To understand fractions, students must first grasp the concept of equal parts. This can be practiced in first and second grade as students share items equally or fold a piece of paper into two or four parts while looking at a visual model. At this age, teachers can draw attention to the meaning of fraction words in everyday life, such as half an hour and a quarter of a dollar. At this stage, students should work exclusively with physical objects, not with written labels or pictures.
The Common Core Standards in math recommend that fractions be introduced in third grade. In this year, the standards require students to understand that a fraction with the numerator "1" means one of an equal number of parts. It also requires students to identify a fraction on a number line, and to use visual models to identify equivalent fractions. All of these skills should be taught first with hands-on materials, and later with pictures and numerical expressions after students are successful with objects.
In fourth grade, according to the Common Core Standards, students should be able to compare fractions by using visual models or by identifying common denominators. They should also be able to add and subtract fractions with a common denominator, multiply fractions by a whole number, and connect fractions with denominators of 10 or 100 with their equivalent decimals. As the denominators of these fractions become larger, it becomes more difficult for students to express them with objects, so they must rely more on their number sense and calculation and less on visual models.
By fifth grade, students should be able to solve problems involving fractions by finding common denominators and reasoning about the size of fractions. They should also be able to multiply two fractions, divide a fraction by a whole number, or divide a whole number by a fraction. It is important that students maintain an understanding of each of these skills in a real-life context as they move through these levels. This can be done by solving word problems or hands-on problems using fractions.