Fractions
When taking up fractions with the elementary child, the same progression exists as with whole numbers. The first presentation is the introduction to the quantity or concept. This lesson shows that a fraction is a unit broken into equal pieces. The etymology of the word fraction is given to the children in order to explain the concept. The word fraction comes from the Latin fractus, which is the past participle of frangere, meaning ‘to break.’
The children begin exploring different equivalencies using the material—a concrete way to see that one half fits in the space of two- fourths, three-sixths, four-eights, and five-tenths. The children will carry this idea to all the fractions from halves to tenths.
Next, we introduce the language of numerator and denominator, relying on the etymology of the words to clarify the idea. The line that separates the numerator and denominator represents the idea of division. The number that you write under the black line tells us how many equal pieces there are in that family or it tells us how many pieces that unit has been divided into. We call this number the denominator. The word denominator comes from the Latin ‘nomen’ meaning name. The denominator tells us the name of the family and it tells us how many equal pieces the unit has been divided into. The number above the line tells how many pieces there are of a fraction This word numerator comes from the Latin ‘numerus’ meaning number.
After the introduction to fractions and a good deal of equivalency experience, we introduce the simple operations (addition, subtraction, multiplication and division) beginning with addition. When approaching the operations in any of the four functions, the first step is always the sensorial manipulation. After the sensorial experience, the writing is introduced to the child, always drawing on their knowledge of what the functions are from their experiences in the primary program.
The child may have already worked with the four functions in the primary program but with common denominators only. In the elementary, the children will begin here again and along with their work in factors and multiples will be able to practice these four functions in the learning of uncommon denominators learning. Improper fractions and reducing are introduced as well.
When the child has an understanding of fractions, we begin decimal fractions in the same manner.
(Overall View of Manipulative) (2/4 is equal to 1/2) (10/10 is equal to 1 whole)
(2/6 is equal to 1/3) (1/8 + 5/8 = 6/8 = 3/4)