Videos and solutions to help Grade 6 students learn about ratios.

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Common Core For Grade 6

### New York State Common Core Math Module 1, Grade 6, Lesson 1 and Lesson 2

Lesson 1 Student Outcomes

• Students understand that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students understand that a ratio is often used instead of describing the first number as a multiple of the second.

• Students use the precise language and notation of ratios (3:2, 3 to 2). Students understand that the order of the pair of numbers in a ratio matters and that the description of the ratio relationship determines the correct order of the numbers. Students conceive of real-world contextual situations to match a given ratio.

Lesson 1 Summary

• A ratio is an ordered pair of non-negative numbers, which are not both zero. The ratio is written or to to indicate the order of the numbers. The number is first, and the number is second.

• The order of the numbers is important to the meaning of the ratio. Switching the numbers changes the relationship. The description of the ratio relationship tells us the correct order for the numbers in the ratio.

**Classwork Example 1**

The coed soccer team has four times as many boys on it as it has girls. We say the ratio of the number of boys to the number of girls on the team is 4:1. We read this as “four to one.”

Suppose the ratio of number of boys to number of girls on the team is 3:2.

**Classwork Example 2: Class Ratios**

Record a ratio for each of the examples the teacher provides.

Exercise 1

Have students look around the classroom to think of their own ratios. Have students create written ratio statements that represent their ratios in one of the summary forms.

Exercise 2

Using words, describe a ratio that represents each ratio below.

a. 1 to 12

b. 12:1

c. 2 to 5

d. 5 to 2

e. 10:2

f. 2:10**Problem Set**

At the 6th grade school dance, there are boys, girls, and adults.

a. Write the ratio of number of boys to number of girls.

b. Write the same ratio using another form (A: B vs. A to B).

c. Write the ratio of number of boys to number of adults.

d. Write the same ratio using another form.

2. In the cafeteria, 100 milk cartons were put out for breakfast. At the end of breakfast, 27 remained.

a. What is the ratio of milk cartons taken to total milk cartons?

b. What is the ratio of milk cartons remaining to milk cartons taken?

3. Choose a situation that could be described by the following ratios, and write a sentence to describe the ratio in the context of the situation you chose.

For example:

3:2 When making pink paint, the art teacher uses the ratio 3:2. For every 3 cups of white paint she uses in the mixture, she needs to use 2 cups of red paint.

a. 1 to 2

b. 29 to 30

c. 52:12

Lesson 2 Student Outcomes

• Students reinforce their understanding that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students continue to learn and use the precise language and notation of ratios (e.g., 3:2, 3 to 2). Students demonstrate their understanding that the order of the pair of numbers in a ratio matters.

• Students create multiple ratios from a context in which more than two quantities are given. Students conceive of real-world contextual situations to match a given ratio.

Lesson 2 Summary

• Ratios can be written in two ways: A to B or A:B.

• We describe ratio relationships with words such as: to, for each, for every.

• The ratio is not the same as the ratio B:A (unless A is equal to B).

Classwork Lesson 2

Exercise 1

Come up with two examples of ratio relationships that are interesting to you.

Exploratory Challenge

A t-shirt manufacturing company surveyed teen-aged girls on their favorite t-shirt color to guide the company’s decisions about how many of each color t-shirt they should design and manufacture. The results of the survey are shown here.

Exercises for Exploratory Challenge

1. Describe a ratio relationship, in the context of this survey, for which the ratio is 3:5.

2. For each ratio relationship given, fill in the ratio it is describing.

3. For each ratio given, fill in a description of the ratio relationship in could describe, using the context of the survey.**Problem Set**

1. Using the floor tiles design shown below, create 4 different ratios related to the image. Describe the ratio relationship and write the ratio in the form A:B or the form A to B.

2. Billy wanted to write a ratio of the number of cars to the number of trucks in the police parking lot. He wrote 1: 3. Did Billy write the ratio correctly? Explain your answer.

Lesson 1 and Lesson 2

1. Write a ratio for the following description: For every 3 cups of flour in a chocolate chip cookie recipe, 1 cup of sugar is used.

