Introduce the concept of fractions by demonstrating visually where the fraction 1/2 falls on the number line. Draw the number line, labeling the whole numbers 0 and 1. Mark the halfway point between 0 and 1 with a mark taller than those used for the whole numbers and label the point 1/2 so it is positioned above the whole numbers. Make sure children understand that dividing 1 into two parts makes the fraction 1/2. Demonstrate the fractions 1/4, 2/4, 3/4 and 4/4 by dividing the space between 0 and 1 into three equal parts; label the first part 1/4, the second part 2/4, the third part 3/4 and show the children that 4/4 is equal to 1 by writing 4/4 above the 1 on the number line. They will see a row with whole numbers and a row with fractions.
Have third-graders draw the position where fractions belong on a number line. Draw a large number line on the blackboard, labeling the whole numbers 0 and 1, and indicator lines for fractional points on the line. Write out various fractions such as 1/2, 1/4 and 1/8 on pieces of paper with adhesive on the back. Hand out one paper to each third grader. Have them take turns going up to the front of the classroom and putting the fraction where it belongs on the number line.
Use several number lines drawn to the same scale to demonstrate equivalent fractions. You would teach third-graders that 1/2, 2/4 and 4/8 are equivalent fractions, for example, by using three number lines each drawn underneath each other. Draw the first number line, marking off the whole numbers 0 and 1 and marking the halfway point between 0 and 1 as 1/2. Draw a second number line underneath the first, but this time divide the line into three intervals between 0 and 1, marking where 2/4 belongs. Draw a third number line, dividing the space between 0 and 1 into 7 equal intervals, marking where 4/8 belongs. Show the children that 1/2 is in the same position as 2/4, which is in the same position as 4/8.
Show children how to add or subtract fractions by drawing these operations on a number line. When adding 1 3/8 + 2/8, for example, drawn a number line, marking the numbers 0 through 2 and mark off 1/8th increments between numbers. Have children circle the 1 3/8 mark and add 2/8 by moving two increments to the right, arriving at 1 5/8, circling the final answer. Show subtraction in the same way, but have the children move to the left on the number line.