Algebraic Reasoning: Determining Solutions [TEKS Tools Grade 7]

This post specifically looks at how algebraic reasoning can be used to solve two-step equations and inequalities. Read more about TEKS Tools and their rationale here.

Algebraic Reasoning

Algebraic reasoning accounts for around 30% of each 7th grade STAAR test. This thinking does not use a visible tool but instead relies on applying algebraic concepts to expressions, equations, and inequalities.

The main function of algebraic reasoning is to identify algebraic relationships in problem situations, interpret data, make predictions, and solve equations and inequalities.

Determining Solutions

Algebraic reasoning can be used to model and solve one-variable equations.

7.10B - represent solutions for one-variable, two-step equations and inequalities on number lines

2023-27: an inequality was given, students had to represent the solution on a number line

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7.11A - model and solve one-variable, two-step equations and inequalities

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2023-18: an inequality was given, students had to find a value not in the solution set

2023-38:  an equation was modeled with algebra tiles, students had to solve for x

2024-10:  two inequalities were given, students had to find each solution set

2024-34: an equation was given, students had to solve for x

2025-16: a verbal description was given, students had to find the solution set

2025-33: an equation was given, students had to solve for x

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GEometric Concepts

When given a one-variable equation or inequality, substitution can be used to verify its validity.

7.11B - determine if the given value(s) make(s) one-variable, two-step equations and inequalities true

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2023-29: a value was given, students had to use substitution to find a valid equation

2024-28: a value was given, students had to use substitution to find if each equation is valid