1. If 5 pencils cost 95 cents, how much does each pencil cost? Explain or show your reasoning.

2. If 68 colored pencils are split evenly between 4 students, how many pencils does each student get? Explain or show your reasoning.

Clare has 194 square tiles. Can Clare put all of her tiles in 6 rows with the same number of tiles in each row? Explain or show your reasoning.

A long, rectangular hallway is 8 feet wide and has an area of 368 square feet. How long is the hallway?

1. Write a multiplication equation and a division equation that represent the situation.
2. Find the length of the hallway. Explain or show your reasoning.

Here is 378 represented with base-ten blocks.

Use words, diagrams, or equations to show how to use the base-ten blocks to find the value of \(378 \div 6\).

Here are 2 incomplete calculations of \(864 \div 4\). Complete each calculation to find the value of the quotient.

A

\(\begin{align} 800\div 4&= 200\\ 40\div 4 &= \phantom{010}\\ 20 \div 4 &= \phantom{005} \\4 \div 4&= \phantom{001} \\ \overline {\hspace{5mm}864 \div 4} &\overline{\hspace{1mm}= \phantom{000000}}\\ \end{align}\)

B

Divide. 8 hundred sixty 4 divided by 4, 6 rows. First row: 1 hundred. Second row: 1 hundred. Third row: 4, long division symbol with 8 hundred sixty 4 inside. Fourth row: minus 4 hundred, side note 4 times 1 hundred. Horizontal line. Fifth row: 4 hundred sixty 4. Sixth row: minus 4 hundred, side note 4 times 1 hundred. Horizontal line.

What is the value of \(3,\!420\div5\)?

Use partial quotients to show your reasoning.

1. Use partial quotients to find the value of \(637 \div 4\).
2. There are 637 toothpicks and 4 people. What could \(637 \div 4\) mean in this situation? What could each step you took in the algorithm mean?
3. What does the value of the quotient represent in the situation?

There are 875 peaches at the orchard. Each box contains 9 peaches. How many boxes are needed for the peaches? Explain your reasoning.

Priya writes the multiples of a number and 63 is on her list. Priya's number is not 1.

1. What could Priya's number be? Explain your reasoning.
2. 112 is the last number on Priya's list. What is Priya's number? How many numbers are on Priya's list?

Consider the expression \(286 \div 5\).

1. Write a division story with a question that can be answered by finding the value of \(286 \div 5\). Then answer the question.

2. Write a different story with a question that can be answered by finding the value of  \(286 \div 5\) but with a different answer than your first story. Answer the question.

Mai has a special way of knowing that 531 is a multiple of 9. She says, “Each hundred is 11 nines and 1 more and each ten is one nine and 1 more, so 531 is 58 nines and 9 more.”

1. Make sense of and explain Mai’s reasoning. Is 531 a multiple of 9?
2. Use Mai's reasoning to decide if 648 is a multiple of 9.