6th graders plot rational-number points in all four quadrants, reflect them across axes, and find distances along grid lines. They interpret coordinates and reflections in maps and real-world contexts, emphasizing precision, units, and quadrant reasoning.

6th graders represent real-world quantities with positive and negative numbers, interpret absolute value as distance from zero, and compare integers on number lines. They explain differences between order and magnitude using clear, contextual reasoning and precise inequality statements.

6th graders master fluency with multi-digit division and decimal operations through estimation, standard algorithms, and real-world contexts. They apply place-value reasoning, check for accuracy and reasonableness, and communicate results clearly with correct units and rounding.

6th graders model and compute fraction-by-fraction division using strips, number lines, and area models. They interpret real-world contexts, justify the reciprocal rule, estimate reasonableness, and explain results with units and clear mathematical reasoning.

6th graders use ratio reasoning to convert measurements within and across systems. They apply tables, double number lines, and unit-canceling to decide when to multiply or divide, estimate reasonableness, and extend understanding to area and volume conversions.

6th graders apply percent reasoning to real-world money problems involving discounts, markups, tax, and tips. They identify the correct base, estimate before calculating, and use ratio tables to organize multistep solutions with accurate units and clear explanations.

6th graders develop strong percent sense using models like bars, grids, and tables. They find parts, wholes, and percents in real contexts, apply benchmarks for estimation, and explain reasoning clearly with accurate units and “per 100” understanding.

6th graders apply ratio reasoning to real-life contexts like prices, recipes, and speed. They compute and interpret unit rates using tables and double number lines, make best-buy and constant-speed decisions, and explain reasoning with precise units and clear mathematical communication.

6th graders extend ratio reasoning by creating and scaling ratio tables, finding missing values, and graphing equivalent pairs through the origin. They connect unit rates to straight-line graphs, compare proportional relationships, and justify conclusions using precise tables, graphs, and units.

6th graders explore ratios and unit rates through real-world contexts like pricing, recipes, and speed. They build tape and double-number-line models, compute “per 1” comparisons, justify best-buy decisions, and communicate reasoning with precise units and representations.

6th graders build classroom math routines, discourse norms, and confidence through ratio and number-sense tasks. They use diagrams, estimation, and error analysis to develop precision, self-checking habits, and clear mathematical communication.