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* *Reflection: Data Analysis
Describing Ratios - Section 2: Intro to New Material

I am focusing on student annotations this year as one way my students make sense of problems. This focus area fits in nicely with this lesson, and helped my students to avoid a common mistake of listing the terms in a ratio in the incorrect order.

I have my students underline the terms that are being compared in the ratio, and then have them annotate by writing x under the first term and y under the second term. I teach ratios as being x to y (or x:y or x/y), so annotating in this way reinforces one of the key ideas from this lesson.

My data from the exit tickets this year shows a stronger level of mastery after this first lesson than I've seen in previous years, and I believe annotations are one reason for this.

You can see a student annotation sample here.

# Describing Ratios

Lesson 1 of 13

## 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.

*60 minutes*

#### Think About It

*5 min*

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.

#### Resources

*expand content*

#### Intro to New Material

*15 min*

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.

#### Resources

*expand content*

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.

#### Resources

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#### Independent Practice

*15 min*

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?

#### Resources

*expand content*

#### Closing and Exit Ticket

*10 min*

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.

#### Resources

*expand content*

*I found your lesson while looking for a way to re-teach. I love the partner talk activity. I wish I had done this the first go around! | one month ago | Reply*

This is a great lesson/unit! To save time, are answer keys available? I don't see them in the lesson materials.

| one year ago | Reply

I am really impressed with the format of this lesson. Encouraging the use of annotations provides students with the foundation to successfully complete more complex lessons. I love the variety of ratio topics and examples.

| 2 years ago | Reply*expand comments*

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- UNIT 1: Number Sense
- UNIT 2: Division with Fractions
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Coordinate Plane
- UNIT 5: Rates and Ratios
- UNIT 6: Unit Rate Applications and Percents
- UNIT 7: Expressions
- UNIT 8: Equations
- UNIT 9: Inequalities
- UNIT 10: Area of Two Dimensional Figures
- UNIT 11: Analyzing Data

- LESSON 1: Describing Ratios
- LESSON 2: Part to Part Ratios Using Tape Diagrams and Tables
- LESSON 3: Tape Diagrams - Part to Part and Part to Total Ratios
- LESSON 4: Part to Total Ratios Using Tape Diagrams and Tables
- LESSON 5: Multistep Tape Diagrams, Part 1
- LESSON 6: Multistep Tape Diagrams, Part 2
- LESSON 7: Comparing Ratios
- LESSON 8: Ratios and Double Number Lines
- LESSON 9: Ratios and Scale Factors
- LESSON 10: Graphing Ratios
- LESSON 11: Unit Rate
- LESSON 12: Converting Measurements In the Same Sytem Using Ratios
- LESSON 13: Converting Measurements in Different Systems Using Ratios