4th and 5th graders will spend the next 3 weeks learning about fractions. We begin by using the Bixby tile system, a set of 13 different plastic, colored rectangles. The largest tile is yellow and it is the whole to begin with. The smallest tile is green and it takes 24 greens to equal a yellow; it is 1/24th of the yellow. White is the next larger color tile; it is equal to 2 greens, so it is one half of a green and one twelfth of the yellow. With 8 different colors and 4 of these colors having more than one shape (the blue tiles are a 1×4 and a 2×2), there are many, many relationships that the students can work with. Besides fractional relationships, students learn to use addition, multiplication and division to solve their problems (if a green is worth one, then the answer to the same question expressed in whites, will be half). Many questions have more than one way to express the solution: two thirds of a yellow = 16 Greens, 2 Browns, 8 Whites, or 4 Blues. The answer can also be written in fractional form: 16/24th, 2/3rds, 8/12ths, or 4/6ths.
After working with the basic tile problems, students move into more complex, multi-step problems:
1/4 + 1/3 + 1/2 = ? /24ths or 1/2 + 1/3 + 1/6 shared by 2 people. Each person gets ?/24ths.
When students are ready to step away from the Bixby tiles and they are ready for a less concrete approach, they may use graph paper rectangles to represent the whole. A typical problem could be: Draw a rectangle with 16 little squares inside (so the first step is to figure out the dimensions of this rectangle; it could be a 4×4, a 2×8 or a 1×16). The next step is to find and draw 1/16th, 1/2, 1/4 and 1/8th of it.
The final step of working with fractions is to work with the numbers only (no manipulatives and no graph paper). A problem might be: A full garbage truck weighed 9 and 3/4 tons. After dumping the garbage, the truck weighed 3 and 5/9 tons. What was the weight of the garbage?
Students also learn to add/subtract fractions with like and then unlike denominators, when a student shows his/her readiness. Children need lots of time and varied experiences to understand and work with fractions. Fun and related activities are a welcome addition to our fraction unit: coming up, we will be using sectioned chocolate bars to find equivalent fractions, as well as adding and subtracting fractions.