- standard
Write expressions in equivalent forms to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Seeing Structure in Expressions
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mor…
- standard
Write expressions in equivalent forms to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Seeing Structure in Expressions
Use the properties of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares t…
- standard
Write expressions in equivalent forms to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Seeing Structure in Expressions
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- standard
Write expressions in equivalent forms to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Seeing Structure in Expressions
Factor a quadratic expression to reveal the zeros of the function it defines.
- standard
Write expressions in equivalent forms to solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Seeing Structure in Expressions
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- standard
Interpret the structure of expressions.
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Seeing Structure in Expressions
Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squa…
- standard
Interpret the structure of expressions.
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Seeing Structure in Expressions
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor no…
- standard
Interpret the structure of expressions.
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Seeing Structure in Expressions
Interpret parts of an expression, such as terms, factors, and coefficients.*
- standard
Interpret the structure of expressions.
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Seeing Structure in Expressions
Interpret expressions that represent a quantity in terms of its context.*
- standard
Perform operations on matrices and use matrices in applications
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associ…
- standard
Perform operations on matrices and use matrices in applications
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Add, subtract, and multiply matrices of appropriate dimensions.
- standard
Perform operations on matrices and use matrices in applications
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
- standard
Perform operations on matrices and use matrices in applications
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
- standard
Perform operations on matrices and use matrices in applications
- 9th - 12th Grade
- Michigan State Math Standards
- Number and Quantity: Vector and Matrix Quantities
(+) Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.