2. Give two different ratios with a description of the ratio relationship using the following information: There are 16 boys in the chorus. There are 24 girls in the chorus.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics:

Lesson Plans and Worksheets for Grade 6

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 6

Common Core For Grade 6

• Students understand that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students understand that a ratio is often used instead of describing the first number as a multiple of the second.

• Students use the precise language and notation of ratios (3:2, 3 to 2). Students understand that the order of the pair of numbers in a ratio matters and that the description of the ratio relationship determines the correct order of the numbers. Students conceive of real-world contextual situations to match a given ratio.

Lesson 1 Summary

• A ratio is an ordered pair of non-negative numbers, which are not both zero. The ratio is written or to to indicate the order of the numbers. The number is first, and the number is second.

• The order of the numbers is important to the meaning of the ratio. Switching the numbers changes the relationship. The description of the ratio relationship tells us the correct order for the numbers in the ratio.

The coed soccer team has four times as many boys on it as it has girls. We say the ratio of the number of boys to the number of girls on the team is 4:1. We read this as “four to one.”

Suppose the ratio of number of boys to number of girls on the team is 3:2.

Record a ratio for each of the examples the teacher provides.

Exercise 1

Have students look around the classroom to think of their own ratios. Have students create written ratio statements that represent their ratios in one of the summary forms.

Exercise 2

Using words, describe a ratio that represents each ratio below.

a. 1 to 12

b. 12:1

c. 2 to 5

d. 5 to 2

e. 10:2

f. 2:10

At the 6th grade school dance, there are boys, girls, and adults.

a. Write the ratio of number of boys to number of girls.

b. Write the same ratio using another form (A: B vs. A to B).

c. Write the ratio of number of boys to number of adults.

d. Write the same ratio using another form.

2. In the cafeteria, 100 milk cartons were put out for breakfast. At the end of breakfast, 27 remained.

a. What is the ratio of milk cartons taken to total milk cartons?

b. What is the ratio of milk cartons remaining to milk cartons taken?

3. Choose a situation that could be described by the following ratios, and write a sentence to describe the ratio in the context of the situation you chose.

For example:

3:2 When making pink paint, the art teacher uses the ratio 3:2. For every 3 cups of white paint she uses in the mixture, she needs to use 2 cups of red paint.

a. 1 to 2

b. 29 to 30

c. 52:12

• Students reinforce their understanding that a ratio is an ordered pair of non-negative numbers, which are not both zero. Students continue to learn and use the precise language and notation of ratios (e.g., 3:2, 3 to 2). Students demonstrate their understanding that the order of the pair of numbers in a ratio matters.

• Students create multiple ratios from a context in which more than two quantities are given. Students conceive of real-world contextual situations to match a given ratio.

Lesson 2 Summary

• Ratios can be written in two ways: A to B or A:B.

• We describe ratio relationships with words such as: to, for each, for every.

• The ratio is not the same as the ratio B:A (unless A is equal to B).

Classwork Lesson 2

Exercise 1

Come up with two examples of ratio relationships that are interesting to you.

Exploratory Challenge

A t-shirt manufacturing company surveyed teen-aged girls on their favorite t-shirt color to guide the company’s decisions about how many of each color t-shirt they should design and manufacture. The results of the survey are shown here.

Exercises for Exploratory Challenge

1. Describe a ratio relationship, in the context of this survey, for which the ratio is 3:5.

2. For each ratio relationship given, fill in the ratio it is describing.

3. For each ratio given, fill in a description of the ratio relationship in could describe, using the context of the survey.

1. Using the floor tiles design shown below, create 4 different ratios related to the image. Describe the ratio relationship and write the ratio in the form A:B or the form A to B.

2. Billy wanted to write a ratio of the number of cars to the number of trucks in the police parking lot. He wrote 1: 3. Did Billy write the ratio correctly? Explain your answer.

1. Write a ratio for the following description: For every 3 cups of flour in a chocolate chip cookie recipe, 1 cup of sugar is used.

2. Give two different ratios with a description of the ratio relationship using the following information: There are 16 boys in the chorus. There are 24 girls in the chorus.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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