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Jayne Halvey
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Mathematics Instructional Aid
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Fraction Square Sets
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1. Major Purpose of Aid:
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The major purpose of this aid is to help students develop relationships
between fractions and to relate them to the real world. Students will be
using manipulatives that represent the values if a whole, halves, thirds,
fourths, fifths, sixths, eighths, tenths, and twelfths to help them gain a better
understanding of relationships between fractions and their real world
applications. For example, the whole square could represent a whole pizza,
or a third might represent the amount of the pizza covered with pineapple.
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2.Ideas for Active Student Learning:
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The first step to introduce fractions would be to explain them in terms of
whole numbers. This could be done by using the whole square to explain
that it is equal to 1, as in 1 whole pizza. The next step would be to ask
students to put half pepperoni on their whole pizza, having the students
place a half piece on top of the whole piece square. Them the teacher could
have the children add more to the pizza, like one fifth olives, having them
place a fifth on top of the whole square beside the one half piece. The
teacher would continue to make questions more complicated by asking
students to add and subtract fractions of the pizza. For example, the
teacher might say, "If there are only five sixths of a pizza left and I eat one
third, how much pizza will I have left to eat?" The students could then use the
manipulatives by placing five sixths of a square in front of them and then
placing a one third piece on top of the five sixth pieces to show that there
are three sixths left over. The same thing could be done with addition of
fractions, the teacher could say, "If I have half of a whole pizza and my friend
gives me one fourth of his whole pizza, how much pizza will I have then?"
The students would then place a one half piece next to a one fourth piece
and then use the other one fourth pieces to cover up the half piece, showing
that the teacher would now have three fourths of a pizza. The teacher would
continue to ask real world questions to keep the students interested and
involved, and to show how fractions are used in real life situations.
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3.Grouping of Students:
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Students will work in pairs, or no more than three per group if there is an odd
number of students in the class. This grouping gives students the chance to
help each other understand fractions and it allows students to individually
have a hands on experience or actively participate in the lesson.
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4.Flexibility:
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This manipulative could also be used to teach decimal computation. The
whole square could equal 100 (the teacher might want to draw the 100
squares on the whole piece). The teacher could then ask the students to
find what decimal one fourth is equal to, having them count the number of
squares that one fourth covers (25), and then seeing that 25/100 is equal to
.25.
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(1/4 = 25/100 = .25)
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5.Description of How the Aid Was Constructed:
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Materials needed:
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36 pieces of polyfoam
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The following ink pads:
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The 20cm square, and its halves, thirds, fourths, fifths, sixths, eighths,
tenths, and twelfths pads.
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An Accu-cut machine
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To get cut outs you place the sheets of polyfoam on top of the inkpads and
roll them through the Accu-cut machine.
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Note: I cut the cut outs from the machine into fourths in order to cut the cost
of the manipulatives down, it is possible to just use the 20cm square instead
of cutting it into fourths.
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There are fifteen sets if fraction square sets and each contains a whole
square, two halves, three thirds, four fourths, six sixths, eight eighths, ten
tenths, and twelve twelfths.
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6.Source of Idea:
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This idea came from the textbook, Elementary and Middle School
Mathematics, by Van De Walle, and from Dr. Zollman.
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