UT--Core Standards

SII.MP.1.a: Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, “Does this make sense?” Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

Biconditional Statements

Estimating Population Size

Linear Inequalities in Two Variables

Modeling One-Step Equations

Solving Equations on the Number Line

Using Algebraic Equations

Using Algebraic Expressions

SII.MP.3.a: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

SII.MP.4.a: Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Determining a Spring Constant

Estimating Population Size

SII.MP.7.a: Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

Arithmetic Sequences

Finding Patterns

Geometric Sequences

SII.MP.8.a: Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

(Framing Text): Extend the properties of exponents to rational exponents.

N.RN.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

(Framing Text): Use properties of rational and irrational numbers.

N.RN.3: Explain why sums and products of rational numbers are rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational. Connect to physical situations (e.g., finding the perimeter of a square of area 2).

Circumference and Area of Circles

Estimating Population Size

(Framing Text): Perform arithmetic operations with complex numbers.

N.CN.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.

Points in the Complex Plane

Roots of a Quadratic

(Framing Text): Use complex numbers in polynomial identities and equations.

N.CN.7: Solve quadratic equations with real coefficients that have complex solutions.

(Framing Text): Interpret the structure of expressions.

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

A.SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Compound Interest

Exponential Growth and Decay

Unit Conversions

A.SSE.1.b: Interpret increasingly more complex expressions by viewing one or more of their parts as a single entity. Exponents are extended from the integer exponents to rational exponents focusing on those that represent square or cube roots.

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

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

Equivalent Algebraic Expressions II

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations II

(Framing Text): Write expressions in equivalent forms to solve problems, balancing conceptual understanding and procedural fluency in work with equivalent expressions.

A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. For example, development of skill in factoring and completing the square goes hand in hand with understanding what different forms of a quadratic expression reveal.

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

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

A.SSE.3.c: Use the properties of exponents to transform expressions for exponential functions.

(Framing Text): Perform arithmetic operations on polynomials. Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of x.

A.APR.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.

(Framing Text): Create equations that describe numbers or relationships. Extend work on linear and exponential equations to quadratic equations.

A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Absolute Value Equations and Inequalities

Arithmetic Sequences

Exploring Linear Inequalities in One Variable

Geometric Sequences

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Using Algebraic Equations

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

2D Collisions

Air Track

Compound Interest

Determining a Spring Constant

Golf Range

Points, Lines, and Equations

Slope-Intercept Form of a Line

A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations; extend to formulas involving squared variables.

Area of Triangles

Solving Formulas for any Variable

(Framing Text): Solve equations and inequalities in one variable.

A.REI.4: Solve quadratic equations in one variable.

A.REI.4.a: Use the method of completing the square to transform 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.

A.REI.4.b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, 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.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Points in the Complex Plane

Roots of a Quadratic

(Framing Text): Interpret quadratic functions that arise in applications in terms of a context.

F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Focus on quadratic functions; compare with linear and exponential functions.

F.IF.6: 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.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

(Framing Text): Analyze functions using different representations.

F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Linear Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Slope-Intercept Form of a Line

Zap It! Game

F.IF.7.b: Graph piecewise-defined functions and absolute value functions. Compare and contrast absolute value and piecewise-defined functions with linear, quadratic, and exponential functions. Highlight issues of domain, range, and usefulness when examining piecewise-defined functions.

Absolute Value with Linear Functions

Radical Functions

Translating and Scaling Functions

F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.8.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.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

F.IF.8.b: Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest

Exponential Growth and Decay

F.IF.9: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Extend work with quadratics to include the relationship between coefficients and roots, and that once roots are known, a quadratic equation can be factored.

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

Zap It! Game

(Framing Text): Build a function that models a relationship between two quantities.

F.BF.1: Write a quadratic or exponential function that describes a relationship between two quantities.

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

Arithmetic Sequences

Geometric Sequences

F.BF.1.b: Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

Addition and Subtraction of Functions

(Framing Text): Build new functions from existing functions.

F.BF.3: 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 the graphs. Focus on quadratic functions and consider including absolute value functions. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

(Framing Text): Construct and compare linear, quadratic, and exponential models and solve problems.

F.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Compare linear and exponential growth to quadratic growth.

Compound Interest

Exponential Functions

Introduction to Exponential Functions

(Framing Text): Prove and apply trigonometric identities. Limit θ to angles between 0 and 90 degrees. Connect with the Pythagorean Theorem and the distance formula.

F.TF.8: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin (θ), cos (θ), or tan (θ), given sin (θ), cos (θ), or tan (θ), and the quadrant of the angle.

Simplifying Trigonometric Expressions

Sine, Cosine, and Tangent Ratios

(Framing Text): Prove geometric theorems. Encourage multiple ways of writing proofs, such as narrative paragraphs, flow diagrams, two-column format, and diagrams without words. Focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning.

G.CO.9: Prove theorems about lines and angles.

G.CO.10: Prove theorems about triangles.

Pythagorean Theorem

Triangle Angle Sum

Triangle Inequalities

G.CO.11: Prove theorems about parallelograms.

Parallelogram Conditions

Special Parallelograms

(Framing Text): Understand similarity in terms of similarity transformations.

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

G.SRT.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G.SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide whether 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.

Circles

Dilations

Similar Figures

(Framing Text): Prove theorems involving similarity.

G.SRT.4: Prove theorems about triangles.

Pythagorean Theorem

Similar Figures

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

Dilations

Perimeters and Areas of Similar Figures

Similarity in Right Triangles

(Framing Text): Define trigonometric ratios and solve problems involving right triangles.

G.SRT.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.

Sine, Cosine, and Tangent Ratios

G.SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine, Cosine, and Tangent Ratios

(Framing Text): Understand and apply theorems about circles.

G.C.2: Identify and describe relationships among inscribed angles, radii, and chords.

(Framing Text): Translate between the geometric description and the equation for a conic section.

G.GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

(Framing Text): Explain volume formulas and use them to solve problems.

G.GMD.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Informal arguments for area formulas can make use of the way in which area scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k² times the area of the first. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

Circumference and Area of Circles

Prisms and Cylinders

Pyramids and Cones

G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Informal arguments for volume formulas can make use of the way in which volume scale under similarity transformations: when one figure results from another by applying a similarity transformation, volumes of solid figures scale by k³ under a similarity transformation with scale factor k.

Prisms and Cylinders

Pyramids and Cones

(Framing Text): Summarize, represent, and interpret data on two categorical or quantitative variables.

S.ID.5: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and condition reltive frequencies). Recognize possible associations and trends in the date.

(Framing Text): Understand independence and conditional probability and use them to interpret data.

S.CP.1: 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”).

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

(Framing Text): Use the rules of probability to compute probabilities of compound events in a uniform probability model.

S.CP.6: 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 model.

Independent and Dependent Events

Correlation last revised: 4/4/2018

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