math ed stuff belleville hs
Trig Tricks with All Sorts of Technology at BHS
© 2014, 2017, Agnes Azzolino

Precalc Index
  • Take notes with Alt+Print Screen and a paint program.
  • Make 30-45-60 functions easy.
  • Think "Oscar Had A Heap Of Apples."
  • Make radian measure easy.
  • Consider reference angles and "Veronica's Bow Tie."
  • Make the Unit circle come alive.
  • "Derive" quadrantals and trig graphs with SketchPad.
  • Graph all 6 functions w/special trig graph paper.
  • "Prove" the Pythagorean identities with the Unit circle.
  • Curve shift with Excel.
  • Review with Windows Explorer. Directory: Individual Pages:















Educational Theory

Choose to Improve Instruction.
  • Choose a modality first.
            Visual, Auditory, Symbolic, or Kinesthetic       web notes
     
  • Introduce in the concrete.
     
  • Review in the abstract.
     
  • Sometimes use multiple modalities at the same time.
     
  • Strive for comfort in all modalities, not just your favorite.
     
  • Repeatition improves retention,
            especially in different modalities.



Vary the technique to achieve the above.
  • Use color rather than black and white.
     
  • Use active rather than passive.
     
  • Use pictures rather than just text.
     
  • Use spoken word rather than just text.
     
  • Use white space to improve clarity.
     
  • Larger is usually clearer than smaller.
     
  • Sometimes start with the big picture rather than the details.
     
  • Reference to earlier work improves comprehension.
     
  • Showmanship -- a performance -- improves retention.




Precalc

Make 30°-45°-60° functions easy.
Think "Oscar Had A Heap Of Apples."
Use connect-the-dots to complete simple compuations.
Use active rather than passive.
 

*Write it in script vs. print it vs. Pre-Print it
*8th grade, to 10th grade, to precalculus
*Start to build a cheat sheet and continue
*Library of connect-the-dots puzzles/worksheets
      *blank connect-the-dots questions *answers
*central angle, clockwise/counter-clockwise, coterminal, negative/positive angle measure


Make radian measure easy.
Consider reference angles and "Veronica's Bow Tie."


*2 mile race (visual with auditory and kinesthetic)
*basic Veronica's bow tie *advanced Veronica's bow tie
*45°s
*internet trig reasources


See the Unit circle move. Derive Pythagorean Identities. Graph tan function.
 
The Unit Circle
*web, static, but with color
*web, active
      The Animated Unit Circle. - animation w/text.
*UNIT CIRCLE JIG SAW PUZZLE, do it kinesthetically
      unit circle jig saw puzzle master
 
The Usual Way vs. The Active Way
*sine/cosine only, web active
*quadrantals notes the usual way
*sine and cosine graphed
*write on similar triangles
    completed notes on similar triangles for tangent
All 6 Functions
*tangent actively
 
Proofs
*Pythagorean Identities -- graphically and by hand symbolically
*Examine odd/even identities
   
Blank 3 plane paper
blank 3 planes per page, web
      3 planes per page gif
Other graph papers



Curve shift with Excel.
Curve shift with an image.


*sine sine on a spreadsheet, web
*blank cut and pasted spreadsheet notes
completed cut and pasted spreadsheet notes
graphic function library



Review with Windows Explorer.
00 01 02 03 04 05 06 07 08 09 10
11 12 13 14 15 16 17 18 19 20 21 22
Review joe17 with Windows Explorer. Review ordered Windows Explorer.



PARCC and Geometry

"Who Has"

Geometry -- Area
Other Games



Algebra I

Kinesthetically Explore Functions
Functions
  Exploring Functions Through the Use of Manipulatives, the entire book
 
 
 
  library
 
curve shifting -- translations, dilations, reflections: algebraically and graphically
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Place the wax paper on top of the coordinate plane to graph:
 
1. y= (x)
 
2. y= - (x)
 
3. y= ( - x)
 
4. y= - (- x)
 
5. y= (x - 3)
 
6. y= (x + 2) - 1
 
7. y= - (x + 2) - 1
 
8. y= (x - 6) + 2
 
9. the inverse of y= (x - 6) + 2

more graphing
*solving
*raw masters
absolute value dilator in hand
*Slopemeter w/movement
Math Exercises (later)
*gif masters
 



Algebra II



The Squares and Cubes of the Sums and Differences of Two Numbers


Unit 17: Algebraic Multiplication


Unit 20. Binomial Squared and Cubed

Try to assemble the cube of the difference of two numbers.




Source page
Appendix and Masters and Digital Manipulatives



Calc

Derivative & Antiderivative of Sine & Cosine Functions

Graphs



Stat

Statistics Computation Resources

stat.xls - a spread sheet completed computes needed for hypothesis tests
HYPOTHESIS TESTS - different tests and their parameters



Closing

It's time for "Math Exercises."


 
Math Exercises web page
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please stand.

Use your body particularly your hands and arms to represent:

The line y = 0, the x-axis.

Represent the y-axis: x = 0

Represent: y = x, the identity.

Represent: y = -x, the opposite.

Represent: y = x², the squaring function.

Represent: y = |x|, the absolute value.

Represent: y = -2x².

Represent: y = 1/x, the reciprocal.

Represent: x = y².

Represent: y - |x-1|, the distance between a number and 1.

Represent: y = |x| - 1, the absolute value, less 1.

Represent: y = |x| + 1, the absolute value, plus 1.

Please take your seat.



 
 
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© 4/2017, A2
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