Introducing Your Children to Fractions
According to the Educational Research Newsletter algebra teachers rank poor understanding of fractions as one of students' biggest weaknesses in preparation for the study of algebra. My girls are still in the first years of elementary school, why am I worried about algebra? All math builds upon the foundations of the previous years. If you want your child to do well in math you need to lay a solid foundation for them.
A panel of mathematic experts believes that one of the problems is that children don’t view fractions as numbers. Fractions are seen as meaningless symbols inflicted upon them by math teachers probably for the purpose of tormenting them. So how do you prevent this?
Introduce you child to fractions early and in a concrete way that can be easily seen and understood. Have a “math party” with pizza, pie, cake or anything else that can easily be divided into equal parts. Cut the pieces in front of your child and explain what happens after each cut. “I made one cut and now the pizza is divided into two pieces – each piece is one half a pizza.” “I made two cuts and now the pizza is divided into four pieces – each piece is one fourth a pizza.” When you are done cutting tell them how much pizza you will eat. “I am having 2/16ths of a pizza.” (Don’t worry about reducing your fractions at this point as that is likely to confuse them.) Then ask your child how much pizza he or she wants and help him or her express the answer in a fraction.
Measuring cups are another way to further your child’s understanding of fractions. Give the children a tub of rice or beans (even water works although it can be difficult to gauge the levels). Then show them how scooping out two halves produces the same amount of rice as scooping one cup. Let them experiment with the different sizes, but be sure to talk them through the amounts they are adding and which amounts will be larger or smaller. You do not need to worry too much about exact amounts at this point, you are introducing concepts.
After you have showed your child several concrete examples of fractions you can move to drawings and paper representations to further his or her understanding. Dissect circles, squares and rectangles on paper for your child to see. Get him or her used to the terminology associated with fractions.
Simple Fraction Story Problems
Fractions are also a great time to have a lesson about sharing. If we have one cake to share with a class of 8 how many pieces should we cut the cake into? If we cut the cake into 10 pieces instead would our pieces be larger or smaller? After your child answers (weather correctly or incorrectly) reiterate that 1/10th is smaller than 1/8th.
Students can become confused by the idea that 1/8th is larger because they are looking at the number 8 instead of 1/8th as a whole. Explain that 1/8 is a different number than 8. If the teacher had brought in eight cakes how much cake would each of the eight students have gotten?
But the teacher only brought in one cake and it was cut into eight pieces, so each student got 1/8th of a cake. After you’ve gone over this concept, your child will quickly realize she would rather have ½ the cake than 1/8th.
Try introducing the idea that you can always divide something into smaller and smaller pieces. Let them expand upon the idea to ridiculous proportions – you’ve divided the cake among so many people that each person only gets a tiny crumb. Then explain that with a share enough knife you could divide the crumbs and have an even smaller fraction.
The bottom line is simply let your children play with fractions. If they have fun with it now it won’t be a torment for them later. I hope this proves helpful to you. I’ve also included some worksheets at various levels to further aid your studies.