Students learn that fractions are a part of a whole as a first fraction concept. You can do this by dividing any geometric figure into evenly distributed parts. For example, equally bisect a square with a line to create two halves and bisect it again at a 90-degree angle and create four fourths. Have the students copy the process using circles and squares. Offer more tasty and enjoyable dividing games using snack-sized bags of colored candies such as Skittles, M&Ms or jelly beans. Sort the candies by color to see that each color represents a part of the whole bag. Challenge the students to graph the fractions or write them in fraction form. You can also divide pizza, pies, cakes and other foods in a similar manner.
Children understand concepts easier if they can see and touch them. Manufactured manipulatives such as segmented blocks, Cuisenaire rods and fraction bars offer you items to purchase. Instead, have the students make fraction manipulatives such as cutting equally divided wedges into a round paper plate. Don't cut the wedges all the way through, so they stay attached at the very center of the plate. Another option includes making four identical items, such as kittens or flowers, and marking each item as one-fourth of the group.
Explain that numerators mean the total number of items in a group, and denominators provide the name of the group. Have them write the fraction and see the denominator as an apple or a bear instead of a number. Show the total number of items in your group name, such as five bears, below the fraction line and three above the line to represent three-fifths of the bears. Alternatively, illustrate one fraction such as one-third and two-fourths on a single sheet of colored paper. On different-colored paper, write the fraction in numbers on one side and an action they must perform on the flip side. Give a child the number fraction and have him hunt to find the pictured match and perform the action when the match is found.
Using the concept of numerators as numbers and denominators as a group name, show the children that you can add two cats and three cats to get five cats, but not two cats and three dogs. They learn they can add or subtract fractions that have similar denominators. Use groups of colored candies or identical tokens to add together to make a fraction.