Math Dictionary Sections: (7) Decimals & Fractions & (8) Estimating to Half or Whole
Upcoming Assessments: Number Theory & Fractions Quiz (complete on Mon. 10/25/10); Multiply & Divide Fractions (TBA)
After reviewing our Number Theory work from last week we went straight into a review of fractions, which includes indentifying fractions being represented in different ways (on a number line, in a 10-by-10 grid, and with pictures), demonstrating equivalent relationships among fractions, and comparing/ordering two or more fractions in ascending and descending order. While all of this is a review of everything learned about fractions in elementary school, our work with fractions the rest of this school year will be more complex, thus students need to fully understand the basics of fractions and their purpose.
We reviewed three ways for comparing/ordering fractions: cross products; converting to equivalent forms of fractions with common denominators; converting to decimals. Using cross products is discouraged since it does not teach number sense in addition to being problematic for many students, who multiply in the wrong direction. We do a brief review since many students were taught that method in elementary school, but they are asked to use that only to check their work. Last week's work on least common multiple (LCM) carried over into the convertion of fractions. To compare fractions with different denominators, students reviewed how to convert fractions to equivalent forms with a common denominator; the least common denominator is the least common multiple of all the fractions' denominators (LCD = LCM). In order to convert and compare fractions in their decimal form, students were taught that the fraction bar also means divide (if you are splitting something into fractions, you are dividing it into groups or pieces that were once part of the whole). For now, students were told to use their calculators to do the division (N/D = N÷D); we will review computation with decimals next term.
Students wrapped up the week by starting a quiz on Number Theory (last week's material) and Fractions (this week's), which will be finished on Monday. Our review of fractions will continue after they complete the quiz in order to prepare for our next unit, multiplication and division of fractions (with mixed and whole numbers).
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