Solving Proportions and Algebraic Proportional Reasoning

Understand ratios as multiplicative comparisons and use visual representations including tape diagrams and double number lines to model relationships.

Compute and interpret unit rates in diverse real-world contexts including unit pricing, speed, recipe scaling, and density.

Construct and analyze tables of equivalent ratios, graph proportional relationships on the Cartesian plane, and interpret linear representations.

Solve unknown quantities in proportional equations using scaling, unit rates, and cross-multiplication strategies.

Divide quantities into given part-to-part and part-to-whole ratios across two-part and multi-part sharing problems.

Master percentages as rates per 100, convert fluently between benchmark fractions, decimals, and percents, and calculate core parts and wholes.

Solve multi-step consumer and financial percent problems including sales tax, tips, discounts, markups, commissions, and percent change.

Convert measurement units within and between metric and customary systems using ratio reasoning, scale factors, and algebraic unit cancellation.