## Engage NY Eureka Math 6th Grade Module 1 Lesson 1 Answer Key

### Eureka Math Grade 6 Module 1 Lesson 1 Example Answer Key

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.

Answer:

â†’ Letâ€™s create a table to show how many boys and how many girls could be on the team.

Create a table like the one shown below to show possibilities of the number of boys and girls on the soccer team. Have students copy the table into their student materials.

# of Boys | # of Girls | Total # of Players |

4 | 1 | 5 |

â†’ So, we would have four boys and one girl on the team for a total of five players. Is this big enough for a team?

â†’ Adult teams require 11 players, but youth teams may have fewer. There is no right or wrong answer;

just encourage reflection on the question, thereby having students connect their math work back to the

context.

â†’ What are some other ratios that show four times as many boys as girls, or a ratio of boys to girls of 4 to 1?

â†’ Have students add each ratio to their table.

# of Boys | # of Girls | Total # of Players |

4 | 1 | 5 |

8 | 2 | 10 |

12 | 3 | 15 |

â†’ From the table, we can see that there are four boys for every one girl on the team.

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

Answer:

Create a table like the one shown below to show possibilities of the number of boys and girls on the soccer team. Have students copy the table into their student materials.

# of Boys | # of Girls | Total # of Players |

3 | 2 | 5 |

â†’ What are some other team compositions where there are three boys for every two girls on the team?

# of Boys | # of Girls | Total # of Players |

3 | 2 | 5 |

6 | 4 | 10 |

9 | 6 | 15 |

â†’ I canâ€™t say there are 3 times as many boys as girls. What would my multiplicative value have to be? There are ________ as many boys as girls.

Encourage students to articulate their thoughts, guiding them to say there are \(\frac{3}{2}\) as many boys as girls.

â†’ Can you visualize \(\frac{3}{2}\) as many boys as girls?

â†’ Can we make a tape diagram (or bar model) that shows that there \(\frac{3}{2}\) are as many boys as girls?

Boys

Girls

â†’ Which description makes the relationship easier to visualize: saying the ratio is 3 to 2 or saying there are 3

halves as many boys as girls?

Example 2.

Write the ratio of the number of boys to the number of girls in our class.

Answer:

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

- Answers will vary. One example is 12: 10.
- Answers will vary. One example is 10: 12.
- Answers will vary. One example is 7: 15.
- Answers will vary. One example is 15: 7.
- Answers will vary. One example is 11: 11.
- Answers will vary. One example is 11: 11.

Write the ratio of the number of girls to the number of boys in our class.

Answer:

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

- Answers will vary. One example is 12: 10.
- Answers will vary. One example is 10: 12.
- Answers will vary. One example is 7: 15.
- Answers will vary. One example is 15: 7.
- Answers will vary. One example is 11: 11.
- Answers will vary. One example is 11: 11.

### Eureka Math Grade 6 Module 1 Lesson 1 Exercise Answer Key

Exercise 1.

My own ratio compares __________________ to __________________.

My ratio is __________________.

Answer:

My own ratio compares the number of students wearing jeans to the number of students not wearing jeans.

My ratio is 16: 6.

Exercise 2.

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

a. 1 to 12

Answer:

For every one year, there ore twelve months.

b. 12: 1

Answer:

For every twelve months, there is one year.

c. 2 to 5

Answer:

For every two non-school days in a week, there are five school days.

d. 5 to 2

Answer:

For every five female teachers I have, there are two male teachers.

e. 10: 2

Answer:

For every ten toes, there are two feet.

f. 2: 10

Answer:

For every two problems I can finish, there are ten minutes that pass.

### Eureka Math Grade 6 Module 1 Lesson 1 Problem Set Answer Key

Question 1.

At the sixth grade school dance, there are 132 boys, 89 girls, and 14 adults.

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

Answer:

132: 89 or 132 to 89

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

Answer:

132 to 89 or 132: 89

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

Answer:

132: 14 or 132 to 14

d. Write the same ratio using another form.

Answer:

132 to 14 or 132: 14

Question 2.

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

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

Answer:

73: 100 or 73 to 100

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

Answer:

27: 73 or 27 to 73

Question 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

Answer:

For every one nose, there are two eyes (answers will vary).

b. 29 to 30

Answer:

For every 29 girls in the cafeteria, there are 30 boys (answers will vary).

c. 52: 12

Answer:

For every 52 weeks in the year, there are 12 months (answers will vary).

### Eureka Math Grade 6 Module 1 Lesson 1 Exit Ticket Answer Key

Question 1.

Write a ratio for the following description: Kaleel made three times as many baskets as John during basketball

Answer:

A ratio of 3: 1 or 3 to 1 can be used.

Question 2.

Describe a situation that could be modeled with the ratio 4: 1.

Answer:

Answers will vary but could include the following: For every four teaspoons of cream in a cup of tea, there is one teaspoon of honey.

Question 3.

Write a ratio for the following description: For every 6 cups of flour in a bread recipe, there are 2 cups of milk.

Answer:

A ratio of 6: 2 or 6 to 2 can be used, or students might recognize and suggest the equivalent ratio of 3: 1.