Give all the children in the class some modeling clay to work with, then ask them to divide their dough into two equal pieces. On the chalkboard, write a large number "2." Tell the kids to notice that they have divided their single piece of clay into two equal pieces, which is what the number on the board represents. Next, instruct the kids to pick up one of their two pieces of clay. Write a "1" over top of the "2" in fraction form, saying, "Now each of you is holding one out of two of your pieces, or one half." Ask the children to explain how they would write the fraction if they were holding both pieces in one hand, or "two out of two" of their pieces. Show the kids how to divide the clay into four, then show them how a half can be divided into quarters, how a quarter can be added to a half, and so on, writing fractions on the board as you go. You can also use a paper circle or square and cut it into pieces to proceed through the exercise.
Like models, diagrams provide another way for kids to associate practical concepts and understanding with numerical fractions. Draw a square on the board, and divide it into eight equal pieces. Show the kids the lines that divide the square into two pieces, four pieces and eight pieces. Demonstrate how you can shade one half, or 1/2 of the square by coloring four pieces. Next, shade the square to show how 1/2 plus 1/8 would look. Ask other addition questions involving halves, quarters and eighths and challenge students to come up to the board and shade the answers.
After your model- and diagram-based lessons, kids should have a grasp of the basics they need to know to add fractions without visual aids: fractions represent parts of wholes, parts can be added and a fraction can be presented numerically in more than one way. Show students the basics of fraction addition using simple examples they're comfortable with. Describe the steps of multiplying to find the lowest common denominator, adding the numerator only, then checking to make sure that the numerator and denominator can't be reduced. Use diagrams to support the lesson at first, then move on to more complex examples.
Sometimes kids get stuck on math problems because they forget where to start or what to do next. Make math problems easier with a step-by-step handout and example that clearly show the process that kids need to follow: 1) Check that the denominators are the same; 2) If they're not, multiply the top and bottom numbers in each fraction by the denominator from the other fraction; 3) Add the numerators; 4) Check to see if you can reduce the answer by dividing the numerator and denominator by a common number.