Tennessee flagTennessee: Integrated Math III | M3 Math Standards

58 standards · 5 domains

M3.A

  • M3.A.APR.A.1 Know and apply the Factor Theorem: For a polynomial p(x) and a number a, p(a) = 0 if and only if (x – a) is a factor of p(x).
  • M3.A.APR.A.2 Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.
  • M3.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems in a real-world context.
  • M3.A.CED.A.2 Create equations in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.
  • M3.A.CED.A.3 Rearrange formulas to isolate a quantity of interest using algebraic reasoning.
  • M3.A.REI.A.1 Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.
  • M3.A.REI.A.2 Solve radical equations in one variable and identify extraneous solutions when they exist.
  • M3.A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
  • M3.A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

M3.F

  • M3.F.BF.A.1.a Combine standard function types using composition.
  • M3.F.BF.A.2 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given graphs.
  • M3.F.BF.A.3.a Determine whether a function is one-to-one.
  • M3.F.BF.A.3.b Find the inverse of a function on an appropriate domain.
  • M3.F.BF.A.3.c Given an invertible function on an appropriate domain, identify the domain of the inverse function.
  • M3.F.IF.A.1.a Use function notation to evaluate functions for inputs in their domains, including functions of two variables.
  • M3.F.IF.A.1.b Interpret statements that use function notation in terms of a context.
  • M3.F.IF.A.2 Understand geometric formulas as functions.
  • M3.F.IF.B.3 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • M3.F.IF.B.4 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate and interpret the rate of change from a graph.
  • M3.F.IF.C.5 Graph functions expressed algebraically and show key features of the graph by hand and using technology.
  • M3.F.IF.C.6.a Compare properties of two different functions. Functions may be of different types and/or represented in different ways.
  • M3.F.IF.C.6.b Compare properties of the same function on two different intervals or represented in two different ways.
  • M3.F.LE.A.1 Know that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or cubically.
  • M3.F.LE.A.2.a Solve exponential equations using a variety of strategies, including logarithms.
  • M3.F.LE.A.2.b Understand that a logarithm is the solution to ab^ct = d, where a, b, c, and d are numbers.
  • M3.F.LE.A.2.c Evaluate logarithms using technology.

M3.G

  • M3.G.C.A.1 Use proportional relationships between the area of a circle and the area of a sector within the circle to solve problems and represent solutions in a real-world context.
  • M3.G.GMD.A.1 Understand and explain the formulas for the volume and surface area of a cylinder, cone, prism, and pyramid.
  • M3.G.GMD.A.2 Use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems in a real-world context.
  • M3.G.MG.A.1 Use geometric shapes, their measures, and their properties to model objects found in a real-world context for the purpose of approximating solutions to problems.
  • M3.G.SRT.A.1.a Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
  • M3.G.SRT.A.1.b Explain and use the relationship between the sine and cosine of complementary angles.
  • M3.G.SRT.A.2.a Know and use the Pythagorean Theorem and trigonometric ratios (sine, cosine, tangent, and their inverses) to solve right triangles in a real-world context.
  • M3.G.SRT.A.2.b Know and use relationships within special right triangles to solve problems in a real-world context.
  • M3.G.SRT.A.2.c Use the Law of Sines and Law of Cosines to solve non-right triangles in a real-world context.

M3.N

  • M3.N.Q.A.1.a Choose and interpret the scale and the origin in graphs and data displays.
  • M3.N.Q.A.1.b Use appropriate quantities in formulas, converting units as necessary.
  • M3.N.Q.A.1.c Define and justify appropriate quantities within a context for the purpose of modeling.
  • M3.N.Q.A.1.d Choose an appropriate level of accuracy when reporting quantities.

M3.S

  • M3.S.CP.A.1.a Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or", "and", "not").
  • M3.S.CP.A.1.b Flexibly move between visual models (Venn diagrams, frequency tables, etc.) and set notation.
  • M3.S.CP.A.2 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. Categorize events as independent or dependent.
  • M3.S.CP.B.3.a Use the Fundamental Counting Principle to compute probabilities of compound events and solve problems.
  • M3.S.CP.B.3.b Use permutations and combinations to compute probabilities of compound events and solve problems.
  • M3.S.CP.B.4 Use the Law of Large Numbers to assess the validity of a statistical claim.
  • M3.S.CP.C.5 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A and interpret the answer in terms of the given context.
  • M3.S.CP.C.6.a Explain the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B) in terms of visual models (Venn diagrams, frequency tables, etc.).
  • M3.S.CP.C.6.b Apply the Addition Rule to solve problems and interpret the answer in terms of the given context.
  • M3.S.CP.D.7 Calculate probabilities using geometric figures.
  • M3.S.IC.A.1 Recognize the purposes of and differences among sample surveys, experiments, and observational studies.
  • M3.S.IC.A.2 Identify potential sources of bias in statistical studies.
  • M3.S.IC.A.3 Distinguish between a statistic and a parameter. Evaluate reports based on data and recognize when poor conclusions are drawn from well-collected data.
  • M3.S.ID.A.1 Use measures of center to solve real-world and mathematical problems.
  • M3.S.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (mean, median, and/or mode) and spread (range, interquartile range, and standard deviation) of two or more different data sets.
  • M3.S.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.
  • M3.S.ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.
  • M3.S.ID.A.5 Compute, interpret, and compare z-scores for normally distributed data in a real-world context.
  • M3.S.ID.B.6 Represent data from two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.