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MA19.6.3
Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

### Unpacked Content

## UP:MA19.6.3

### Vocabulary

- Rate
- Ratio
- Rate reasoning
- Ratio reasoning
- Transform units
- Quantities
- Ratio Tables
- Double Number Line Diagram
- Percents
- Coordinate Plane
- Ordered Pairs
- Quadrant I
- Tape Diagrams
- Unit Rate
- Constant Speed

### Knowledge

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.

### Skills

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.

### Understanding

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.