You child might know what half a cookie is, but how about 4/8 of a pie, or 2/4 of a pizza? If your child knows that all of these fractions mean the same thing, she's well on her way to understanding equivalent fractions. But if fractions strike fear into your child during homework hour, here’s a hands-on way to help her understand how common fractions can be equivalent.
Begin by asking your child what equivalent means. If she's having trouble, help her find a familiar word within the word (“equal”). To gauge how clear or unclear she is on the concept, ask her to explain it to you. You can even mention that you can't remember the concept from when you were in school, and that you would love a refresher course from her. This may relieve whatever pressure your child may feel if she is uncertain about the concept. Tell her that you will work together to figure it out.
Give your child the piece of 8 ½ x 11 paper. Have her hold it horizontally (if your child confuses horizontal with vertical, tell him/her that horizontal is like the horizon). Have her fold the paper in half, then open it up again, and ask her to shade in half the paper using a colored pencil.
Tell your child to now fold the paper into fourths (i.e. half, then half again). Ask her child to open up the paper. Ask her how many fourths are equivalent to one half. When your child figures out that 2/4 = 1/2, encourage your child write this equation on the lined piece of notebook paper for future reference and review.
Repeat Step 3, but go on to fold it into eighths and then sixteenths, each time having your child write down the fractions that are equivalent to 1/2.
As an extension activity, you can have your child write down all the other equivalent fractions he/she sees, like 2/8 = 1/4 and 2/16 =1/8, etc. You can continue this activity with thirds, sixths, twelfths and twenty-fourths. You child will be surprised at how fractions that look big and "scary" as actually the very same fractions that they are familiar with!
Vanessa Genova DeSantis has been teaching for fourteen years in public and private school settings in grades 4-8. She's also an educational freelance writer as well as a private tutor for elementary, middle and high school students.