem with using rulers or number lines to identify and read fractions is that many students don’t know how to number the ticks accurately. These pages start with a blowup of a ruler from 0 to 3 inches, on which students number each fraction and mixed number.
Another problem is simply that rulers showing sixteenths or thirty-seconds are simply hard to read. These number lines resemble rulers which are delineated in fourths for the first set of activities, and in eighths in the second. This removes the visual clutter which is present in rulers delineated to sixteenths and removes the problem of how to read those fractions accurately. Students can then focus on the main topic of adding and subtracting mixed numbers.
There are five sets of problems. The first two sets use rulers delineated in fourths: one including fourths only, and the second including fourths and halves. The third set has eighths only on a ruler delineated to eighths; the fourth set includes eighths, fourths, and halves on the same ruler. The last set incorporates all of the above.
The first two activities include an illustration of how the Associative Property can be used to add mixed numbers in different orders. Students should recognize that in some cases it’s appropriate to add the fractions first, while in others it’s easier to begin by adding whole numbers separately, and many times when using or visualizing a number, you add begin at a point determined by the first addend and add whole number and fraction separately (and in either order).
Common Core Standards:
4.NF.3.c: “Add and subtract mixed numbers with like denominators…”
5.NF.2: “Solve word problems involving addition and subtraction of fractions...by using a visual fraction model or equations to represent the problem.”
Subjects: Math, Fractions, Measurement
Level: Grades 4-5
Duration: 14 pages, 3-4 days
Answer Key: included
A Smart Notebook 10 file is also included.