Generate Patterns

10 min

Narrative

The purpose of this Choral Count is to invite students to notice patterns and relationships in two different counts. These understandings help students develop fluency with multiples and will be helpful when students identify relationships between corresponding terms in two patterns in the next several lessons.

This is the first time students experience the Choral Count routine in IM Grade 5. 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 6, starting at 0.”
  • Record as students count.
  • Stop counting and recording at 60.
Teacher Instructions
  • “What patterns do you see?”
  • 1–2 minutes: quiet think time
  • Record responses.
  • “Now count by 12, starting at 0.”
  • Record as students count.
  • Stop counting and recording at 120.
  • “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 6.” Record the second count next to the first with the title “count by 12.”

Sample responses:

  • Pattern in counting by 6:
    • The digits in the ones place repeat 0, 6, 2, 8, 4, 0, 6, 2, 8, 4.
    • All of the numbers are even.
    • If there’s a 4 in the one’s place, it’s the only number for that multiple of 10. For example, there’s two numbers when 1 is in the tens place - 12 and 18, but only 1 number when 2 or 5 is in the tens place – 24 and 54.     
  • Pattern in counting by 12:
    • The digits in the ones place alternate 0, 2 ,4, 6, 8, 0, 2, 4, 6, 8. It’s the same pattern when you count by 2.
    • All of the numbers are even.
    • The number in the tens place skips one number. It’s 0, 1, 2, 3, 4, 6, 7, 8, 9, 0, 2. In the first hundred it skips 5, in the second hundred it looks like it skips at least 1. 
Activity Synthesis (Teacher Notes)
  • “If we continue counting, what numbers will be in both counts?” (All of the numbers on the second list, the ones where we count by 12)
  • “Why do you think that happens?” (Each of the numbers in the second list are double the number in the first, so they’ll still be counted when you count by 6. 12 is 6×26 \times 2, so 6 is a factor in all the numbers in both lists.)
Standards
Building On
  • 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
  • 5.OA.3·Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. <em>For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.</em>
  • 5.OA.B.3·Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. <span>For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.</span>

20 min

15 min