Grades 9–10 Math (North Dakota Content Standards)

Mathematical Attributes, grades 9–12 (MA)

• 9-12.MA.P Analyze, carry out, critique and adapt approaches to solve problems in new situations (applies to grades 9–12).
• 9-12.MA.C Connect ideas within and across concepts, showing with evidence how they arise and relate to other learning and life (applies to grades 9–12).
• 9-12.MA.R Reason logically, using evidence to critique and explain thinking through exploring, generalizing and validating (applies to grades 9–12).

Number and Operations (NO)

• 9-10.NO.1 Explain how rational exponents follow from integer exponent rules and rewrite expressions with radicals and rational exponents.
• 9-10.NO.2 Simplify simple radical expressions, including rationalizing denominators without conjugates.
• 9-10.NO.3 Choose and interpret scales and units in graphs and data displays and spot misleading scales.
• 9-10.NO.4 Define suitable quantities and units for modeling, e.g. square feet or square yards, or converting rates (modeling standard).
• 9-10.NO.5 Choose a level of accuracy suited to the limits of measurement when reporting quantities.

Algebraic Reasoning (AR)

• 9-10.AR.1 Use the structure of quadratic and exponential expressions to find ways to rewrite them.
• 9-10.AR.2 Solve a formula for a chosen quantity using the same steps as solving equations.
• 9-10.AR.3 Write one-variable equations and inequalities, including from linear, quadratic and exponential functions, and solve problems with them. (modeling standard)
• 9-10.AR.4 Write linear or exponential equations with two or more variables for relationships and graph them on labeled, scaled axes. (modeling standard)
• 9-10.AR.5 Justify each step of solving a linear equation, including ones with no solution.
• 9-10.AR.6 Solve one-variable linear equations and inequalities, including compound inequalities.
• 9-10.AR.7 Solve systems of linear equations by graphing and algebra, and set up and solve them in context. (modeling standard)
• 9-10.AR.8 Graph the solution set of a system of two-variable linear inequalities, including in context.
• 9-10.AR.9 Solve equations and inequalities with absolute value in one or two variables.
• 9-10.AR.10 Solve one-variable quadratics by inspection, square roots, factoring or the quadratic formula, as suits the form.
• 9-10.AR.11 Add, subtract and multiply polynomials.

Algebraic Reasoning: Functions (AR.F)

• 9-10.AR.F.1 Decide if a relationship given as a table, graph or words is a function, and find domain and range, including in context.
• 9-10.AR.F.2 Use function notation, evaluate functions at inputs in the domain and interpret notation in context. (modeling standard)
• 9-10.AR.F.3 Sketch key features such as intercepts, extremes and symmetry of linear, exponential and quadratic models from tables, graphs, words or equations. (modeling standard)
• 9-10.AR.F.4 Link the domain of linear, quadratic or exponential functions to their graphs and to the modeled situation. (modeling standard)
• 9-10.AR.F.5 Find and interpret rates of change of linear, quadratic or exponential functions over intervals and estimate them from graphs. (modeling standard)
• 9-10.AR.F.6 Rewrite a function in equivalent forms to reveal and explain its properties. (modeling standard)
• 9-10.AR.F.7 Compare the main features of two functions (linear, exponential or quadratic) given in different forms. (modeling standard)
• 9-10.AR.F.8 Recognize situations suited to linear, quadratic or exponential models and justify the choice from rates of change, including growth and decay. (modeling standard)
• 9-10.AR.F.9 Describe how a, h and k change linear, absolute value or quadratic graphs, and find them from a graph. (modeling standard)
• 9-10.AR.F.10 Find a linear function's inverse and relate its domain, range and graph to the original in context. (modeling standard)
• 9-10.AR.F.11 Interpret the parameters of linear, quadratic or exponential functions in context. (modeling standard)
• 9-10.AR.F.12 Use graphs or tables to solve f(x) = g(x) for linear and exponential functions as the x-values where outputs match.

