proportional reasoning
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Proportional Reasoning. Equivalents. Integer Rods. White 1 cm x 1 cm W Red 2 cm x 1 cm R Lime 3 cm x 1 cm L Purple 4 cm x 1 cm P Yellow 5 cm x 1 cm Y Green 6 cm x 1 cm G Black7 cm x 1 cmK Brown 8 cm x 1 cm N Blue 9 cm x 1 cm B - PowerPoint PPT PresentationTRANSCRIPT
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Proportional Reasoning
Equivalents
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Integer Rods
WhiteWhite 1 cm x 1 cm WW Red 2 cm x 1 cm R Lime 3 cm x 1 cm L Purple 4 cm x 1 cm P Yellow 5 cm x 1 cm Y Green 6 cm x 1 cm G Black 7 cm x 1 cm K Brown 8 cm x 1 cm N Blue 9 cm x 1 cm B Orange 10 cm x 1 cm E
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Equivalent Rods
Equivalents How many combinations can be made of each
type of rod? Is there a pattern?
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How many different ways are there to make W?
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How many different ways are there to make R?
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How many different ways are there to make L?
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How many different ways are there to make P?
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What is the pattern?
How many different ways are there to make Y?
Rods # of Units in Rod
# of Equivalents
W 1 1
R 2 2
L 3 4
P 4 8
Generalization n ?
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How many different ways are there to make G?
What is the pattern? Number of Equivalents = 2(n-1),
where n is the number of units in a rod
Should you assign your students to find all of the equivalents for K or N?
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On a test or quiz you will have to give a semi-concrete model of the rods
It is important that your semi-concrete models be as accurate as you can make them
The letter representing the color of the rod should be placed in each rod’s representation once and only once – see class notes
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Equivalent Fractions How do we represent fractions using
integer rods? Part to whole Whole changes as necessary to make
equivalents A train is two rods put together We will ALWAYS use the least number of
rods possible to make a representation Do NOT draw more lines on
representations than necessary
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One half is W over R:
One half is R over P:
One half is ? over ?:
How many half equivalents are there up to an EE train?
R
W
P
R
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One third is W over L:
One third is R over G:
One third is ? over ?:
How many third equivalents are there up to an EE train?
L
W
G
R
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One fourth is W over P:
One fourth is R over N:
One fourth is ? over ?:
How many fourth equivalents are there up to an EE train?
P
W
N
R
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What rational number does this represent?
What rational number does this represent?
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Other Manipulatives
We have just looked at two manipulative that can be used to model rational numbers, there are MANY others
Check out some other electronic manipulative listed under http://ejad.best.vwh.net/java/patterns/patterns_j.shtml and http://nlvm.usu.edu/en/nav/topic_t_1.html