Unit 2, Lesson 1
Introducing Ratios and Ratio Language
Grade 6
Preparation
Lesson Narrative
In this lesson, students use collections of objects to make sense of and use ratio language. They see that there are several different ways to describe a situation using ratio language. For example, if we have 12 squares and 4 circles, we can say the ratio of squares to circles is and the ratio of circles to squares is 4 to 12. We may also see a structure that prompts us to regroup them and say that there are 6 squares for every 2 circles, or 3 squares for every one circle (MP7).
Expressing associations of quantities in a context—as students will be doing in this lesson—requires students to use ratio language with care (MP6). Making groups of physical objects that correspond with “for every” language is a concrete way for students to make sense of the problem (MP1).
It is important that in this first lesson students work with objects that can be physically rearranged. This experience can help students make sense of the increasingly abstract representations that they will encounter as the unit progresses.
- Comprehend the word “ratio” (in written and spoken language) and the notation $a:b$ (in written language) to refer to an association between quantities.
- Describe (orally and in writing) associations between quantities using the language “For every $a$ of these, there are $b$ of those” and “The ratio of these to those is $a:b$ (or $a$ to $b$).”
Let’s describe two quantities at the same time.
Required Materials
Required Preparation
A few days before this lesson, ask students to bring a personal collection of 10–50 small objects. Examples include rocks, seashells, trading cards, or coins. Bring in your personal collection, and display it ahead of time. Think of possible ways to sort your collection. (See the Launch of “The Teacher’s Collection” for details.) Prepare a few extra collections for students who don’t bring one.
A ratio is a way to relate 2 or more quantities.
For example, the ratio could describe:
- A recipe that uses 3 cups of flour for every 2 eggs.
- A boat that moves 3 meters every 2 seconds.
- A diagram that has 3 blue squares for every 2 green squares.