compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships

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compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x + a in order to differentiate between additive and multiplicative relationships

apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates

give examples of ratios as multiplicative comparisons of two quantities describing the same attribute

give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients

represent ratios and percents with concrete models, fractions, and decimals

represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers

generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money

convert units within a measurement system, including the use of proportions and unit rates

represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions

solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models

use equivalent fractions, decimals, and percents to show equal parts of the same whole