Computation with Fractions

MATH first page

(Under Construction)

I. The Danger of Rules

A. No rule helps students think in any way about meaning

B. Because of this mastery becomes short lived

II. Number Sense

A. There is a need for teachers and students to connect fraction computation to whole number computation

B. As with whole numbers, estimating answers is a very important skill to be developed when dealing with

C. Teachers and students alike are encouraged to explore each operation using manipulatives

III. Addition and Subtraction

A. Estimation is important

Is a given fraction more or less than half. Use circles, Cuisenaire rods, beans, construction paper, etc. to visualize.
Is a given fraction is closer to O, or 1?
In short speed drills estimate sums for two given common fractions. Use manipulatives to verify answers

B. Unlike denominators

1. Using fraction parts (1/4's, 1/2's, 1/8's, 1/3's, 1/6's, 1/16's, 1/5's ) cut from construction paper circles compare fractions with unlike denominators. Do the same with Cuisenaire rods, construction paper rectangles, colored beans, etc. Stress that though circles are the most common way to represent fractions, the whole does not always have to look like a circle.
2. In groups of three, add 5/8 to 1/4, estimate the answer as being more or less than one first, and then modeling the sum using the variety of manipulatives,. One member of the group records the comments of group members as the task is completed. The comments when read back reveal the solution process for adding unlike denominators.
3. Repeat the activity with different fraction sums. Participants must able to illustrate these sums using each of the manipulatives ( circles, rectangles, beans, rods, etc.) and discuss the process through which each sum was determined.
4. Discuss the circumstances under which the sum of two fractions would be more than 1.
5. Record fractions and their sums using fraction symbols. Develop a personal algorithm for adding fractions with unlike denominators.

Repeat the activity with different fraction sums. Participants must able to illustrate these sums using each of the manipulatives ( circles, rectangles, beans, rods, etc.) and discuss the process through which each sum was determined.

Discuss the circumstances under which the sum of two fractions would be more than 1.

Record fractions and their sums using fraction symbols. Develop a personal algorithm for adding fractions with unlike denominators.