“What is ½ plus ½ ?” Ask that to a child, in higher elementary or middle school, and too often they’d answer “2/4”. Even some high school students would answer “2/5” when asked “what is ½ plus 1/3?”

When a whole is divided into a number of equal parts, they are called fractions. When a person encounters the word “fractions” the images “part of a whole” and “equal parts” must come to mind.

This concept must be second nature and deeply embedded in the child’s consciousness, and the earlier in life the better.

Half: Two Parts The Same

Start by teaching children the basic principles of half. Once the idea of half is learned thoroughly, its attributes can be easily applied to all other fractions.

Teaching Two Parts The Same

Children often call any division into two pieces “half” whether the pieces are the same (equal) or not. Correct the child and say that the two parts must be the same to have halves.

Next, ask ”what is half of 4?” then half of 6, 8. Then ask “what is half of 3?” Most likely they will answer “there is no such thing as half of 3”. Ask the child to imagine 3 cookies and to divide them into “two parts the same”. They will discover that one cookie must be broken into two pieces.

Now you have introduced the child to a very important mathematical concept: All wholes can be broken down into parts.

Next ask “what is half of 5? … of 7?”

In a couple of weeks the child will have mastered the skill.

Next, ask a reverse question: “half of what number is 3?” and the next reverse question is “half of what number is two and a half?”

If your child has trouble with these reverse questions, have them draw pictures of the parts, both separate and combined. Or break up and recombine cookies until they see the concept.

Bring on the Reinforcements

Ask questions like:

• “What is half of 10?”
• “Half of what number is 4?”
• “I have 8 books. If you take half, how many will you have?”
• “Half of the cookies are missing and we have 6 left. How many did we start with?”

Movin’ On

Draw five sandwiches in a row. Then draw with a line dividing them all in half and ask:

• “If you have 5 whole sandwiches, how many half sandwiches can you make?”
• “If you have 8 half sandwiches, how many whole sandwiches can you make?”
• “If you have 3 half sandwiches, how many sandwiches do you have?"
• “If you have 5 sandwiches and eat one and a half of them, how many do you have left?
• “If you have two and a half sandwiches and I have one and a half sandwiches, how many do we have altogether?”

After mastering the above questions, comes “what is half of a half?”; when explaining this, remind them that half means two parts the same.

Next, try a more complex reverse question like:

“You have a box of cookies. You eat half of them after lunch and half of what’s left after dinner. After dinner, you have two cookies left. How many cookies did you start with?”

If you do these things on a daily basis, one day it will “just happen” that your child will be able to intelligently talk about half. They already understand the basic concepts of fractions and ready to move on to the next level.