Understanding Ratios and Proportions

Mrs. Hassner introduces a lesson on equivalent ratios for sixth-grade students using Eureka Math. The lesson covers examples and exercises, including determining equivalent ratios, using tape diagrams, and solving problems involving library books and mixed nuts. Students are guided through exercises and homework to reinforce their understanding of equivalent ratios.

What is the first step to determine if 24 students have overdue books based on the ratio 2 to 7?

• Divide 24 by 7

• Divide 24 by 2

• Multiply 7 by 12

• Multiply 2 by 12

In Exercise 1, if the ratio 6:7 is not equivalent to 42:77, what should you do?

• Find a new ratio equivalent to 6:7

• Multiply both numbers by 7

• Add 7 to both numbers

• Divide both numbers by 7

What is the value of 'c' that makes the ratio 0:5 equivalent to 0:20?

• 4

• 5

• 2

• 3

In Exercise 2, how many walnuts are there if the ratio of walnuts to cashews is 5:6 and there are 54 cashews?

• 45

• 50

• 54

• 60

What is the purpose of using a tape diagram in Exercise 2?

• To divide the numbers

• To visually verify the ratio

• To subtract the numbers

• To add the numbers

Which of the following sets of ratios are equivalent according to the homework section?

• 2:3, 4:6, 8:10

• 2:3, 4:5, 8:12

• 2:3, 5:6, 8:12

• 2:3, 4:6, 8:12

How can you prove that the ratio 3:8 is equivalent to 12:32?

• Multiply both numbers by 3

• Multiply both numbers by 4

• Divide both numbers by 4

• Add 4 to both numbers

If Isabella has $33 and the ratio of her money to Shane's is 3:11, how much money does Shane have?

• $132

• $99

• $110

• $121

What is the total amount of money Isabella and Shane have together?

• $154

• $155

• $156

• $157

What is the multiplier used to find Shane's money if Isabella has $33?

• 9

• 10

• 11

• 12