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There are never enough strategies for teachers to help students understand what fractions are and why we need to know and work with them.
Having students color parts of the whole is a good way to start out. For primary grades, the students should color half of objects, then moving into fourths, thirds, and so on. Once they start to grasp the concept of part of a whole, work backwards by having them reconstruct a whole from its parts.
Using a rectangular model and having students divide the whole rectangle into a given set of parts, and then combining that rectangle with another divided into different parts, is a way to show addition of fractions. For subtraction, again use the rectangle, and by removing the overlapping pieces, the answer is what remains. Multiplication is easiest. Simply slide the two rectangles one over the other, and the combined color or the squares that are on top of each other is the answer. Enough demonstration of this, and students start to see the pattern and realize the standard algorithm used. Division has always been difficult. One way is to have a length of ribbon, say Н yard. If bows are to be made from 1/8 yard of ribbon, how many bows can be made from the Н yard of ribbon? Using the same measurements, ask how many eighths are in a whole. The ask how many halves are in 1/8. Again, this can be shown using rectangles and sliding one over the top of the other and visually seeing where the parts come from. Lastly is the trick of cross multiplying. Using the same measurements:
If students have a grasp of greatest common factor, then reducing fractions isnt difficult. However, using the TI-73 as an instructional tool, teachers can ask questions that allow students to discover when fractions need to be reduced (in traditional terms).
Display the fraction 2/4 on the calculator. Press enter, and the fraction shows up with a down arrow. The arrow means that there is a factor hidden in the fraction. If SIMP is pressed after the fraction, and then enter is pressed, the calculator simplifies the fraction, listing the factor that was removed from the fraction. To have students work with reducing fractions and not having the calculator do it for them, after entering the fraction and pressing SIMP, the students should enter what they think a factor of the fraction might be. If they are correct, the reduced fraction is shown on the right of the screen. If not, the fraction remains the same.
Using the fraction to decimal key ( ) students can become familiar with common fractions and their decimal equivalent, even to toggle back and forth between the two.
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