- standard
Solve equations and inequalities in one variable
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
- standard
Understand solving equations as a process of reasoning and explain the reasoning
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
- standard
Understand solving equations as a process of reasoning and explain the reasoning
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the o…
- standard
Create equations that describe numbers or relationship
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Creating Equations
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight …
- standard
Create equations that describe numbers or relationship
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Creating Equations
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in…
- standard
Create equations that describe numbers or relationship
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Creating Equations
Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equation…
- standard
Create equations that describe numbers or relationship
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Creating Equations
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rat…
- standard
Rewrite rational expressions
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Arithmetic with Polynomials and Rational Functions
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a…
- standard
Rewrite rational expressions
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Arithmetic with Polynomials and Rational Functions
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the…
- standard
Use polynomial identities to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Arithmetic with Polynomials and Rational Functions
(+) Know and apply that the Binomial Theorem gives the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, wit…
- standard
Use polynomial identities to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Arithmetic with Polynomials and Rational Functions
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can …
- standard
Understand the relationship between zeros and factors of polynomial
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Arithmetic with Polynomials and Rational Functions
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomia…
- standard
Understand the relationship between zeros and factors of polynomial
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Arithmetic with Polynomials and Rational Functions
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a…
- standard
Perform arithmetic operations on polynomials
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Arithmetic with Polynomials and Rational Functions
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication;…