Gizmos for Tennessee - Mathematics: Integrated Mathematics 2 (Academic Standards adopted 2016)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

M2.N: : Number and Quantity

M2.N.RN: : The Real Number System

M2.N.RN.A: : Extend the properties of exponents to rational exponents.

M2.N.RN.A.2: : Rewrite expressions involving radicals and rational exponents using the properties of exponents.

M2.N.CN: : The Complex Number System

M2.N.CN.A: : Perform arithmetic operations with complex numbers.

M2.N.CN.A.1: : Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

M2.N.CN.A.2: : Know and use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

M2.N.CN.B: : Use complex numbers in polynomial identities and equations.

M2.N.CN.B.3: : Solve quadratic equations with real coefficients that have complex solutions.

M2.A: : Algebra

M2.A.SSE: : Seeing Structure in Expressions

M2.A.SSE.A: : Interpret the structure of expressions.

M2.A.SSE.A.1: : Interpret expressions that represent a quantity in terms of its context.

M2.A.SSE.A.1.a: : Interpret complicated expressions by viewing one or more of their parts as a single entity.

M2.A.SSE.A.2: : Use the structure of an expression to identify ways to rewrite it.

M2.A.SSE.B: : Write expressions in equivalent forms to solve problems.

M2.A.SSE.B.3: : Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

M2.A.SSE.B.3.a: : Factor a quadratic expression to reveal the zeros of the function it defines.

M2.A.SSE.B.3.b: : Complete the square in a quadratic expression in the form Ax² + Bx + C to reveal the maximum or minimum value of the function it defines.

M2.A.APR: : Arithmetic with Polynomials and Rational Expressions

M2.A.APR.A: : Perform arithmetic operations on polynomials.

M2.A.APR.A.1: : Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

M2.A.CED: : Creating Equations

M2.A.CED.A: : Create equations that describe numbers or relationships.

M2.A.CED.A.1: : Create equations and inequalities in one variable and use them to solve problems.

M2.A.CED.A.2: : Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales.

M2.A.CED.A.3: : Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

M2.A.REI: : Reasoning with Equations and Inequalities

M2.A.REI.A: : Understand solving equations as a process of reasoning and explain the reasoning.

M2.A.REI.A.1: : Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

M2.A.REI.B: : Solve equations and inequalities in one variable.

M2.A.REI.B.2: : Solve quadratic equations and inequalities in one variable.

M2.A.REI.B.2.a: : Use the method of completing the square to rewrite any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

M2.A.REI.B.2.b: : Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

M2.A.REI.C: : Solve systems of equations.

M2.A.REI.C.3: : Write and solve a system of linear equations in context.

M2.F: : Functions

M2.F.IF: : Interpreting Functions

M2.F.IF.A: : Interpret functions that arise in applications in terms of the context.

M2.F.IF.A.1: : 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.

M2.F.IF.A.2: : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

M2.F.IF.A.3: : Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

M2.F.IF.B: : Analyze functions using different representation.

M2.F.IF.B.4: : Graph functions expressed symbolically and show key features of the graph, by hand and using technology.

M2.F.IF.B.4.a: : Graph linear and quadratic functions and show intercepts, maxima, and minima.

M2.F.IF.B.4.b: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

M2.F.IF.B.4.c: : Graph exponential and logarithmic functions, showing intercepts and end behavior.

M2.F.IF.B.5: : Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

M2.F.IF.B.5.a: : Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

M2.F.IF.B.5.b: : Know and use the properties of exponents to interpret expressions for exponential functions.

M2.F.BF: : Building Functions

M2.F.BF.A: : Build a function that models a relationship between two quantities.

M2.F.BF.A.1: : Write a function that describes a relationship between two quantities.

M2.F.BF.A.1.a: : Determine an explicit expression, a recursive process, or steps for calculation from a context.

M2.F.BF.A.1.b: : Combine standard function types using arithmetic operations.

M2.F.BF.B: : Build new functions from existing functions.

M2.F.BF.B.2: : Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

M2.G: : Geometry

M2.G.SRT: : Similarity, Right Triangles, and Trigonometry

M2.G.SRT.A: : Understand similarity in terms of similarity transformations.

M2.G.SRT.A.1: : Verify informally the properties of dilations given by a center and a scale factor.

M2.G.SRT.A.2: : Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

M2.G.SRT.A.3: : Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

M2.G.SRT.B: : Prove theorems involving similarity.

M2.G.SRT.B.4: : Prove theorems about similar triangles.

M2.G.SRT.B.5: : Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.

M2.G.SRT.C: : Define trigonometric ratios and solve problems involving triangles.

M2.G.SRT.C.6: : 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.

M2.G.SRT.C.7: : Explain and use the relationship between the sine and cosine of complementary angles.

M2.G.SRT.C.8: : Solve triangles.

M2.G.SRT.C.8.a: : Know and use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

M2.G.GMD: : Geometric Measurement and Dimension

M2.G.GMD.A: : Explain volume and surface area formulas and use them to solve problems.

M2.G.GMD.A.1: : Give an informal argument for the formulas for the circumference of a circle and the volume and surface area of a cylinder, cone, prism, and pyramid.

M2.G.GMD.A.2: : Know and use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems.

M2.S: : Statistics and Probability

M2.S.ID: : Interpreting Categorical and Quantitative Data

M2.S.ID.A: : Summarize, represent, and interpret data on two categorical and quantitative variables.

M2.S.ID.A.1: : Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

M2.S.ID.A.1.a: : Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

M2.S.CP: : Conditional Probability and the Rules of Probability

M2.S.CP.A: : Understand independence and conditional probability and use them to interpret data.

M2.S.CP.A.2: : Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

M2.S.CP.A.4: : Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Correlation last revised: 2/1/2022

Tennessee - Mathematics: Integrated Mathematics 2

Academic Standards | Adopted: 2016

M2.N: : Number and Quantity

M2.A: : Algebra

M2.F: : Functions

M2.G: : Geometry

M2.S: : Statistics and Probability