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Montana Math Standards - 12th Grade
MathScore aligns to the Montana Math Standards for 12th 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 Montana Math Standards at other levels.
Standard 1: Problem Solving and Reasoning
1. recognize and formulate problems from situations within and outside mathematics and apply solution strategies to those problems. (Age Problems , Distance, Rate, and Time , Train Problems , Mixture Word Problems , Work Word Problems , Integer Word Problems )2. select, apply, and evaluate appropriate estimation strategies throughout the problem-solving process. (Estimated Multiply Divide Word Problems )
3. formulate definitions, make and justify inferences, express generalizations, and communicate mathematical ideas and relationships.
4. apply and translate among different representations of the same problem situation or of the same mathematical concept. Model connections between problem situations that arise in disciplines other than mathematics.
5. select and use appropriate technology to enhance mathematical understanding. Appropriate technology may include, but is not limited to, paper and pencil, calculator, computer, and data collection devices.
Standard 2: Numbers and Operations
1. use and understand the real number system, its operations, notations, and the various subsystems. (Exponent Basics , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Scientific Notation )2. use definitions and basic operations of the complex number system.
Standard 3: Algebraic Concepts
1. use algebra to represent patterns of change. (Determining Slope , Function Tables , Function Tables 2 )2. use basic operations with algebraic expressions. (Variable Substitution , Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , Foil Method , Trinomial Factoring , Binomial Fraction Simplification , Polynomial Fraction Simplification , Two Variable Equations , Variable Substitution 2 , Roots Of Exponential Expressions , Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
3. solve algebraic equations and inequalities: linear, quadratic, exponential, logarithmic, and power. (Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , Quadratic Zero Equations , Quadratic Formula , Quadratic X-Intercepts )
4. solve systems of algebraic equations and inequalities, including use of matrices. (System of Equations Substitution , System of Equations Addition )
5. use algebraic models to solve mathematical and real-world problems. (Age Problems , Train Problems , Mixture Word Problems , Work Word Problems , Integer Word Problems )
Standard 4: Geometry
1. construct, interpret, and draw three-dimensional objects.2. classify figures in terms of congruence and similarity and apply these relationships. (Congruent And Similar Triangles , Proportions 2 )
3. translate between synthetic and coordinate representations.
4. deduce properties of figures using transformations, coordinates, and vectors in problem solving.
5. apply trigonometric ratios (sine, cosine and tangent) to problem situations involving triangles.
Standard 5: Measurement
1. apply concepts of indirect measurements (e.g., using similar triangles to calculate a distance). (Unit Cost , Proportions 2 , Distance, Rate, and Time , Train Problems )2. use dimensional analysis to check reasonableness of procedures. (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion )
3. investigate systems of derived measures (e.g., km/sec, g/cm3). (Area and Volume Conversions )
4. apply the appropriate concepts of estimates in measurement, error in measurement, tolerance, and precision.
Standard 6: Data Analysis, Probability, and Statistics
1. use curve fitting to make predictions from data.2. apply measures of central tendency and demonstrate understanding of the concepts of variability and correlation.
3. select an appropriate sampling method for a given statistical analysis.
4. use experimental probability, theoretical probability, and simulation methods to represent and solve problems, including expected values. (Probability , Probability 2 , Object Picking Probability , Batting Averages )
5. design a statistical experiment to study a problem and communicate the outcomes.
6. describe, in general terms, the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed.
Standard 7: Patterns, Relations, and Functions
1. describe functions and their inverses using graphical, numerical, physical, algebraic, and verbal mathematical models or representations.2. analyze the graphs of the families of polynomial, rational, power, exponential, logarithmic, and periodic functions. (Nonlinear Functions )
3. analyze the effects of parameter changes on the graphs of functions and relations, including translations.
4. model real-world phenomena with a variety of functions.
5. use graphing for parametric equations, three-dimensional equations, and recursive relations.
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