Equivalent Expressions - Grades 6-8

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Rationale

What?

Students will be engaged in opportunities to process their thinking during dialogue with others. They will apply prior knowledge and skills to create and use multiple representations of equivalent algebraic expressions in various contexts. Students will use factoring, combining like terms, integer operations, and geometric applications during the lesson.

Why?

Students bring both understanding as well as misunderstandings into new learning opportunities. Surfacing all thoughts, both correct and incorrect,(without affirming or negating) provides an important component in the learning process. The opportunity to correct misunderstandings, replacing them with new learning and thinking supports success and mastery of current and future learning.

"Teachers should be sensitive and recognize that students come into their classrooms with misunderstandings and misconceptions. It is imperative that they work toward detecting the existing misconceptions that students may have and work purposefully to correct them. This is to avoid a situation whereby students move from one grade to another with these harmful misconceptions. Teachers should acknowledge that learners can overcome misconceptions by planning and consciously providing opportunities for learning through effective teaching strategies.”

(Ojose, Bobby. "Students' Misconceptions in Mathematics: Analysis of Remedies and What Research Says.” Ohio Journal of School Mathematics, Vol. 72, 2015, pp. 30–34, https://doi.org/https://kb.osu.edu/server/api/core/bitstreams/5c4f895c-64a7-5018-921a-475db38d03ca/content. )

How?

Place the responsibility for learning in the hands of the students, using the teacher as a facilitator, to empower students to formulate expressions and confirm their understanding. A good facilitator helps students to identify and correct misunderstandings, enabling confidence to apply their knowledge in future lessons.

Decorative question mark:

Summary

Students will apply skills like factoring, combining like terms, integer operations, and geometric concepts to solve a variety of mathematical problems. They'll work both independently and in small groups to explore expressions, discuss their thought processes, and create equivalent expressions in different formats

Goals & Standards

Colorado Academic Standards:

7.EE.A. Expressions & Equations: Use properties of operations to generate equivalent expressions.
- 7.EE.A.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Mathematical Practice Standards:

Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.

Learning Goal:

Be able to create and use multiple representations of equivalent algebraic expressions using factoring, combining like terms, integer operations, and geometric applications.