The purpose of this activity is to prompt students to use the relationship between multiplication and division and their understanding of factors and multiples to solve problems about an unknown factor (MP7). Students recognize such problems as division situations. In this activity, the dividends are three-digit numbers and the divisors are one-digit numbers. Students use the context of factors and multiples to interpret division that results in a remainder.

One approach for solving these problems is by decomposing the dividend into familiar multiples of 10 and then dividing the remaining number (which is now smaller) by the divisor. Another is to find increasingly greater multiples of the divisor until reaching the dividend. Both are productive and appropriate. In the Activity Synthesis, help students see the connections between the two paths.

• Invite students to share responses for the last set of questions.
• Highlight that to divide a number by a smaller number—say, divide 150 by 7, we can:
  • Use familiar multiples or multiplication facts to help us. For example, if we know , we know the result is 21 with a remainder of 3, or .
  • Think of the dividend in smaller chunks. For example: We can see the 150 as and divide each 140 and 10 by 7 separately, which gives with a remainder of 3.

The purpose of this optional activity is for students to continue to use the relationship between multiplication and division to reason about situations that involve division. Students divide three-digit numbers by single-digit divisors and find results with and without a remainder. This activity provides more practice applying the relationship between multiplication and division.

• “How could we use division to help us find the mystery number?” (If the result has a remainder, then the divisor could not be the mystery number. 153 divided by 6 has 3 as a remainder. 153 divided by 9 has no remainder, so 9 is the mystery number.)

The purpose of this activity is to introduce the center activity Watch Your Remainder, Stage 1. Students spin a spinner to get the divisor for the round. Each student picks 5 cards and chooses 3–4 of them to create a dividend. Each student finds their quotient. The score for the round is the remainder from each expression. Students pick new cards so they have 6 cards in their hand and then start the next round. The player with the lowest score after 6 rounds wins.

The Activity Synthesis provides suggested cards to display to discuss strategies for the game. Consider having a group of 2 share one of the rounds from their game instead.

• Invite selected students to show the number cards for the round with no remainder or display the number cards 0, 1, 2, 3, 7 with a divisor of 5.
• “How would you use these cards to get the smallest remainder?”
• Invite selected students to show the number cards for the round with a remainder or display the number cards 0, 1, 2, 3, 7 with a divisor of 9.
• “How would you use these cards to get the smallest remainder?”