Students will demonstrate their understanding of the concept of a ratio by using ratio language to describe relationships between quantities.

**Class:** 6th Grade

**Duration:** One class period, or approximately 60 minutes

**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.”

**Lesson Introduction:** Take 5-10 minutes to do a class survey, depending on the time and the 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. Get information such as:

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

**Step-by Step Procedure:**

- Show picture of a bird. How many legs? How many beaks?
- Show a picture of a cow. How many legs? How many heads?
- Define the learning target for the day: 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 on the board. In one column, write “legs”, in another, write “beaks”. Barring any truly injured birds, if we have 2 legs, we have one beak. What if we have 4 legs? (2 beaks)
- Tell students that for birds, the ratio of their legs to beaks is 2:1. 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.
- Bring it to the students’ bodies. How many fingers do you see? (10) How many hands? (2)
- On the t-chart, write 10 in one column, and 2 in the other. Remind students that our 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!) What if we only had one hand? (5 fingers) So the ratio of fingers to hands is 5:1.
- Do a quick check of the class. After they write the answers to these questions, do a choral response so that students who are truly confused don’t stand out to their peers:
- 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 velcro, etc.)

**Homework/Assessment:** As this is the student’s first exposure to ratios, homework may not be appropriate in this circumstance.

**Evaluation:** As students are working on these answers, do a quick walk around the class so that you can see who is having a hard time recording anything, and who writes their answers down quickly and confidently.