Interpret Remainders in Division Situations

10 min

Narrative

The purpose of this Warm-up is to invite students to count by 2, 3, and 5, notice patterns in the count, and think about multiples. It gives the teacher an opportunity to observe strategies or understandings students have for identifying multiples of small numbers, primarily by looking for and making use of structure (MP7). These understandings will be helpful later when students solve division problems that involve distinguishing quotients with and without a remainder.

Launch

  • “Count by 2 starting at 90.”
  • Record as students count.
  • Stop counting and recording at 112.
Teacher Instructions
  • “What patterns do you notice in the recorded count?” (Count by 2: Ones digit is 0, 2, 4, 6, or 8. )
  • Repeat with 3 and 5.
  • “Count by 3 starting at 90.”
  • Stop counting and recording at 114.
  • “What patterns do you notice in the recorded counts?” (Count by 2 and 3: The numbers 90, 96, 102, 108, and 114 are in both lists. These numbers are multiples of both 2 and 3. They have an add 6 pattern to get from one term to the next: 90+6=9690+6=96.)
  • “Count by 5 starting at 90.”
  • Stop counting and recording at 115.
  • “What patterns do you notice in the recorded counts?” (Count by 2, 3, and 5: The only number in all three lists is 90. 90 is a multiple of 2, 3, and 5. Count by 3 and 5: 90 and 105 are in both lists 90+15=10590+15=105.)

Sample Response

Counts by 2:

  • 90 92 94 96
  • 98 100 102 104
  • 106 108 110 112

Counts by 3:

  • 90 93 96
  • 99 102 105
  • 108 111 114

Counts by 5:

  • 90 95 100
  • 105 110 115
Activity Synthesis (Teacher Notes)
  • “Is 105 a multiple of 2, 3, or 5? How do you know?” (3 and 5. I know 90 is a multiple of 2, 3, and 5 so I can use the recorded counts to identify multiples. 105 is in the recorded counts for 3 and 5.)
  • “Is 105 a multiple of 15?” (Yes. I can count by 15s to get to 90: 15, 30, 45, 60, 75, 90 and then 15 more is 105.)
Standards
Building On
  • 4.OA.4·Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.
  • 4.OA.B.4·Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
Addressing
  • 4.NBT.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • 4.NBT.B.6·Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

15 min

20 min