Integrated Math III (WA Math 2026)

Data Analysis (DA)

• M.HS.DA.DS.1 Pose multivariable investigative questions, plan how data could answer them and think about cause and prediction when framing them.
• M.HS.DA.DS.2 Understand bias and confounding variables in data collection, and good practice for handling data, including sensitive and private information.
• M.HS.DA.DS.3 Use technology to clean, sort or filter data sets, then summarize relationships between quantitative variables with scatter plots, regressions, histograms and box plots.
• M.HS.DA.DS.4 Recognize missing values and the bias they can cause, weigh competing explanations such as confounding variables and respond to other interpretations.
• M.HS.DA.SID.4 Fit a normal distribution using mean and standard deviation to estimate population percentages, knowing when this is not suitable, with technology or tables.
• M.HS.DA.SID.6 Plot two quantitative variables on a scatter plot, describe the relationship and fit functions to solve problems in context.
  • a. Use a given function or one the context suggests; any function family may be used.
  • b. Judge informally how well a function fits by plotting and studying residuals.
  • c. Fit a linear function when the scatter plot looks linear.
• M.HS.DA.SIC.1 See statistics as a way to infer population parameters from a random sample.
• M.HS.DA.SIC.2 Decide, for example by simulation, whether a model fits the results of a data-generating process.
• M.HS.DA.SIC.3 Know what sample surveys, experiments and observational studies are for, how they differ and how randomization fits each.
• M.HS.DA.SIC.4 Estimate a population mean or proportion from survey data and build a margin of error with random-sampling simulations.
• M.HS.DA.SIC.5 Compare two treatments with data from a randomized experiment, using simulation to judge whether differences are significant.
• M.HS.DA.SIC.6 Evaluate reports that are based on data.

Quantity (Q)

• M.HS.Q.ASSE.1 Explain what an expression means in its context, for any family of functions.
  • a. Name and explain parts of expressions such as terms, factors and coefficients.
  • b. Make sense of complicated expressions by treating some parts as single quantities.
• M.HS.Q.ASSE.2 Spot structure or patterns in an expression and use them to rewrite it.
• M.HS.Q.FIF.7 Graph function families from their equations, by hand or with technology, showing intercepts, increase and decrease, maxima and minima, symmetry and end behavior.
  • a. Show intercepts, maxima and minima.
  • b. Graph square root, cube root and piecewise functions, including step and absolute value functions.
  • c. Graph polynomials, showing zeros when they factor and the end behavior.
  • d. Graph logarithmic functions (intercepts, end behavior) and trig functions (period, midline, amplitude).
  • e. (+) Graph rational functions, showing zeros, asymptotes and end behavior.
• M.HS.Q.FIF.8 Rewrite a function in equivalent forms to bring out and explain different properties.
  • a. Factor or complete the square to reveal a quadratic's zeros, maximum or minimum and line of symmetry in context.
  • b. Use exponent rules to interpret exponential growth and decay expressions, including non-integer time constants.
• M.HS.Q.FIF.9 Compare properties of two functions shown in different forms, across many function families.
• M.HS.Q.ACED.3 Model constraints with equations, inequalities or systems and decide whether solutions are workable in context.
• M.HS.Q.ACED.4 Rearrange formulas to isolate a quantity of interest, reasoning as when solving equations.
• M.HS.Q.FBF.1 Write a function for the relationship between two quantities, including linear, exponential and sequence relationships in context.
  • a. Find an explicit formula, a recursive rule or calculation steps from a context.
  • b. Combine standard functions with arithmetic operations.
  • c. (+) Compose functions.
• M.HS.Q.FBF.2 Write arithmetic and geometric sequences recursively and explicitly, model with them and convert between the forms.
• M.HS.Q.ASSE.4 Derive the sum formula for a finite geometric series (ratio not 1) and use it to solve problems.
• M.HS.Q.FBF.3 Identify how adding k, multiplying by k or replacing x with kx or x + k changes a graph, find k from graphs and explain the effects.
• M.HS.Q.NCN.1 Know there is a number i with i² = −1 and every complex number can be written a + bi with a and b real.
• M.HS.Q.NCN.2 Add, subtract and multiply complex numbers using i² = −1 and the usual properties.
• M.HS.Q.NCN.7 Solve quadratics with real coefficients that have complex solutions.
• M.HS.Q.AAPR.1 Show polynomials behave like the integers (closed under +, −, ×) and add, subtract and multiply them.
• M.HS.Q.AAPR.2 Know and use the Remainder Theorem: p(a) is the remainder on dividing by x − a, so x − a is a factor exactly when p(a) = 0.
• M.HS.Q.AAPR.3 Find zeros of polynomials from suitable factorizations and use them to sketch the graph.
• M.HS.Q.AAPR.4 Prove identities involving polynomials and use them to explain number patterns.
• M.HS.Q.AAPR.6 Rewrite simple rational expressions as a polynomial plus a remainder over the divisor, by inspection, long division or technology.

