Montana Math MT.CORE.ALG.QUAD.4
The Standard
Solve quadratic equations by factoring, graphing, completing the square, using inverse operations, and the quadratic formula. Use technology and representations strategically.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the values that make a quadratic equation true. They choose a method that fits the equation, then check their answers by substitution or with a graph.
What Mastery Looks Like
- Students spot when factoring or undoing a square is quickest. They use completing the square or the quadratic formula when needed. They can explain when a graph has no x-intercepts because the equation has no real solutions.
Common Misconceptions
- Students may add 6 instead of 9 when completing the square for x² + 6x. They may forget the negative root when taking a square root, or mistake no x-intercepts for a graphing error.
How to Assess It
- Exit ticket: Solve x² − 6x + 2 = 0 exactly, name your method, and check one root by substitution.
Lesson moves
Ways to Teach It
Build x² + 6x + 8 with algebra tiles; arrange a rectangle and use its side lengths to find the roots.
Ask, “How does rewriting x² + 6x + 5 as (x + 3)² − 4 help find roots?” Compare answers with factoring.
Race to solve cards labeled x² = 16 and x² + x − 1 = 0; choose methods and check roots.
Graph h(t) = −5t² + 10t + 2 in Desmos, estimate when a tossed ball lands, and explain why negative time is rejected.
Free download
Printable MT.CORE.ALG.QUAD.4 Worksheet
A ready-to-print activity worksheet aligned to MT.CORE.ALG.QUAD.4, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- MT.CORE.ALG.QUAD.3
Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by: Choosing the form strategically when writi...
- MT.CORE.ALG.EXP.5
Solve exponential equations graphically, while using technology strategically.
- MT.PLUS.ALG.POLY.4
Solve quadratic equations that have complex solutions and understand why the solutions form a conjugate pair.
- MT.CORE.ALG.LIN.6
Solve systems of linear equations by graphing, substitution, and elimination, including systems with zero, one, or infinite solutions, while using technology an...
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.
Also for this standard:Make a WorksheetMake a QuizMake a Sub Lesson