Linear Equations and Complex Numbers

CHAPTER

Babylonian Method Simulator

Babylonian Scribe Simulator

Apply the Science of Learning: Use elaborative interrogation to translate the ancient "Method of False Position" into modern linear equations.

Linear vs Quadratic Shape Shifter

Shape Shifter: Linear vs. Quadratic

Apply the Science of Learning: Use dual coding to visually connect the exponent in an algebraic formula to the shape of its graph.

Equation: y = x^1.00

Complex Conjugate Pair Matcher

Complex Conjugate Matcher

Apply the Science of Learning: Use active retrieval to test your memory of complex conjugates by pairing equivalent tiles.

Discriminant Root Visualizer

Apply the Science of Learning: Use dual coding to link the mathematical value of the discriminant to the visual intersection of roots on a graph.

a = 1

b = 0

c = -4

Δ = b² - 4ac = 16

Extraneous Solution Detective

Apply the Science of Learning: Use metacognition to self-monitor your work. Interrogate calculated roots to discover which are valid and which are extraneous false-positives.

Case File Equation:

Is this suspect a valid root or extraneous?

Interval Notation Bracket Builder

Apply the Science of Learning: Use scaffolding to bridge algebraic inequalities, visual number lines, and proper interval notation.

Distance and Midpoint Mapper

Distance & Midpoint Mapper

Apply the Science of Learning: Use elaborative interrogation. By placing points and physically visualizing the right triangle, you interrogate the components required to calculate distance and midpoint.

Step 1: Click anywhere on the grid to place City A.

Temperature Conversion Slider

Temperature Scale Mapper

Apply the Science of Learning: Use dual coding. Manipulate the slider to see how identical physical mercury levels translate into different linear numeric scales (Celsius vs Fahrenheit).

Celsius

50 °C

Fahrenheit

122 °F

Pythagorean Area Proof

Apply the Science of Learning: Use dual coding. Physically transfer the area blocks from legs 'a' and 'b' to prove they perfectly fill the hypotenuse square 'c'. Click blocks to transfer them!

Leg a²

Leg b²

Hypotenuse c²

Rational Equation Balancer

Apply the Science of Learning: Use metacognition to self-monitor. Multiply by the Least Common Denominator (LCD) carefully—if you don't apply it to both sides, the equation will crash!

Determine the LCD and how to correctly apply it to clear the fractions.

Chapter 01: Linear Equations and Complex Numbers