altering the complexity of the numbers involved, or the relationships between numerators and denominators.The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include: If each quarter is equally partitioned into 25 parts, those parts are called hundredths since 4 x 25 of those parts fit into one. Both 0.75 and 75% represent 75/100 which is an equivalent fraction to 3/4. Understanding equivalent fractions is critical to making sense of decimals and percentages. Therefore, each third can be divided into four twelfths. The relationship between two thirds and eight twelfths can be represented in this equality.įour times as many twelfths comprise one as thirds. Twelfths are quarter the size of thirds so four times as many twelfths fit into the same length as thirds. Sixths are half the size of thirds so twice as many sixths fit into the same length as thirds. A fraction strip (length) model of the relationships looks like this: Consider these equivalent fractions: 2/3 = 4/6 = 8/12. The symbolic expression does not explain why equivalent fractions represent the same amount. Any fraction can be expressed as an infinite number of equivalent fractions that represent the same quantity and occupy the same position on the number line.įractions are important to measurement, especially where whole units are not precise enough for the purpose. Four tenths are the same quantity of chocolate as two fifths. If the bar was made up of ten pieces then each person might be given two tenths from each bar, giving them four tenths in total. In practical terms the equal share can occur by dividing each of the two bars into fifths, then giving each person one fifth from each bar. Note that the number two fifths, is composed of two units of one fifth. The operation might be recorded as 2 ÷ 5 = 2/5. Sharing two chocolate bars equally among five people requires that the bars be cut into smaller equal parts. Division often requires equal partitioning of ones. Fractions are needed when wholes (ones) are not adequate for a task. Fractions are an extension of whole numbers and integers.
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