Geometry and Measurement (GM)

• 9-10.GM.1 Know exact definitions and notation for angle, circle, perpendicular and parallel lines and segment, built on point, line and plane.
• 9-10.GM.2 Represent plane transformations as functions on points and compare rigid motions with ones that change distance or angle.
• 9-10.GM.3 Describe rotations and reflections that map a triangle, quadrilateral or regular polygon onto itself or another figure.
• 9-10.GM.4 Develop or check the properties of rotations, reflections and translations using angles, circles, lines and segments.
• 9-10.GM.5 Draw a figure after a sequence of rigid transformations using paper, tracing or geometry software.
• 9-10.GM.6 Predict the effect of a rigid motion on a figure and use rigid motions to decide if figures are congruent.
• 9-10.GM.7 Use rigid-motion congruence to show triangles are congruent exactly when matching sides and angles are congruent.
• 9-10.GM.8 Prove triangles congruent with the congruence theorems.
• 9-10.GM.9 Prove and use theorems about lines and angles.
• 9-10.GM.10 Prove and use theorems about triangles.
• 9-10.GM.11 Prove and use theorems about parallelograms.
• 9-10.GM.12 Do basic constructions such as copying segments and angles, bisecting, and parallel or perpendicular lines with various tools.
• 9-10.GM.13 Use basic constructions to inscribe an equilateral triangle, square or regular hexagon in a circle. (plus standard)
• 9-10.GM.14 Check by experiment and justify the properties of dilations given a center and scale factor.
• 9-10.GM.15 Use transformations to decide if figures are similar and explain triangle similarity as equal angles and proportional sides.
• 9-10.GM.16 Prove theorems about similar triangles.
• 9-10.GM.17 Use triangle congruence and similarity criteria to solve problems and prove relationships in figures.
• 9-10.GM.18 See how similar right triangles define the trig ratios and find sine, cosine and tangent of acute angles.
• 9-10.GM.19 Explain and use how the sine and cosine of complementary angles relate. (plus standard)
• 9-10.GM.20 Solve applied right-triangle problems with trig ratios, the Pythagorean Theorem and 30-60-90 and 45-45-90 triangles. (modeling standard)
• 9-10.GM.21 Solve for missing sides and angles of oblique triangles with the Laws of Sines and Cosines. (plus, modeling standard)
• 9-10.GM.22 Use circle theorems about radii, diameters, secants, tangents and chords to find missing lengths or angles.
• 9-10.GM.23 Construct a triangle's incenter and circumcenter and relate them to its inscribed and circumscribed circles. (plus standard)
• 9-10.GM.24 Construct a tangent to a circle from an outside point. (plus standard)
• 9-10.GM.25 Explain and use formulas for arc length and sector area.
• 9-10.GM.26 Recognize radian measure as the ratio of arc length to radius.
• 9-10.GM.27 Develop the slope tests for parallel and perpendicular lines and use them to solve problems.
• 9-10.GM.28 Use coordinates to check simple theorems, e.g. that given points form a particular triangle or quadrilateral.
• 9-10.GM.29 Find a segment's midpoint or endpoint from coordinates; (+) find the point dividing a directed segment in a given ratio.
• 9-10.GM.30 Use coordinates to find polygon perimeters and the areas of triangles, parallelograms, trapezoids and kites. (modeling standard)
• 9-10.GM.31 Explain where the formulas for circle circumference and area and for cylinder, pyramid and cone volume come from.
• 9-10.GM.32 Solve problems by finding surface area of prisms, cylinders, pyramids, cones and spheres.
• 9-10.GM.33 Solve problems using volume formulas for prisms, cylinders, pyramids, cones or spheres.
• 9-10.GM.34 Identify 2D cross-sections of 3D objects and 3D solids made by rotating 2D shapes.
• 9-10.GM.35 Use area- and volume-based density in modeling, e.g. people per square mile. (modeling standard)
• 9-10.GM.36 Solve design problems with geometric methods, e.g. meeting constraints, keeping cost low or scaling a model. (modeling standard)

Data, Probability and Statistics (DPS)

• 9-10.DPS.1 Show data on a number line with dot plots, histograms and box plots. (modeling standard)
• 9-10.DPS.2 Compare center and spread of two or more data sets with statistics suited to the distribution's shape. (modeling standard)
• 9-10.DPS.3 Make a scatter plot of two numeric variables and describe how they relate. (modeling standard)
• 9-10.DPS.4 Tell correlation apart from causation. (modeling standard)
• 9-10.DPS.5 Describe events as parts of a sample space or as unions, intersections or complements (or, and, not). (modeling standard)
• 9-10.DPS.6 See events as independent when B leaves A's chance unchanged, and multiply their probabilities for A and B. (modeling standard)
• 9-10.DPS.7 Understand conditional probability of A given B, compute it and interpret it in context. (modeling standard)
• 9-10.DPS.8 Use the addition rule for P(A or B) and interpret the result in context. (modeling standard)
• 9-10.DPS.9 Count outcomes with permutations and combinations in context. (modeling standard)
• 9-10.DPS.10 Build and read two-way tables for two categorical variables and use them to judge independence and estimate conditional probabilities. (modeling standard)