# Describing Ratios

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## Objective

SWBAT understand the concept of ratio and use ratios to describe a relationship between two quantities

#### Big Idea

A ratio expresses a relationship where for every x units of one quantity there are y units of another quantity.

## Think About It

5 minutes

In this Think About It problem, students work in partners and use what they know to make comparisons between the quantities of cats, dogs, and the total number of pets.  Because the previous unit was an inequalities unit, many pairs will make comparisons using greater than or less than.

I have 2-3 different students share out a comparison (s)he talked about with his/her partner.  I then frame the lesson by letting students know that we are working on new material now. Ratios!  I let them know that ratios will give us another option when we want to describe the relationship between two quantities.

## Intro to New Material

15 minutes

After the Think About It discussion, we move into the Intro to New Material.  In this lesson, I start by modeling how to express the relationship between the cats and dogs, using a ratio.  I model all three versions of the notation:  10 to 21, 10:21, and 10 over 21.  I am explicit with students that we must use the horizontal fraction bar and not the diagonal fraction bar.  I then tell them that all of these notations tell us that for every 10 cats in the group, there are 21 dogs.

As a quick check for understanding, I display the number of boys and the number of girls in the class on the board.  I ask for the ratio of boys to girls, girls to boys, boys to the total, and girls to the total.  I have students express the ratios using "to,' a colon, and a fraction bar.

## Partner Practice and Discussion

15 minutes

Students work in pairs for the Partner Practice.   Students are practicing using the language of ratios.  I circulate throughout the classroom and listen to every student compare two quantities.  I am listening for students to say "The ratio of x to y is (#) to (#)"

After I've had the chance to hear from every student, I then bring the class back together.  I cold call on 5 students to share out a comparison.  If a student makes a mistake (for example, does not say the word 'to' in between the two items), I correct it and have the student repeat the ratio correctly.

## Independent Practice

15 minutes

Students work on the Independent Practice  problem set.  As they work, I circulate around the room.  I am looking for:

• Are students annotating each problem?
• Are students correctly identifying the terms and putting them in the correct order?
• Are students correctly expressing the ratio in three different ways?
• Are students correctly comparing parts to parts and parts to total?

I am asking:

• How did you know which was a part?
• How did you know what the total was?
• What does your ratio represent?

## Closing and Exit Ticket

10 minutes

After independent work time, I bring the class back together to discuss Problem 7.  This problem is multiple choice, and requires students to simplify the ratio to lowest terms.  It also requires students to find the total number of squares on their own, so it makes for a nice problem to discuss, from start to finish.  We read and annotate together, create our own ratio and express it in three ways, and then consider the answer choices.

Students work independently on the Exit Ticket to end the lesson.