 ## Grade 6 Math: Ratios and Rates

### Ratios

In earlier lessons, students learned to solve application problems in a variety of situations based on multiplicative relationships. In this lesson, ratios are introduced as another kind of situation in which multiplicative relationships occur. They are situations that are those described previously as “multiplicative comparison” situations.

Ratios are also defined as the result you get when you divide one number by another number, or the quotient in a division problem.

This fact is used to define what is called the unit ratio. The unit ratio is the multiplicative relationship between two numbers expressed as a ratio (which is the same as the quotient) in which the denominator is 1.

In these lessons students learn to recognize these situations as involving ratios, and apply the methods they have learned previously to solve problems based on these ratios. These problems require that the student find the unit ratio for a given situation, or to find either value in the ratio expressed in larger terms. They use the same systematic strategy used earlier to solve application problems based on multiplicative relationships.

### Ratio Notation

In this lesson, students learn to write ratios in each of three types of notation: fraction notation and two forms of ratio notation.

### Applications: Rates

Students have previously learned how to solve application problems based on multiplicative relationships, and they have learned that ratios are one way to express these multiplicative relationships.

In this lesson, students learn to solve application problems based on rates using the same systematic approach used earlier to solve problems based on multiplicative relationships.

### Applications: Unit Cost

In prior lessons, students have learned to solve a variety of problems based on multiplicative relationships using a systematic strategy.

In this lesson, students learn to apply the same solution strategy to another kind of application situation based on multiplicative relationships – unit cost problems.

The only difference in these and problems in earlier lessons based on multiplicative relationships is that the problems in this lesson all involve situations in which one of the measurement dimensions is cost (or price), which is expressed in dollars as the units.

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