Students are typically introduced to fractions in second grade. If you are teaching third grade students this year, start by reviewing concepts they would have learned last year, such as visually representing basic fractions, comparing simple fractions and the terms numerator and denominator. After a brief refresher, you can lead your students on a more advanced study of fractions including ordering fractions, equivalent fractions and adding and subtracting fractions. Use different teaching approaches, including demonstrations on the board, experiential activities with manipulative's, worksheets and games, so that all students are more likely to comprehend this major mathematical curriculum area.
Review what students would have learned last year about fractions by drawing a circle and dividing it into four equal pieces on the board. Color in one of the pieces and ask if anyone knows what fraction this represents.
Write the correct answer, 1/4, on the board and ask students if they remember what the top number and the bottom number are called. Students should say numerator and denominator respectively.
Pass out a sandwich bag of small candies of different colors to each student. Call out a color and ask several students what fraction of their candies are that color. Check each student to see if they have counted the total number of candies and the fraction correctly.
Introduce the concept of equivalent fractions by passing out copies of rectangular, fraction manipulatives, such as those available on Kitchen Table's Math website.
Ask children to color each bar a different color. Thus the whole, 1 piece would be one color, the half, 1/2 pieces would be another color, and so on.
Demonstrate to students how to determine equivalent fractions with their rectangular manipulatives once they have cut them out. Use your own set of manipulatives or draw something similar on the board. For example, ask students how many quarter, 1/4, pieces can fit underneath one of the half, 1/2, pieces. The students should answer two pieces, meaning that one half is equivalent to two quarters -- 1/2 and 2/4 are equivalent fractions.
Repeat this practice of determining equivalent fractions with the whole class at least 10 times; pass out a follow-up worksheet for students to work on.
Teach students how to order fractions on a number line and to determine which fractions are worth more using the same rectangular manipulatives. For example, students can determine that 2/3s is greater than 1/2 by placing two 1/3 pieces (1/3 1/3) under one 1/2 piece. Also show students that if the numerator and the denominator are the same, the fraction always equals a whole or 1. Provide students with a follow-up worksheets.
Teach students how to add and subtract fractions that have the same denominator. Tell them that they add or subtract the numerators and leave the denominators as is. For example one quarter plus two quarters equal three quarters: 1/4 + 2/4 = 3/4. Provide demonstrations on the board and with manipulatives and provide follow-up exercises.
Allow students to practice the new skills they have learned through playing individual or group games. Assign 10 minutes of playing online fraction games for homework or to a student who has finished his in-class work ahead of time. Organize a fraction scavenger hunt by hiding equivalent fraction cards around the classroom or a team competition where players race to determine the answer to fraction problems.
TL;DR (Too Long; Didn't Read)
From the beginning of the fractions unit, it is a good idea to call fractions by their common names such as "one third", rather than "one over three," or "half" rather than "one over two."