factoring and solving quadratic equations

During this time students should be given time to individually practice these processes and for discussion with classmates. Students should be introduced, through teacher instruction, to the concepts and procedures for solving quadratics by factoring. This lesson is organized so that students can build upon prior knowledge of factoring and solving linear equations to solve quadratic equations. Students with the knowledge and skills to factor trinomials of higher difficulty will also appreciate this basic technique.

$factoring and solving quadratic equations$

The property is easy to understand and use, and makes the steps to solving quadratic equations by identifying and deconstructing binomials more accessible. Students who find the factoring of trinomials a challenging operation will get some satisfaction in the application of the Zero Product Property. This activity encourages them to use the specific traits of the trinomial to find the unique binomial factors. The classification tasks engage students in reviewing their understanding of the individual characteristics of the three types of trinomials. The Solve by Factoring Worksheet requires students to classify as well as factor the trinomials presented. In sharing their solution methods and results with partners, they can expand their understanding by seeing different solutions and correcting their own and their partners’ errors. By attempting solutions individually, students gain an immediate sense of how well they understand the techniques. The think-pair-share activity presents students with representations of all three types of trinomial factoring. Students are able to recognize that the property applies not only to monomials, but also to binomials, and is applicable for all real numbers. In applying it to binomial factors, they can use the property as a tool in a way that has not previously been represented. The Zero Product Property is an elementary concept that is familiar to students. By illustrating these connections, students can see how general solutions are possible.

The example of x² + x - 6 shows students the relationship between the zeros of the function, the roots of the equation, and the constant terms of the binomial factors of the trinomial. The lesson includes recognizing and using trinomials in various forms. This lesson helps students to develop skills in solving quadratic equations by factoring and provides them with useful techniques for factoring and for understanding the rationale that supports finding solutions. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.Īctive Engagement, Modeling, Explicit Instruction W:.Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.Patterns exhibit relationships that can be extended, described, and generalized.Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations. Families of functions exhibit properties and behaviors that can be recognized across representations.

Factoring and solving quadratic equations