Secondary Mathematics I (Utah Core Standards)

Number and Quantity

• SI.N.Q.1 Use units to understand and guide multistep problems, read units in formulas and choose scales and origins for graphs and data displays.
• SI.N.Q.2 Define suitable quantities when building a descriptive model.
• SI.N.Q.3 Report quantities with a level of accuracy that fits the limits of measurement.

Algebra

• SI.A.SSE.1 Interpret linear expressions and exponential expressions with integer exponents in terms of their context.
  • a. Interpret terms, factors and coefficients in an expression.
  • b. Interpret complex expressions by treating parts as single quantities, e.g. P(1 + r)ⁿ.
• SI.A.CED.1 Create one-variable equations and inequalities from linear and exponential situations and use them to solve problems.
• SI.A.CED.2 Create equations in two or more variables for relationships and graph them with labeled axes and scales.
• SI.A.CED.3 Express constraints with equations, inequalities or systems and judge whether solutions are viable in context.
• SI.A.CED.4 Rearrange formulas to isolate a quantity of interest (e.g. solve V = IR for R).
• SI.A.REI.1 Justify each step in solving a linear equation from the equality before it.
• SI.A.REI.3 Solve one-variable linear equations and inequalities, including literal equations.
  • a. Solve literal equations for a chosen variable.
  • b. Solve compound inequalities and absolute value inequalities in one variable.
  • c. Solve simple exponential equations using only the laws of exponents.
• SI.A.REI.5 Prove that replacing an equation by its sum with a multiple of the other keeps a system's solutions.
• SI.A.REI.6 Solve linear systems exactly and approximately (e.g. by graphing), mainly pairs of equations in two variables.
• SI.A.REI.10 Know a two-variable equation's graph shows every one of its solutions on the plane.
• SI.A.REI.11 Explain why intersections of y = f(x) and y = g(x) solve f(x) = g(x) and find them approximately with graphs, tables or technology.
• SI.A.REI.12 Graph two-variable linear inequalities as half-planes and systems of them as overlapping half-planes.

Functions

• SI.F.IF.1 Know a function assigns each domain element exactly one range element; f(x) is the output for input x.
• SI.F.IF.2 Use function notation, evaluate functions and interpret notation in context.
• SI.F.IF.3 Recognize sequences as functions on the integers, focusing on arithmetic and geometric sequences.
• SI.F.IF.4 Interpret key graph and table features in context (intercepts, increase/decrease, maxima, symmetry, end behavior) and sketch graphs.
• SI.F.IF.5 Link a function's domain to its graph and to the situation it models.
• SI.F.IF.6 Calculate and interpret average rate of change over an interval and estimate it from a graph.
• SI.F.IF.7 Graph functions from their equations and show key features, by hand or with technology.
  • a. Graph linear and quadratic functions showing intercepts, maxima and minima.
  • e. Graph exponential functions, showing intercepts and end behavior.
• SI.F.IF.9 Compare properties of two functions shown in different ways.
• SI.F.BF.1 Write a function for a relationship between two quantities.
  • a. Find an explicit expression, recursive process or calculation steps from a context.
  • b. Combine standard function types with arithmetic operations to model a situation.
• SI.F.BF.2 Write arithmetic and geometric sequences recursively and explicitly, model with them and convert between forms.
• SI.F.BF.3 Describe how adding or multiplying by a constant k changes a graph, and find k from graphs. (being checked)
• SI.F.LE.1 Tell situations modeled by linear functions from those modeled by exponential functions.
  • a. Prove linear functions grow by equal differences and exponential functions by equal factors over equal intervals.
  • b. Recognize situations with a constant rate of change per unit.
  • c. Recognize situations with a constant percent rate of growth or decay per unit.
• SI.F.LE.2 Build linear and exponential functions, including sequences, from a graph, a description or two input-output pairs.
• SI.F.LE.3 Use graphs and tables to see that exponential growth eventually exceeds linear growth.
• SI.F.LE.5 Interpret the parameters of linear and exponential functions in context.

Geometry

• SI.G.CO.1 Know precise definitions of angle, circle, perpendicular and parallel lines and segment from undefined terms.
• SI.G.CO.2 Represent transformations as functions on points and compare rigid motions with others such as stretches.
• SI.G.CO.3 Describe the rotations and reflections that map a rectangle, parallelogram, trapezoid or regular polygon onto itself.
• SI.G.CO.4 Define rotations, reflections and translations using angles, circles, perpendicular and parallel lines and segments.
• SI.G.CO.5 Draw the image of a figure under a rotation, reflection or translation and specify sequences of moves.
• SI.G.CO.6 Use rigid motions to transform figures, predict effects and decide whether two figures are congruent.
• SI.G.CO.7 Use rigid motions to show triangles are congruent exactly when corresponding sides and angles are congruent.
• SI.G.CO.8 Explain how ASA, SAS and SSS follow from congruence defined by rigid motions.
• SI.G.CO.12 Make formal constructions with compass and straightedge, paper folding or software (copying, bisecting, perpendiculars, parallels).
• SI.G.CO.13 Construct an equilateral triangle, square and regular hexagon inscribed in a circle.
• SI.G.GPE.4 Prove simple geometry theorems algebraically with coordinates.
• SI.G.GPE.5 Prove the slope tests for parallel and perpendicular lines and apply them to problems.
• SI.G.GPE.7 Use coordinates (e.g. the distance formula) to find polygon perimeters and triangle and rectangle areas.

Statistics and Probability

• SI.S.ID.1 Show data with dot plots, histograms and box plots on the real number line.
• SI.S.ID.2 Compare center (median, mean) and spread (IQR, standard deviation) of data sets using statistics suited to their shape.
• SI.S.ID.3 Explain how data sets differ in shape, center and spread in context, allowing for outliers, and find weighted averages.
• SI.S.ID.6 Make a scatter plot of two quantitative variables and describe how they are related.
  • a. Fit a function (linear, quadratic or exponential) to data and use it to solve problems.
  • b. Judge the fit of a function informally by plotting and analyzing residuals.
  • c. Fit a line to a scatter plot that looks linear.
• SI.S.ID.7 Interpret the slope and intercept of a linear model in context.
• SI.S.ID.8 Use technology to find the correlation coefficient of a linear fit and interpret it.
• SI.S.ID.9 Tell correlation apart from causation.