Fractions are introduced in the third grade in the Common Core Standards. This first step includes developing a basic understanding of fractions, particularly unit fractions. Breaking items into smaller parts is a good way to start developing understanding of fractions. Instruction might include monetary examples -- such as the idea that a quarter is 1/4 of a dollar -- or cooking examples -- such as 1/3 cup of flour. Most students will be able to recognize common denominations or measurements of this sort. The unit fraction, the concept of having one piece of a whole object, is also introduced during the same year. Students should be able to identify basic fractions -- 1/2, 1/3 and 1/4.
Beginning in the fourth grade, students should be introduced to the idea of equivalent fractions. A basic introduction can be made through images or fraction manipulatives. Students should build on their understanding of fractions as pieces of a whole to compare equivalencies. In studying equivalencies, students will also learn how to order fractions from least to greatest value. This year should focus on deeper understanding of the unit fraction. Students are shown how fractions can be combined and how to determine which fractions have larger or smaller values. According to the Common Core Standards, students should also learn to combine their understanding of multiplication with their understanding of fractions as they begin to complete basic multiplication problems using fractions.
Once students understand equivalent fractions, they should begin to learn how to add and subtract fractions during their fifth grade year. Manipulatives are a good way to begin teaching addition of fractions. Students might begin with adding identical unit fractions before adding fractions with similar denominators. Finally, students should be able to find equivalent fractions to add fractions with unlike denominators. Learning to subtract fractions should follow a format similar to addition. Students should begin with unit fractions before moving to fractions with similar and dissimilar denominators.
Students also learn division during the fifth grade year. This should include an understanding of what it means to divide a fraction and a review of multiplying fractions. Once students have mastered basic understanding of operations and the related number sense, more complex examples should be introduced.
As a final step in using fractions, students begin to learn the use of division of fractions during their sixth grade year. They should be able to explain why division of fractions makes sense and should be able to use the principles of division to solve word problems. At this stage, students should also learn basic ratios as a means of expressing amounts. The relationship between a fraction and a ratio should be explained, and students should use their understanding of this relationship to solve problems and illustrate measurements.
Teaching fractions is an ongoing process. Use the students' developmental stage to your advantage when teaching fractions by using examples they will readily understand. The foundation required to understand fractions lends itself to many visual examples. Students should explore fractions through drawings, stories and blocks to fully understand them and to gain a solid foundation for later mathematics courses.