Algebraic Reasoning: Order of Operations [TEKS Tools Grade 5]

This post specifically looks at how algebraic reasoning can be used to simplify expressions using the order of operations. Read more about TEKS Tools and their rationale here.

Algebraic Reasoning

Algebraic reasoning, the fifth TEKS Tool, accounts for around 9% of each 5th 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 patterns, use the order of operations, and understand the functioning of equations and expressions.

---

Order of Operations

5.4B - represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity

Students are asked to apply the order of operations to solve problems involving the four operations.

Click on each > to expand

2023-5: an equation was given, students had to apply the order of operations to solve for the unknown value

---

5.4E - describe the meaning of parentheses and brackets in a numeric expression

Students are asked to recognize when volume is the correct measurement to use in problem situations.

Click on each > to expand

2025-12: A series of steps to simply an expression was given, students had to identify and explain the error

---

5.4F - simplify numerical expressions that do not involve exponents, including up to two levels of grouping

Students are asked to simplify expressions without exponents that involve one or two levels of grouping (i.e., brackets and parentheses).

Click on each > to expand

2023-2: a value was given, students had to solve for the expression (one-level grouping) that did NOT simplify to that value

2024-4: an expression (two-level grouping) was given, students had to simplify

2024-18: an expression (two-level grouping) was given, students had to simplify

2025-15: an expression (one-level grouping) was given, students had to find two equivalent expressions

2025-33: an expression (two-level grouping) was given, students had to simplify