Proportional Reasoning

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Proportional Reasoning

• Equivalents

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Integer Bars

• 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
• 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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Integer Bars

• On a test or quiz you will have to give a
  semi-concrete model of the bars
• It is important that your semi-concrete models be
  as accurate as you can make them
• The letter representing the color of the bar
  should be placed in each bars representation
  once and only once see class notes

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Equivalent Fractions

• How do we represent fractions using integer bars?
• Equal parts to whole
• Whole changes as necessary to make equivalents
• A train is two bars put together
• We will ALWAYS use the least number of bars
  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?

6

• 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?

7

• 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?

8

• What rational number does this represent?
• What rational number does this represent?

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Pattern Blocks

• Pattern blocks can be used to represent
  fractional ideas, but they are much more limited
  in the fractions they can be used to represent
• There are six basic shapes of blocks
• Hexagon Yellow
• Square Orange
• Rhombus (small) Beige
• Rhombus (large) Blue
• Triangle Green
• Trapezoid Red

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Equivalent Blocks

• Hexagon
• Trapezoid
• Rhombus

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Equivalent Fractions

• How do we represent fractions using pattern
  blocks?
• Equal parts to whole
• Whole changes as necessary to make equivalents
• We will ALWAYS use the least number of blocks
  possible to make a representation
• Do NOT draw more lines on representations than
  necessary

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• One half
• One Third
• Two Thirds
• One Sixth

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Practice It is the BEST way to learn! ?

• Go to the websites for the different
  manipulative.
• Practice multiple types of fractions using the
  different manipulative.
• What are the advantages of each?
• Disadvantages of each?
• When do we introduce manipulative?