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.


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
*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
*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

PARCC and Geometry

"Who Has"

Geometry -- Area
Other Games

Algebra I

Kinesthetically Explore Functions
  Exploring Functions Through the Use of Manipulatives, the entire book
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
*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


Derivative & Antiderivative of Sine & Cosine Functions




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