- standard
Analyze and solve linear equations and pairs of simultaneous linear equations
- 8th Grade
- Michigan State Math Standards
- Expressions and Equations
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case …
- standard
Analyze and solve linear equations and pairs of simultaneous linear equations
- 8th Grade
- Michigan State Math Standards
- Expressions and Equations
Solve linear equations in one variable.
- standard
Understand the connections between proportional relationships, lines, and linear equations
- 8th Grade
- Michigan State Math Standards
- Expressions and Equations
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equatio…
- standard
Understand the connections between proportional relationships, lines, and linear equations
- 8th Grade
- Michigan State Math Standards
- Expressions and Equations
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in differe…
- standard
Work with radicals and integer exponents
- 8th Grade
- Michigan State Math Standards
- Expressions and Equations
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notati…
- standard
Work with radicals and integer exponents
- 8th Grade
- Michigan State Math Standards
- Expressions and Equations
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times…
- standard
Work with radicals and integer exponents
- 8th Grade
- Michigan State Math Standards
- Expressions and Equations
Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate squa…
- standard
Work with radicals and integer exponents
- 8th Grade
- Michigan State Math Standards
- Expressions and Equations
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^(–5) = 3^(–3) = 1/(3^3) = 1/27.
- standard
Know that there are numbers that are not rational, and approximate them by rational numbers
- 8th Grade
- Michigan State Math Standards
- The Number System
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate t…
- standard
Know that there are numbers that are not rational, and approximate them by rational numbers
- 8th Grade
- Michigan State Math Standards
- The Number System
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that …
- standard
Solve real-world and mathematical problems involving volume of cylinders, cones and spheres
- 8th Grade
- Michigan State Math Standards
- Geometry
Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- standard
Understand and apply the Pythagorean Theorem
- 8th Grade
- Michigan State Math Standards
- Geometry
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
- standard
Understand and apply the Pythagorean Theorem
- 8th Grade
- Michigan State Math Standards
- Geometry
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
- standard
Understand and apply the Pythagorean Theorem
- 8th Grade
- Michigan State Math Standards
- Geometry
Explain a proof of the Pythagorean Theorem and its converse.