Maryland Math A.SSE.A.2.a
The Standard
- A.SSE.A.2
- Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ − y⁴ as (x²)² − (y²)², thus recognizing it as a difference of squares that can be factored as (x² + y²)(x² − y²).
Analyze the structure of the general form of a second degree equation, Ax² + Bxy + Cy² + Dx + Ey + F = 0, to identify the conic section represented by the equation.
Maryland College and Career Ready Standards for Mathematics (2025) · Interpret the structure of expressions.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the coefficients of x², xy, and y² and use B² − 4AC to predict the curve. They check whether the equation gives a real curve, a point, two lines, or no real graph.
What Mastery Looks Like
- A student can classify an equation with an xy term, not just one with separate x² and y² terms. They can spot a circle and explain why x² + y² + 1 = 0 has no real graph.
Common Misconceptions
- Students often ignore the xy term or make a sign error in B² − 4AC. They may call x² − y² = 0 a hyperbola, though it graphs as two lines.
How to Assess It
- Exit ticket: Classify x² + 4y² − 16 = 0, x² + 4xy + y² − 1 = 0, x² − 4y = 0, and x² + y² + 1 = 0. Show the coefficient test and flag any equation with no real graph.
Lesson moves
Ways to Teach It
Give pairs printed equation cards; have them circle A, B, and C, then sort the cards by the sign of B² − 4AC.
Ask students to explain in writing why x² + y² + 1 = 0 has no real graph.
Play four corners with circle, ellipse, hyperbola, and parabola signs; display x² + y² − 9 = 0, x² + 4y² − 16 = 0, x² − y² − 1 = 0, and x² − 4y = 0.
Show a satellite dish cross section labeled y = x² and a circular fountain labeled x² + y² = 25; have students name both curves.
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