exploring sticky problems in algebra ii using algorithms

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Teaching and doing TI-83 BASIC programming in Algebra II Liz McClain and Steve Rives NCTM, October 2007, Kansas City

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Teaching and doing TI-83 BASIC programming in Algebra II. Exploring Sticky Problems in Algebra II using Algorithms. Liz McClain and Steve Rives NCTM, October 2007, Kansas City www.NCTM.mrrives.com. Exploring Possibilities. You Can Do It! … They Need You To. Programs: Simple and Powerful. - PowerPoint PPT Presentation

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Page 1: Exploring Sticky Problems in Algebra II using Algorithms

Teaching and doing TI-83 BASIC programming in Algebra II

Liz McClain and Steve RivesNCTM, October 2007, Kansas City

www.NCTM.mrrives.com

Page 2: Exploring Sticky Problems in Algebra II using Algorithms
Page 3: Exploring Sticky Problems in Algebra II using Algorithms
Page 4: Exploring Sticky Problems in Algebra II using Algorithms

:Input "Real Comp: ",R:Input "Imaginary: ",I:Input "Size: ", S:ClrDraw:For(J,1,94) :For(K,1,64) :0->C :R+J*S->A :I+K*S->B :0->G :0->H :Pt-On(J,K) :Lbl TP :C+1->C :G^2 - H^2->T :2*G*H+B->H :T+A->G :G^2+H^2->V :If C>=25:Goto EP :If V>=4:Goto EP :Goto TP :Lbl EP :If V>4:Pt-Off(J,K) :End:End

Page 5: Exploring Sticky Problems in Algebra II using Algorithms

Problem Solving with Algorithms

Exploring Patterns with Algorithms

Page 6: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive? I.e., where is f(x) > 0

Page 7: Exploring Sticky Problems in Algebra II using Algorithms

How can we find the roots?

Math Knowledge Thinking

Chair

Assign open-ended problems

Page 8: Exploring Sticky Problems in Algebra II using Algorithms

Algorithms Promote THINKING.

Page 9: Exploring Sticky Problems in Algebra II using Algorithms
Page 10: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Page 11: Exploring Sticky Problems in Algebra II using Algorithms

List all factors of p and all factors of q Loop through all p/q Check to left and right of each root to

find where function is positive or negative

Print results in interval format

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive? I.e., where is f(x) > 0

Page 12: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 13: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 14: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 15: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 16: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 17: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 18: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 19: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 20: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 21: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 22: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 23: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 24: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 25: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 26: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 27: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 28: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 29: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 30: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 31: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 32: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 33: Exploring Sticky Problems in Algebra II using Algorithms
Page 34: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 35: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 36: Exploring Sticky Problems in Algebra II using Algorithms

f(x) = 6x4 – x3 + 4x2 – x – 2

Where is f(x) positive. I.e., where is f(x) > 0

Page 37: Exploring Sticky Problems in Algebra II using Algorithms

An Open Ended Problem

Page 38: Exploring Sticky Problems in Algebra II using Algorithms

YOU CAN PROGRAM! Pass it along…

Page 39: Exploring Sticky Problems in Algebra II using Algorithms
Page 40: Exploring Sticky Problems in Algebra II using Algorithms

3D-Rotation and Rendering (Trig) Monte Carlo Method (Calc) Newton’s Method (Calc) Snake Game (Algebra I and II) Finding Roots (Algebra II) Gaussian Elimination (College) Fractals and Complex Numbers (Pre Calc) Finding area under the Bell Curve for z-

scores using a for loop taking small steps (Pre Calc).