A ratio** **is a numerical comparison of two or more quantities that indicates their relative sizes. Help sixth-grade students demonstrate their understanding of the concept of a ratio by using ratio language to describe relationships between quantities in this lesson plan.

### Lesson Basics

This lesson is designed to last one standard class period or 60 minutes. These are the key elements of the lesson:

**Materials:**Pictures of animals**Key vocabulary:**ratio, relationship, quantity**Objectives:**Students will demonstrate their understanding of the concept of a ratio by using ratio language to describe relationships between quantities.**Standards met:**6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1 because for every two wings there was one beak.”

### Introducing the Lesson

Take five to 10 minutes to do a class survey. Depending on the time and management issues you may have with your class, you can ask the questions and record the information yourself, or you can have the students design the survey themselves. Gather information such as:

- Number of people with blue eyes compared to brown eyes in the class
- Number of people with shoelaces compared to fabric fastener
- Number of people with long sleeves and short sleeves

### Step-by-Step Procedure

Start by showing a picture of a bird. Ask students questions such as, "How many legs? How many beaks?" Then follow these steps.

- Show a picture of a cow. Ask students: "How many legs? How many heads?"
- Define the learning target for the day. Tell the students: "Today we will explore the concept of ratio, which is a relationship between two quantities. What we will try to do today is compare quantities in ratio format, which usually looks like 2:1, 1:3, 10:1, etc. The interesting thing about ratios is that no matter how many birds, cows, shoelaces, etc. you have, the ratio—the relationship—is always the same."
- Review the picture of the bird. Construct a T-chart—a graphical tool used for listing two separate viewpoints of a topic—on the board. In one column, write “legs,” in another, write “beaks.” Tell the students: "Barring any truly injured birds, if we have two legs, we have one beak. What if we have four legs? (two beaks)"
- Tell students that for birds, the ratio of their legs to beaks is 2:1. Then add: "For every two legs, we’ll see one beak."
- Construct the same T-chart for the cows. Help students see that for every four legs, they’ll see one head. Consequently, the ratio of legs to heads is 4:1.

- Use body parts to further demonstrate the concept. Ask students: "How many fingers do you see? (10) How many hands? (two)"
- On the T-chart, write 10 in one column, and 2 in the other. Remind students that the goal with ratios is to get them to look as simple as possible. (If your students have learned about greatest common factors, this is much easier.) Ask students: "What if we only had one hand? (five fingers) So the ratio of fingers to hands is 5:1."
- Do a quick check of the class. After students write the answers to these questions, have them do a choral response, where the class gives answers orally in unison for the following concepts:
- Ratio of eyes to heads
- Ratio of toes to feet
- Ratio of legs to feet
- Ratio of: (use survey answers if they are easily divisible: shoelaces to fabric fastener, for example)

### Evaluation

As students are working on these answers, walk around the class so that you can see who is having a hard time recording anything, and which students write their answers down quickly and confidently. If the class is struggling, review the concept of ratios using other animals.