In 2006, the National Math Panel reported that knowledge of fractions is the most important foundational skill for algebra that is not developed among American students.
Research shows that fractions are one of the most difficult topics for students to understand in elementary school. I think the problem lies in the fact that children are expected to be passive receivers of information rather than be actively involved with the subject matter.
CGI (Cognitively Guided Instruction) has been stressing for many years that the best way to help children really understand fractions is to begin with “fair shares”.
Start with situations of 2 or 4 children, as children’s earliest partitions are based on halving:
4 children share 4 cookies so that each child gets the same amount.
4 children want to share 10 brownies so that each child gets the
4 child want to share 22 apples so that each child gets the same
Move to situations with more sharers:
3 children want to share 7 candy bars.
6 children have ordered blueberry pancakes at a restaurant. The
waiter brings 8 pancakes to their table. If the children share the
pancakes evenly, how much can each child have?
Matthew has 13 licorice sticks. He wants to share them with 8
20 friends are sharing eight cakes.
Ask your child or your students to solve the problems using a strategy that makes sense to them. Strategy is the primary dimension of development because student-generated strategies can (and I believe should) serve as the foundation for mathematics instruction. A focus on student-generated strategies allows a teacher or a parent to begin with, and build on, what children already know, and it allows children to participate in instruction by making contributions that are personally meaningful.
Give children pencils and paper and access to any kind of manipulative they find helpful and allow them to work out the problem by themselves.
Once the task is completed, children need to be able to demonstrate to each other what they did and the answer that was found. The more students are encouraged to contribute the intact products of their own thinking to class discussions, the more likely they are to identify themselves as understanding math – no matter the level of the thinking.
The key in fraction instruction is to pose tasks that will elicit a variety of strategies and representations. Equal-sharing tasks are not the only problems that can do that, but many teachers, like myself, have found them to be a definite source of variety in thinking. Children learn from each other, and the teacher begins to get a picture of what each child knows.
Another great way to help your child or your students to understand fractions is to play a fraction game. I have found that Fraction War can be highly effective. The first level begins simply, and it is probably best to start here, even with older children. Once you are sure they understand this concept, move to the next concept level.
One deck of cards
Fraction War Game Board (following)
Players draw cards and create a fraction. The player with the fraction with the greatest value wins a point for that round. The player with the most points when all the cards have been used is the winner.
Each player finds and places a one in the numerator position on his/her game board. This card remains in place until the end of the game. Each player draws a card and places it in the denominator position. The player with the greatest fraction wins the point. Play continues until all cards have been used.
Place a one in the denominator position and play as above.
Decide on a number between 2 and 10. Each player places that number in the denominator position. Play as above.
Place the same number in the numerator position. Play as above.
Each player draws 2 cards. The first is the denominator, the second is the numerator. Play as above.
Fraction War Game Board
Player #1 Player #2