Prime and Composite Numbers

10 min

Narrative

The purpose of this Choral Count is to invite students to practice counting by 2 and 5 and notice patterns in each count. These understandings help students develop fluency and will be helpful later when students find factor pairs. In the Activity Synthesis, students are also invited to notice numbers that are in both counts and begin to reason why this may happen based on their emerging understanding of factors and multiples.

When students identify and predict common multiples for 2 and 5 based on the numbers recorded from the count and what they know about multiplication, they look for and express regularity in repeated reasoning (MP8).

This is the first time students experience the Choral Count routine in IM Grade 4. Students are familiar with this routine from a previous grade. However, they may benefit from a brief review of the steps involved.

Launch

  • “Count by 2, starting at 0.”
  • Record as students count.
  • Stop counting and recording at 30.
Teacher Instructions
  • “What patterns do you see?”
  • 1–2 minutes: quiet think time
  • Record responses.
  • “Now count by 5, starting at 0.”
  • Record as students count.
  • Stop counting and recording at 75.
  • “What patterns do you see?”
  • 1–2 minutes: quiet think time
  • Record responses.

Sample Response

  • Record the first count in a column with the title “count by 2.” Record the second count next to the first with the title “count by 5.”

Sample responses:

  • Pattern in counting by 2:
    • The digits in the ones place repeat 2, 4, 6, 8, 0, 2, 4, 6, 8, 0.
    • All of the numbers are even.
    • After you count 5 numbers, the tens place increases by 1.
  • Pattern in counting by 5:
    • The digits in the ones place alternate 5, 0, 5, 0.
    • After every even number, there's an odd number. The pattern is even, odd, even, odd, even, odd.
    • After you count 2 numbers, the tens place increase by 1.
Activity Synthesis (Teacher Notes)
  • Select 1–2 patterns for each count to discuss. Consider asking:
    • “Does anyone want to add an observation on why that pattern is happening here?”
    • “Do you agree or disagree? Why?”
  • “What numbers are in both lists? Why do you think that happens?” (10, 20, and 30 are in both lists. It’s because they are multiples of both 2 and 5. 2 and 5 are both factors for each of those numbers.)
  • “If the counts continue, what other numbers would you see that are multiples of both 2 and 5?” (I think 40 would be the next common multiple because the multiples are going up by 10. I think 100 would be a common multiple because 2×50=1002 \times 50 = 100 and 5×20=1005 \times 20 = 100.)
Standards
Addressing
  • 4.OA.5·Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. <em>For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.</em>
  • 4.OA.C.5·Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. <span>For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.</span>
Building Toward
  • 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.

15 min

20 min