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Colorado Math Standards - 9th Grade
MathScore aligns to the Colorado 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 Colorado Math Standards at other levels.
Number Sense
1.1 Demonstrate meanings for real numbers, absolute value, and scientific notation using physical materials and technology in problem solving situations. (Absolute Value 1 )1.1a Compare and order sets of rational numbers and common irrational numbers (v2, √5, and π.). (Estimating Square Roots )
1.1b Recognize and use equivalent representations of rational numbers and common irrational numbers (v2, √5, and π.), including scientific notation. (Scientific Notation 2 , Scientific Notation )
1.1c Use very large and very small numbers in real life situations to solve problems (scientific notation, powers).
1.2 Develop, test, and conjectures about the properties of number systems and sets of numbers.
1.2a Verify and apply the properties of the operation "to the power of" (for example, 23 = 8, 22 = 4, 21 = 2, 20 = ___, 2-1 = ___2-2 = ___ ). (Exponent Basics , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions )
1.3 Use number sense to estimate and justify the reasonableness of solutions to problems involving real numbers.
1.3a Use number sense to estimate and justify the reasonableness of solutions to problems involving rational numbers and common irrational numbers (for example, circumference, area of a circle, and Pythagorean Theorem).
Algebraic Methods
2.1 Model real world phenomena (for example, distance-versus-time relationships, compound interest, amortization tables, mortality rates) using functions, equations, inequalities, and matrices.2.1a Model real world phenomena involving linear and non-linear relationships using multiple repre-sentations of rules that can take the form of recursive processes, functions, equations, or inequalities. (Compound Interest , Continuous Compound Interest )
2.2 Represent functional relationships using written explanations, tables, equations, and graphs and describe the connections among these representations.
2.2a Represent functional relationships using written explanations, tables, equations, and graphs, and describe the connections among these representations.
2.2b Convert from one functional representation to another. (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Applied Linear Equations 1 , Applied Linear Equations 2 , Nonlinear Functions , Number Line Inequalities )
2.2c Interpret a graphical representation of a real-world situation.
2.3 Solve problems involving functional relationships using graphing calculators and/or computers as well as appropriate paper-and-pencil techniques.
2.3a Solve problems involving functions and relations using calculators, graphs, tables, and algebraic methods. (Quadratic Zero Equations , Quadratic Formula , Quadratic X-Intercepts )
2.3b Solve simple systems of equations using algebraic, graphical or numeric methods. (System of Equations Substitution , System of Equations Addition )
2.3c Solve equations with more than one variable for a given variable (for example, solve for p in I = prt or for r in C=2πr). (Triangle Area 2 , Rectangular Solids 2 , Distance, Rate, and Time , Two Variable Equations )
2.4 Analyze and explain the behaviors, transformations, and general properties of types of equations and functions (for example, linear, quadratic, exponential).
2.4a Identify and interpret x and y intercepts in the context of a problem.
2.4b Using a graph, identify the maximum and minimum value within a given domain. (Domain and Range )
2.4c Analyze the effects of change in the leading coefficient and/or the vertical translation (for example, given y = kx2 + c, how do changes in k and/or c affect the graphs?
2.5 Interpret algebraic equations and inequalities geometrically and describe geometric relationships algebraically.
2.5a Graph solutions to equations and inequalities in one-and two-dimensions and determine solutions. (Number Line Inequalities )
2.5b Express the perimeter, area and volume relationships of geometric figures algebraically.
Data Analysis, Statistics, and Probability
3.1 Design and conduct a statistical experiment to study a problem, and interpret and communicate the results using the appropriate technology (for example, graphing calculators, computer software).3.1a Identify factors which may have affected the outcome of a survey (for example, biased questions or collection methods).
3.1b Using large populations, formulate hypothesis, draw conclusions, and make convincing arguments based on data analysis.
3.1c Select and use an appropriate display to represent and describe a set of data (for example, scatter plot, line graph and histogram). (Line Graphs )
3.2 Analyze statistical claims for erroneous conclusions or distortions.
3.2a Analyze a graph, table, or summary for misleading characteristics.
3.2b Recognize the misuse of statistical data in written arguments.
3.2c Describe how data can be interpreted in more than one way or be used to support more than one position in a debate.
3.3 Fit curves to scatter plots using informal methods or appropriate technology to determine the strength of the relationship between two data sets and to make predictions.
3.3a Fit curves to scatter plots using informal methods or appropriate technology to make predictions about the data.
