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Minnesota Math Standards - 9th Grade
MathScore aligns to the Minnesota Math Standards for 9th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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View the Minnesota Math Standards at other levels.
Mathematical Reasoning
Apply skills of mathematical representation, communication and reasoning throughout the remaining three content strands.
1. Assess the reasonableness of a solution by comparing the solution to appropriate graphical or numerical estimates or by recognizing the feasibility of solutions in a given context and rejecting extraneous solutions.
2. Appropriately use examples and counterexamples to make and test conjectures, justify solutions, and explain results.
3. Translate a problem described verbally or by tables, diagrams or graphs, into suitable mathematical language, solve the problem mathematically and interpret the result in the original context. (Age Problems , Train Problems , Mixture Word Problems , Work Word Problems , Integer Word Problems , Function Tables , Function Tables 2 )
4. Support mathematical results by explaining why the steps in a solution are valid and why a particular solution method is appropriate.
5. Determine whether or not relevant information is missing from a problem and if so, decide how to best express the results that can be obtained without that information.
6. Know and use the relationship that exists among a logical implication of the form "if A, then B," its converse "if B, then A," its inverse "if not A, then not B," and its contrapositive "if not B, then not A."
Number Sense, Computation and Operations
A. Number SenseUse real numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems.
B. Computation and Operation
Appropriately use calculators and other technologies to solve algebraic, geometric, probabilistic and statistical problems.
1. Apply the correct order of operations and grouping symbols when using calculators and other technologies.
2. Know, use and translate calculator notational conventions to mathematical notation.
3. Recognize the impact of units such as degrees and radians on calculations.
4. Recognize that applying an inverse function with a calculator may lead to extraneous or incomplete solutions.
5. Understand the limitations of calculators such as missing or additional features on graphs due to viewing parameters or misleading representations of zero or very large numbers.
6. Understand that use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.
Patterns, Functions and Algebra
A. Patterns and FunctionsRepresent and analyze real-world and mathematical problems using numeric, graphic and symbolic methods for a variety of functions.
1. Know the numeric, graphic and symbolic properties of linear, step, absolute value and quadratic functions. Graphic properties may include rates of change, intercepts, maxima and minima.
2. Model exponential growth and decay, numerically, graphically and symbolically, using exponential functions with integer inputs.
3. Analyze the effects of coefficient changes on linear and quadratic functions and their graphs. (Nonlinear Functions )
4. Apply basic concepts of linear, quadratic and exponential expressions or equations in real-world problems such as loans, investments and the path of a projectile. (Simple Interest , Compound Interest , Continuous Compound Interest )
5. Distinguish functions from other relations using graphic and symbolic methods.
B. Algebra (Algebraic Thinking)
Solve simple equations and inequalities numerically, graphically, and symbolically. Use recursion to model and solve real-world and mathematical problems.
1. Translate among equivalent forms of expressions, such as, simplify algebraic expressions involving nested pairs of parentheses and brackets, simplify rational expressions, factor a common term from an expression and apply associative, commutative and distributive laws. (Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 , Distributive Property , Distributive Property 2 , Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , Binomial Fraction Simplification , Polynomial Fraction Simplification , Exponent Rules For Fractions )
2. Understand the relationship between absolute value and distance on the number line and graph simple expressions involving absolute value such as, |x - 3| = 6 or |x + 2| < 5. (Absolute Value 1 , Absolute Value 2 , Absolute Value Equations )
3. Find equations of a line given two points on the line, a point and the slope of the line or the slope and the y-intercept of the line. (Applied Linear Equations 1 )
4. Translate among equivalent forms of linear equations and inequalities. (Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities )
5. Use a variety of models such as equations, inequalities, algebraic formulas, written statements, tables and graphs or spreadsheets to represent functions and patterns in real-world and mathematical problems. (Function Tables , Function Tables 2 )
6. Apply the laws of exponents to perform operations on expressions with integer exponents. (Simplifying Algebraic Expressions 2 , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions )
7. Solve linear equations and inequalities in one variable with numeric, graphic and symbolic methods. (Linear Equations , Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , Number Line Inequalities )
8. Find real solutions to quadratic equations in one variable with numeric, graphic and symbolic methods. (Quadratic Zero Equations , Quadratic Formula , Quadratic X-Intercepts )
9. Use appropriate terminology and mathematical notation to define and represent recursion.
10. Create and use recursive formulas to model and solve real-world and mathematical problems.
11. Solve systems of two linear equations and inequalities with two variables using numeric, graphic and symbolic methods. (System of Equations Substitution , System of Equations Addition )
12. Understand how slopes can be used to determine whether lines are parallel or perpendicular. Given a line and a point not on the line, find the equations for the lines passing through that point and parallel or perpendicular to the given line. (Applied Linear Equations 2 )
Data Analysis, Statistics and Probability
A. Data and StatisticsRepresent data and use various measures associated with data to draw conclusions and identify trends. Understand the effects of display distortion and measurement error on the interpretation of data.
