Order of Operations and Algebraic Expressions with Brackets

Model, write equations for, and solve single-step and multi-step multiplicative and additive comparison and scaling problems.

Evaluate, write, and interpret numerical and algebraic expressions using parentheses, brackets, and the standard order of operations.

Formulate equations with variables and use strip diagrams to solve complex multi-step real-world problems with all four operations.

Find all factor pairs, identify multiples, apply divisibility tests, and classify numbers up to 100 as prime, composite, or square.

Decompose numbers into prime factor products using factor trees and solve real-world problems with greatest common factors and least common multiples.

Generate, analyze, and extend arithmetic number sequences, including counting in steps of 6, 7, 9, 25, and 1000 across boundary numbers.

Formulate explicit algebraic rules from input-output tables, analyze geometric spatial patterns, and identify structural invariants.