Describing Ratios with "For Every" and "For Each"
Ratios compare two quantities and can be described using the phrases for every or for each to express the relationship in everyday language. If a fruit bowl has 3 apples and 2 oranges, the relationship is described as for every 3 apples there are 2 oranges. If a teacher gives 1 marker to each student, there is 1 marker for each student. These verbal descriptions from Reveal Math, Course 1, Module 1 are the first step in 6th grade ratio understanding before formal notation and proportion solving.
Key Concepts
A ratio is a comparison between two quantities. The phrases for every and for each are used to define and describe this relationship verbally.
If a ratio compares quantity $a$ to quantity $b$, it can be stated as: $$a \text{ for every } b$$ or $$a \text{ for each } b$$.
Common Questions
How do I describe a ratio using words?
Use the phrases for every or for each. For a ratio of 3 red to 2 blue, say: for every 3 red there are 2 blue. For a 1-to-1 ratio, say: 1 item for each person.
What is the difference between for every and for each?
Both phrases describe a ratio relationship. For every is typically used for comparing two groups. For each often implies a 1-to-1 or unit distribution, like 1 marker for each student.
A recipe uses 2 cups flour for every 3 cups sugar. How would you write this as a ratio?
The ratio is 2 to 3, or 2:3. In words: for every 2 cups of flour, there are 3 cups of sugar.
Why do we describe ratios verbally before writing them as fractions?
Verbal descriptions make the meaning of a ratio concrete and accessible before introducing formal notation. They also train students to recognize ratio language in word problems.
What words in a problem signal a ratio relationship?
Words and phrases like for every, for each, per, to, out of, and compared to all signal a ratio relationship between two quantities.
When do 6th graders learn to describe ratios verbally?
Module 1 of Reveal Math, Course 1 introduces ratio language as the foundation of the Ratios and Rates unit.