High School Number and Quantity (Wisconsin Standards)

The Real Number System (N.RN)

• M.N.RN.A.1 Explain how rational exponents are defined by extending the rules for integer exponents.
• M.N.RN.A.2 Rewrite expressions with radicals and rational exponents using exponent properties.
• M.N.RN.B.3 Explain why sums and products of rational numbers are rational and when results with irrationals are irrational.

Quantities (N.Q)

• M.N.Q.A.1 Use units to understand and guide multi-step problems and choose scales and origins for graphs.
• M.N.Q.A.2 Define appropriate quantities for descriptive modeling.
• M.N.Q.A.3 Choose a level of accuracy that fits the limits of measurement.

The Complex Number System (N.CN)

• M.N.CN.A.1 Know the number i with i² = −1, that complex numbers have the form a + bi, and why they exist.
• M.N.CN.A.2 Use i² = −1 and properties of operations to add, subtract and multiply complex numbers.
• M.N.CN.A.3 Find complex conjugates and use them to find moduli and quotients.
• M.N.CN.B.4 Show complex numbers as points in rectangular and polar form and explain why both forms name the same number.
• M.N.CN.B.5 Show sums, differences, products and conjugates of complex numbers geometrically.
• M.N.CN.B.6 Find distance and midpoint in the complex plane using modulus and averages.
• M.N.CN.C.7 Solve quadratics with real coefficients and complex solutions, writing them as a ± bi.
• M.N.CN.C.8 Extend polynomial identities to complex numbers, e.g. factor x² + 4.
• M.N.CN.C.9 Know the Fundamental Theorem of Algebra and show it holds for quadratics.

Vector and Matrix Quantities (N.VM)

• M.N.VM.A.1 Recognize vectors as having magnitude and direction and represent them with directed segments and symbols.
• M.N.VM.A.2 Find vector components by subtracting initial-point coordinates from terminal-point coordinates.
• M.N.VM.A.3 Solve problems with velocity and other vector quantities.
• M.N.VM.B.4 Add and subtract vectors.
  • a. Add vectors end to end, by components and by the parallelogram rule.
  • b. Find the magnitude and direction of a sum.
  • c. Understand and perform vector subtraction.
• M.N.VM.B.5 Multiply a vector by a scalar.
  • a. Show scalar multiplication graphically and by components.
  • b. Find the magnitude and direction of a scalar multiple.
• M.N.VM.C.6 Use matrices to represent and manipulate data, such as networks or payoffs.
• M.N.VM.C.7 Multiply matrices by scalars.
• M.N.VM.C.8 Add, subtract and multiply matrices of suitable dimensions.
• M.N.VM.C.9 Understand matrix multiplication is not commutative but is associative and distributive.
• M.N.VM.C.10 Understand zero and identity matrices and that a square matrix has an inverse only if its determinant is nonzero.
• M.N.VM.C.11 Multiply a vector by a matrix and treat matrices as transformations of vectors.
• M.N.VM.C.12 Use two-by-two matrices to transform the plane and link the determinant's absolute value to area.