IA2.NOS.B: Reason about the complex number system.
IA2.NOS.B.2: Use the knowledge that 𝑖² = –1 to write complex numbers in standard form, 𝑎 + 𝑏𝑖, and use them to represent solutions to quadratics that have no real solutions.
Points in the Complex Plane
Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.
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Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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IA2.AT.A: Look for and make use of structure to rewrite expressions in equivalent forms and reason about Their properties.
IA2.AT.A.1: Rewrite and interpret quadratic expressions to explain key properties of a relationship.
IA2.AT.A.2: Given a polynomial of degree 3 or higher in factored form, use the Zero Product Property to identify its zeros and sketch a graph of the function.
Polynomials and Linear Factors
Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function.
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IA2.AT.A.3: Add, subtract, and multiply polynomials to rewrite expressions in equivalent forms for clarity, efficiency, or problem-solving applications. Use these operations to represent and analyze polynomial relationships in context. Multiplication of polynomials includes multiplying a binomial and a trinomial.
Addition and Subtraction of Functions
Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response.
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Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps.
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Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes.
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IA2.AT.B: Make sense of and solve equations and systems of equations.
IA2.AT.B.4: Create and solve quadratic equations in one variable.
IA2.AT.B.5: Solve radical equations in one variable that contain a single radical term. Explain why some solutions may be extraneous and justify whether a given solution is valid based on a given context.
Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation.
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IA2.AT.D.11: Write a quadratic function to model relationships between quantities given a narrative description, table of values, or graph.
Roots of a Quadratic
Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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IA2.AT.D.12: Represent and interpret quadratic functions using tables and graphs and apply them in context.
IA2.AT.D.13: Find and interpret the inverse of quadratic and exponential functions using algebraic and graphical representations.
IA2.AT.D.14: Represent and interpret higher degree polynomial (degree 3 or higher), and radical functions in context using tables and graphs.
IA2.AT.D.15: Analyze how transformations affect the graph of a polynomial function given in vertex form and interpret their meaning in context.
GR: Geometric Reasoning
IA2.GR.A: Reason about transformations and similarity.
IA2.GR.A.1: Describe the effect of dilations on two-dimensional figures using coordinates, including how scale factor and center of dilation impact side lengths and angle measures.
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form.
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IA2.GR.A.3: Apply properties of similar triangles to solve geometric problems in context.
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles.
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Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related.
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IA2.GR.B: Reason about right triangle relationships.
IA2.GR.B.5: Use similarity of right triangles to explain and define trigonometric ratios (sine, cosine, and tangent) for acute angles as properties of the angles, based on side ratios.
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change.
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IA2.GR.B.6: Justify the side length relationships in special right triangles (30°-60°-90° and 45°-45°-90°).
IA2.GR.B.7: Use trigonometric ratios, the Pythagorean Theorem, and special right triangle relationships to solve right triangles in applied contexts.
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation.
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Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle.
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IA2.GR.C: Make sense of circles and their properties.
IA2.GR.C.8: Apply similarity to develop and use formulas involving arc length, radian measure, and sector area.
IA2.GR.C.9: Create the equation of a circle given the center and radius; identify the center and radius of a circle given the equation.
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response.
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IA2.GR.D.11: Rearrange geometric formulas to isolate and interpret a quantity of interest in context (e.g., solving for height in a volume formula), using reasoning aligned with solving equations and modeling with mathematics.
Solving Formulas for any Variable
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps.
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DS: Reasoning with Data, Statistics, and Probability
IA2.DS.A: Make sense of statistical inquiry.
IA2.DS.A.1: Evaluate and refine statistical study designs and critically analyze data-based claims to improve the quality and validity of inferences.
Correlation last revised: 7/9/2026
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
