Multiplication is the major operation used with equivalent fractions. Students must understand that when they multiply the denominator by a number, they must multiply the numerator by that same number. For example, suppose you begin with the fraction 1/4. If you multiply the denominator by 5, the new denominator is 20. Then you must multiply the numerator by 5 to get 5. This makes 1/4 and 5/20 equivalent fractions.
Pizza slices can help teach children equivalent fractions. Break students into groups of four and provide them with a paper circle representing a pizza. Ask each group to cut the pizza in such a way that each member of the group gets one slice. The students must then write down how many pieces they have out of the entire pizza. Once the students have done so, ask them to cut their one slice of pizza in half, giving them two pieces. Again ask the students to record how many pieces they have out of the total number of slices. Have them cut their pizza slices one more time and record their findings as before. Remind the students that they have had the same amount of pizza all along and point out that all the fractions they recorded are equivalent.
Fraction bars are paper bars of the same length composed of different fractions that students can use to make equivalent fractions. For example, suppose the first bar has two parts each equaling 1/2. The next bar down would then have four parts each equaling 1/4. Students could cut the bars apart to use as tools for making equivalent fractions. For example, if the teacher asks, "How many 1/8ths does it take to make 1/2," students could place the 1/8 bar underneath the 1/2 bar, line them up and count how many 1/8ths make 1/2, which would be 4.
Draw three number lines on the board. Each number line should begin with 0 and end with 1. Write three equivalent fractions on the board, for example, 1/3, 2/6 and 4/12. Ask the students to make hash marks on the number lines (e.g., divide the first number line into three parts, the second into six and the third into twelve) and place the three points (one each) on the number lines. Then ask the student to draw a vertical line between the points (1/3, 2/6 and 4/12). The student will see that the point on the number line does not change position, just the number of hash marks.