Proportional Reasoning Equivalents

Integer Bars WhiteW White1 cm x 1 cmW Red2 cm x 1 cmR Lime3 cm x 1 cmL Purple4 cm x 1 cmP Yellow5 cm x 1 cmY Green6 cm x 1 cmG Black7 cm x 1 cmK Brown8 cm x 1 cmN Blue9 cm x 1 cmB Orange 10 cm x 1 cmE

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 bar’s representation once and only once – see class notes

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

 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?

 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?

 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?

 What rational number does this represent?

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

Equivalent Blocks  Hexagon  Trapezoid  Rhombus

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

 One half  One Third  Two Thirds  One Sixth

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?