A1.A.3.3 Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1.
In a Nutshell
Students will factor polynomial expressions, including quadratics. They will factor out the greatest common factor from polynomials of any degree and factor quadratics with a lead coefficient of one into two binomials.
Student Actions
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Teacher Actions
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Students will develop accurate and appropriate procedural fluency by finding the factors of a polynomial expression or quadratic equation.
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Students will develop a deep and flexible conceptual understanding by comparing the quadratic equations and their graphs to see that the factors are solutions called x-intercepts (zeros) of the graphed equation.
- Students will develop mathematical reasoning when they observe and explain how factoring is the reverse of distributing.
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Use and connect mathematical representations by helping students discover the relationships between quadratic equations and their graphs, including those that model real-world situations.
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Pose purposeful questions that guide students toward discovering factors of expressions.
- Implement tasks that promote reasoning and problem solving by guiding students to interpret the mathematical relationship in the original context of the problem algebraically
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Key Understandings
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Misconceptions
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Students may forget to factor the greatest value possible from an expression before beginning to factor the polynomial.
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Students may not take the real-world context for a quadratic relationship into account when giving solutions, causing them to include solutions that would not fit the situation.
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Students may not identify the correct sign of the factors involved.
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OKMath Framework Introduction
Algebra 1 Introduction
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