1. Proportional Reasoning Equivalents

2. Integer Rods 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

3. Equivalent Rods  Equivalents How many combinations can be made of each type of rod? Is there a pattern?

4.  How many different ways are there to make W?

5.  How many different ways are there to make R?

6.  How many different ways are there to make L?

7.  How many different ways are there to make P?

8.  What is the pattern?  How many different ways are there to make Y? Rods# of Units in Rod # of Equivalents W11 R22 L34 P48 Generalizationn?

9.  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?

10.  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

11. 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

12.  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?

13.  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?

14.  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?

15.  What rational number does this represent?

16. 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/patte rns/patterns_j.shtml and http://nlvm.usu.edu/en/nav/topic_t _1.html http://ejad.best.vwh.net/java/patte rns/patterns_j.shtml http://nlvm.usu.edu/en/nav/topic_t _1.html