# Sixth Grade Math Lesson: Take Your Class On a Ratio Tour!

Let your students get comfortable with the ratios they see on a daily basis!

## Objective

Students will identify ratios in their surroundings and use ratio language to describe the relationships between them.

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

## Materials

- Clipboards
- Writing utensils
- Paper
- Access to general classroom and campus materials

## Lesson Procedure

**Step One: Introduce Ratios**

Demonstrate to students the concept of using ratios to compare objects. Begin by providing objects for students on a table in the front of the room or at students’ desks to compare during a whole class discussion (for example, rulers and pencils, erasers and markers, etc.). Ask students to count the number of each object, and demonstrate how to write ratios to compare the quantities of the objects using the following formats:

Using slash (resembling a fraction): Rulers/Pencils or Erasers/ Markers

Using colon: Rulers: Pencils or Erasers: Markers

You can vary items in the ratios or add additional items as needed until students appear confident in writing ratios based on the number of objects in relation to each other.

**Step Two: Ratio Tour (Counting Items)**

Assisting students as a class, compile a list of objects in the classroom and outside the classroom, which they will be able to count and record in ratios. Objects might include general items, such as textbooks, or specific categories of items, such as novels, textbooks or workbooks. Outside items might include tables and chairs, flagpoles, playground equipment, or landscaping items such as boulders and trees.

Once students have a general list of available items, ask students to choose 20 items from the list to count. This will encourage variety among the items so that there is less congestion around different parts of the classroom while students are counting. You may wish to ask students to work in teams so that they are counting items accurately or divide the work of counting if it becomes tedious.

Once students have counted the items, they will return to a designated workspace to begin using the collected numbers to make ratios.

**Step Three: Creating Ratios with Collected Quantities and Analyzing Experience**

Using the numbers they collected on their tour, students will begin organizing them into ratios. Ask students to group objects into pairs that make sense (such as lunch tables and chairs) so that they can think about why the numbers in the ratio might be higher or lower (tables can be shared, chairs cannot).

Instruct students to create at least 10 sets of ratios from the 20 objects they counted (more if students need more practice or appear to be working quickly). After creating their ratios, ask students to analyze their experience by writing briefly on the following topics using the back of the papers with the counted numbers and ratios:

When is it helpful to know the ratio of quantities of objects (or people)?

What are some explanations for the ratios they found in the classroom, such as numbers of textbooks and workbooks, or numbers of supplies that are used or less commonly used?

What is the current ratio of teacher to students in their classroom? Why would this information be useful to students and parents?

Which way do they prefer to write ratios: resembling a fraction or using a colon? Why?

**Step Five (optional): Brief Closing Discussion**

You may want to lead students in a quick discussion of their experience finding and writing ratios and ask them to share a few responses to the topics they discussed in the writing exercise.

## Assessment

Collect students’ work and evaluate the accuracy of the counted objects and created ratios. Assess the understanding students have of ratios based on their answers to the writing topics.

## Extension

To help students further relate using ratios to their own experiences, ask them to consider taking a few notes on where they see ratios involving people, such as ratios of teachers to students in other classes, cashiers to customers at stores, servers to customers at restaurants, or people to cars they see on the road. Students can bring in their notes and discuss whether they think changing the ratios they observed would improve the conditions they experience. For example, having more people in fewer cars would make for less traffic, or having fewer students per teacher might improve student learning.