4g End-Of-Year Goals - Equivalent Fractions - Mesa Public Schools

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Dear   P arents   a nd   C aregivers,  
 
Thank   you   for   the   support   you   give   your   child   in   learning   mathematics.     We   w ould   l ike   t o   s hare   s ome  
information   t o   h elp   y ou   b etter   u nderstand   Arizona’s   C ollege   a nd   C areer   R eady   S tandards.   This  is  one  in  
our  series  of   letters   intended   to   help   you   understand   the   work   your   child   brings   home.   W e   w ill  
highlight   s ome   n ew   l anguage   a nd   s trategies   w e  will   u se   t o  build   u nderstanding,   help   c hildren   m ake  
sense   o f   n umbers,   a nd   k now   t he   c ommon   m ethods   w e   l earned   i n   school.     T his   l etter   a ddresses  
equivalent   f ractions   i n   f ourth   g rade.  
 
End-­‐of-­‐year   g oals  
One   o f   t he   more   challenging   concepts   for   fourth   graders   is   that   of   equivalent   f ractions.     U sing   visuals   a nd  
illustrations   i s   a   g reat   w ay   f or   t hem   t o   u nderstand   a nd   “ see”   e quivalent   fractions.   J ust   a s   5   +   5   o r   8   +   2   n ame   t he  
same   a mount   a s   1 0,   t here   a re   d ifferent   f ractions   that   n ame   t he   s ame   a mount.   F or   e xample,  
  a nd  
  a ll  
name   t he   s ame   a mount   that   i s   h alfway   b etween   z ero   a nd .   T hat   m akes   t hem   e quivalent.   H ere   a re   s ome  
examples   y our   s tudent   m ay   u se   t o   v isualize   e quivalent   f ractions.  
Rectangular   m odels  
In   e ach   p icture   b elow     o f   t he   r ectangle   i s   s haded.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
If   t he   r ectangle   i s   s plit   i nto   3   p arts,  
Now   t he   r ectangle   h as   b een  
This   r ectangle   s hows  
half   o f   t he   r ectangle   i s   s till   s haded,  
two   e qual   p arts,   w ith   1  
divided   i nto   3 6   e qual   p arts.   T here  
but   n ow   t here   a re   3   o f   t he   6   e qual  
of   2   e qual   p arts   s haded.  
are   1 8   s haded   p arts   i n   .   T his   i s  
parts   s haded.   T his   i s   t he   s ame   a s  
This   i s   w ritten   a s     a nd  
multiplying   t he   n umerator   a nd  
like   m ultiplying     b y   6 .     ,  
  a nd  
is   c alled   a   u nit   f raction.  
denominator   o f     b y   3 .  
  a ll   n ame   t he   s ame   s haded  
1   x   3   =   3  
2   x   3   =   6  
amount   a nd   a re   e quivalent  
fractions.  
The   n ew   f raction   n ame   i s   .    
Multiplying   t he   n umerator   a nd   t he  
denominator   o f   a   f raction   b y   t he  
  a nd     n ame   t he   s ame   s haded  
same   n umber   c an   m ake   e quivalent  
amount.   T hey   a re   c alled  
fractions.  
equivalent   f ractions.  
  a nd  
all   n ame   t he   s ame   s haded   a mount   a nd   a re   e quivalent   f ractions.   T hey   a ll   e qual     b ecause   t hey   a ll   s how  
 
the   s ame   s ize   e ven   t hough   t he   n umber   a nd   s ize   o f   p arts   d iffer.  
Mesa   P ublic   S chools/Grade   4 /Equivalent   F ractions/2013  
 
Authorization   t o   r eprint   o r   d isseminate   m ust   b e   g ranted   b y   M esa   P ublic   S chools   ( February-­‐2014).

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