Find the value of each expression mentally.

1. Han starts writing multiples of a number. When he reaches 104, he has written 8 numbers.

   For each of the following questions, explain or show your reasoning.

   

   1. What number is Han writing multiples of?
   2. What is the 15th multiple of this number?
   3. Han gets to 286. How many numbers has he written at that point?

2. Kiran wants to know how many multiples of 7 are between 0 and 150.

   1. He thinks he can use division to find out. Do you agree? Explain your reasoning.
   2. How many multiples will he find? Show your reasoning.
   3. Is 150 a multiple of 7? Show how you know.
3. Han writes the number 295. He is wondering if he made a mistake. Determine if 295 is a multiple of 8 and explain your reasoning.

Jada writes multiples of a mystery number. After writing some numbers, she writes the number 126.

• Mai says 6 is the mystery number.
• Priya says 8 is the mystery number.
• Andre says 9 could be the mystery number.

1. Which student do you agree with? Show how you know using equations.

2. Jada gives one more clue: “If I keep writing multiples, I’ll get to 153.”

   What is the mystery number? Explain or show your reasoning.

Directions:

• Spin the spinner to get your one-digit divisor.
• Each partner:
  • Use 3–4 cards to create a dividend. 
  • Write a multiplication equation to represent the quotient. (For example,  is written as  and your score is 1.)
  • Check your partner’s work to make sure you agree.
  • Your score for each round is the remainder.
• Take new cards so that you have 4 cards to start the next round.
• The partner who has the fewest points once the recording sheet is full wins the game.