1. Construct and analyze circle graphs, bar graphs, histograms, box-and-whisker plots, scatter plots and tables, and demonstrate the strengths and weaknesses of each format by choosing appropriately among them for a given situation. (Bar Graphs )
2. Use measures of central tendency and variability, such as, mean, median, maximum, minimum, range, standard deviation, quartile and percentile, to describe, compare and draw conclusions about sets of data. (Stem And Leaf Plots )
3. Determine an approximate best-fit line from a given scatter plot and use the line to draw conclusions.
4. Know the influence of outliers on various measures and representations of data about real-world and mathematical problems.
5. Understand the relationship between correlation and causation.
6. Interpret data credibility in the context of measurement error and display distortion.
7. Compare outcomes of voting methods such as majority, plurality, ranked by preference, run-off and pair-wise comparison.
B. Probability
Use appropriate counting procedures, calculate probabilities in various ways and apply theoretical probability concepts to solve real-world and mathematical problems.
1. Select and apply appropriate counting procedures to solve real-world and mathematical problems, including probability problems.
2. Use area, trees, unions and intersections to calculate probabilities and relate the results to mutual exclusiveness, independence and conditional probabilities, in real-world and mathematical problems.
3. Use probability models, including area and binomial models, in real-world and mathematical problems.
4. For simple probability models, determine the expected values of random variables.
5. Know the effect of sample size on experimental and simulation probabilities.
6. Use a variety of experimental, simulation and theoretical methods to calculate probabilities. (Probability , Probability 2 , Object Picking Probability , Batting Averages )
Spatial Sense, Geometry and Measurement
A. Spatial SenseUse models to represent and understand two- and three-dimensional shapes and how various motions affect them. Recognize the relationship between different representations of the same shape.
1. Use models and visualization to understand and represent three-dimensional objects and their cross sections from different perspectives.
B. Geometry
Apply basic theorems of plane geometry, right triangle trigonometry, coordinate geometry and a variety of visualization tools to solve real-world and mathematical problems.
1. Know and use theorems about triangles and parallel lines in elementary geometry to justify facts about various geometrical figures and solve real-world and mathematical problems. These theorems include criteria for two triangles to be congruent or similar and facts about parallel lines cut by a transversal. (Identifying Angles , Angle Measurements 2 )
2. Know and use theorems about circles to justify geometrical facts and solve real-world and mathematical problems. These theorems include the relationships involving tangent lines and radii, the relationship between inscribed and central angles and the relationship between the measure of a central angle and arc length.
3. Know and use properties of two- and three-dimensional figures to solve real-world and mathematical problems such as: finding area, perimeter, volume and surface area; applying direct or indirect methods of measurement; the Pythagorean theorem and its converse; and properties of 45-45-90 and 30-60-90 triangles. (Triangle Area , Triangle Area 2 , Parallelogram Area , Perimeter , Rectangular Solids , Rectangular Solids 2 , Compare Rectangle Area and Perimeter , Circle Area , Circle Circumference , Triangular Prisms , Cylinders , Pythagorean Theorem , Irregular Shape Areas , Solving For Angles , Perimeter and Area of Composite Figures , Perimeter and Area Word Problems , Trapezoids )
4. Apply the basic concepts of right triangle trigonometry including sine, cosine and tangent to solve real-world and mathematical problems.
5. Use coordinate geometry to represent and examine geometric concepts such as the distance between two points, the midpoint of a line segment, the slope of a line and the slopes of parallel and perpendicular lines. (Line Segments , Determining Slope )
6. Use numeric, graphic and symbolic representations of transformations such as reflections, translations and change of scale in one, two and three dimensions to solve real-world and mathematical problems.
7. Perform basic constructions with a straightedge and compass. (Requires outside materials )
8. Draw accurate representations of planar figures using a variety of tools.
C. Measurement
Use the interconnectedness of geometry, algebra and measurement to explore real-world and mathematical problems.
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