Relationships (R)

• M.HS.R.FIF.4 Read key features of graphs and tables of a function in context and sketch graphs from a description of key features.
• M.HS.R.FIF.5 Link a function's domain to its graph and to the situation it models, across many function families.
• M.HS.R.FIF.6 Find what a non-linear function's average rate of change is over an interval, explain it and estimate it from a graph.
• M.HS.R.ACED.1 Model a situation with a one-variable equation or inequality and solve problems with it.
• M.HS.R.ACED.2 Write equations in two or more variables for relationships and graph them on labeled, scaled axes.
• M.HS.R.ASSE.3 Rewrite expressions in equivalent forms chosen to reveal and explain a particular property.
  • a. Factor a quadratic to show the zeros of its function.
  • b. Complete the square to show a quadratic function's maximum or minimum.
  • c. Use exponent rules to rewrite exponential function expressions.
• M.HS.R.AREI.4 Solve one-variable quadratic equations with a method suited to the equation's form.
  • a. Complete the square to get the form (x − p)² = q and derive the quadratic formula from it.
  • b. Solve quadratics by inspection, square roots, completing the square, the formula or factoring, recognizing complex solutions.
• M.HS.R.AREI.2 Solve one-variable rational and radical equations and show how extraneous solutions can arise.
• M.HS.R.FBF.4 Find inverse functions by focusing on how inputs and outputs relate.
  • a. Solve f(x) = c for an invertible function and write an equation for its inverse.
  • b. (+) Check by composition that two functions are inverses.
  • c. (+) Read inverse-function values from a graph or table.
  • d. (+) Restrict a domain to make a non-invertible function invertible.
• M.HS.R.FLE.4 Write the solution of an exponential equation as a logarithm (base 2, 10 or e) and evaluate it with technology.

Spatial Reasoning (SR)

• M.HS.SR.FTF.1 Understand a radian as the unit-circle arc length cut off by an angle.
• M.HS.SR.FTF.2 Explain how the unit circle extends trig functions to all real numbers as radian angles measured counterclockwise.
• M.HS.SR.FTF.5 Choose trig functions to model periodic events with a given amplitude, frequency and midline.
• M.HS.SR.FTF.8 Prove sin²θ + cos²θ = 1 and use it with the quadrant to find other trig values.
• M.HS.SR.GGPE.1 Use the Pythagorean Theorem to write a circle's equation from its center and radius, and complete the square to recover the center.
• M.HS.SR.GGPE.2 Derive the equation of a parabola from its focus and directrix.
• M.HS.SR.GGMD.4 Identify cross-sections of solids and the solids made by rotating flat shapes.
• M.HS.SR.AREI.11 Explain why the x-values where y = f(x) and y = g(x) meet solve f(x) = g(x), and find them approximately with graphs, tables or approximation.