3.3b Fit curves to scatter plots using informal methods or appropriate technology to determine the type (positive, negative, or non-existent) of relationship between two data sets.
3.4 Draw conclusions about distributions of data based on analysis of statistical summaries (for example, the combination of mean and standard deviation, and differences between the mean and median).
3.4a Determine, analyze, and use measure of central tendency (such as mean, median, and mode) and measures of variability (such as range and quartiles) in problem solving situations. (Mean, Median, Mode , Stem And Leaf Plots )
3.4b Use averages (including averages per trial, expected value) to draw conclusions about distributions of data (for example, if there are 10 people with one five dollar bill and one dollar bill in their wallets and they each randomly place one of the bills in a donation box, what will be the average amount of money donated per person?). (Batting Averages )
3.5 Use experimental and theoretical probability to represent and solve problems involving uncertainty (for example, the chance of playing professional sports if a student is a successful high school athlete).
3.5a Determine the probability of an identified event using the sample space. (Probability , Probability 2 , Object Picking Probability )
3.5b Make predictions using theoretical probability in real-world problems. (Batting Averages )
3.5c Use a model (list, tree diagram, area model) to determine theoretical probabilities to solve problems involving uncertainty.
3.6 Solve real-world problems with informal use of combinations and permutations for example, determining the number of possible meals at a restaurant featuring a given number of side dishes).
3.6a Solve real-world problems with informal use of combinations and permutations (for example, determining the number of possible meals at a restaurant featuring a given number of side dishes).
Geometry
4.1 Find and analyze relationships among geometric figures using transformations (for example, reflections, translations, rotations, dilations) in coordinate systems.4.1a Find and analyze relationships among geometric figures using transformation (for example, reflections, translation, rotations, dilation) in coordinate systems.
4.2 Derive and use methods to measure perimeter, area, and volume of regular and irregular geometric figures.
4.2a Solve problems involving perimeter, area, and volume of regular and irregular geometric figures. (Triangle Area , Triangle Area 2 , Parallelogram Area , Perimeter , Rectangular Solids , Rectangular Solids 2 , Circle Area , Circle Circumference , Triangular Prisms , Cylinders , Irregular Shape Areas , Perimeter and Area of Composite Figures , Perimeter and Area Word Problems , Trapezoids )
4.2b Use the Pythagorean theorem to solve real-world problems.
4.3 Make and test conjectures about geometric shapes and their properties, incorporating technology where appropriate.
4.3a Make and test conjectures about geometric shapes and their properties (for example, parallelism, perpendicularity, similarity, congruence, symmetry). (Congruent And Similar Triangles )
4.3b Use coordinate geometry to solve problems involving shapes and their properties.
Measurement
5.1 Measure quantities indirectly using techniques of algebra, geometry, or trigonometry.5.1a Use appropriate measurements to solve problems indirectly (for example, find the height of a flagpole using similar triangles.
5.1b Use measurement to solve real-world problems involving rate of change (for example, distance traveled using rate and time). (Unit Cost , Distance, Rate, and Time , Train Problems )
5.1c Describe how changing one attribute of a shape affects its angle measure, perimeter, circumference, area, surface area and volume. (Area And Volume Proportions )
5.2 Select and use appropriate tools and techniques to measure quantities in order to achieve specified degrees of precision, accuracy and error (or tolerance) of measurements.
5.2a Select and use appropriate tools and techniques to measure quantities in order to achieve specified degrees of precision, accuracy, and error (or tolerance) of measurements.
Mathematical Reasoning
6.1 Use ratios, proportions, and percents in problem solving situations.6.1a Use ratios, proportions, and percents in problem solving situations that involve rational numbers. (Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Percent of Quantity , Proportions 2 )
6.1b Convert from one set of units to another using proportions (for example, feet/minute to miles/hour). (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion , Area and Volume Conversions )
6.1c Apply direct variation to problem solving situations.
6.2 Select and use appropriate methods for computing with real numbers in problem-solving situations from among mental arithmetic, estimation, paper-and-pencil, calculator, and computer methods, and determine whether the results are reasonable.
6.2a Apply appropriate computational methods to solve multi-step problems involving rational numbers. (Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , Absolute Value 2 , Absolute Value Equations , Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , System of Equations Substitution , System of Equations Addition , Age Problems , Train Problems , Mixture Word Problems , Work Word Problems , Integer Word Problems )
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