UP:MA19.6.3

Students know:

Strategies for representing contexts involving rates and ratios including. tables of equivalent ratios, changing to unit rate, tape diagrams, double number lines, equations, and plots on coordinate planes.
Strategies for finding equivalent ratios,
Strategies for using ratio reasoning to convert measurement units.
Strategies to recognize that a conversion factor is a fraction equal to 1 since the quantity described in the numerator and denominator is the same.
Strategies for converting between fractions, decimals and percents.
Strategies for finding the whole when given the part and percent in a mathematical and contextual situation.
Strategies for finding the part, given the whole and the percent in mathematical and contextual situation.
Strategies for finding the percent, given the whole and the part in mathematical and contextual situation.

Students are able to:

Represent ratio and rate situations using a variety of strategies (e.g., tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes).
Use ratio, rates, and multiplicative reasoning to explain connections among representations and justify solutions in various contexts, including measurement, prices and geometry.
Understand the multiplicative relationship between ratio comparisons in a table by writing an equation.
Plot ratios as ordered pairs.
Solve and justify solutions for rate problems including unit pricing, constant speed, measurement conversions, and situations involving percents.
Solve problems and justify solutions when finding the whole given a part and the percent.
Model using an equivalent fraction and decimal to percents.
Use ratio reasoning, multiplication, and division to transform and interpret measurements.

Students understand that:

A unit rate is a ratio (a:b) of two measurements in which b is one.
A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation.
When computing with quantities the transformation and interpretation of the resulting unit is dependent on the particular operation performed.