math ed stuff
"Functions from a Standard 4.5 Perspective Grades 9 - 12"
© Agnes Azzolino
10/2014, AMTNJ




      Create and use mathematical processes and representations to organize and communicate mathematical ideas through concrete, pictorial, symbolic and graphic representations. Graph and take inverses in four modalities.



Standard 4.5 REPRESENTATIONS
Create and use representations to organize, record, and communicate mathematical ideas through concrete, pictorial, symbolic and graphic representations
 
Select, apply, and translate among mathematical representations to solve problems
 
Use representations to model and interpret physical, social, and mathematical phenomena
 


The Languages of the Math Classroom
© '98, '08, '09 Agnes Azzolino
 
MOTHER TONGUE & OTHER TONGUE(S)
Most Sophisticated and also the Most Basic
 
MOSTLY MATH TONGUES
Most Sophisticated, Most Basic
 
VERBAL / Auditory WRITTEN / Symbolic     PICTORIAL / Visual     CONCRETE / Kinesthetic    
  formal spoken mathematics   written word   DIGITAL MANIPULATIVE     object
  informal spoken mathematics       written symbol   moving picture   model
  spoken symbol   semisymbolic   static picture   manipulative/token
  symbol speak   calculator symbol   numeral
  calculatoreze/computereze   graph
  web speak   nonverbal body language


Graph
 
Graph by placement on the coordinate plane. DTWYP.
a. the identity function
b. the opposite function
c. the reciprocal function
d.
e.
f.
g.
h.
i. y = (x - 4)²
j. y = - (x - 2)² + 3
k. x = y²
m.
n. the distance between a number and 3


Solve
Solve the statements by graphing 2 functions on the same plane:
[a.] |x - 3| = 4
[b.] |x - 3| = 0
[c.] |x - 3| = -4
[d.] |x - 3| = |x + 2|
[e.] |x - 3| = ( x + 2 )² + 1


Take Inverses in Four Modalities

        An example

        Some problems


Resources
The coordinate plane is at:
        www.mathnstuff.com/gif/mciplane.gif .
 
The inverse function problems are at:
        www.mathnstuff.com/math/spoken/here/2class/300/invfp.htm
 
Hand out for the Exploring Functions Lecture is at:
        www.mathnstuff.com/papers/ef/efho.htm
 


Math "Exercises"(www.mathnstuff.com/papers/langu/exerc.htm)
a) Use your body, arms, and hands to represent the graph of:
1. y = 0
2. x = 0
3. y = x
4. y = -x
5. y = x²
6. x = y²
7. y = -2x²
8. y = - |x|
9. y = 2|x|
10. y = |x| - 2
11. y = |x| + 2
12. y = 1/x
b) Please be seated.
 


Thanks for Playing


 
 
[MC,i. Home, site home page] [Good Stuff -- free & valuable resources] math games toc
[MSH! Home -- arithmetic & algebra dictionary home page] [master list of all MSH! dictionary words] math tokens
© 10/2014, A2
www.mathnstuff.com/papers/amtnjeb.htm