Patterns in Multiplication

10 min

Narrative

The purpose of this Choral Count is to invite students to practice counting by a unit fraction and to notice patterns in the count. These understandings will be helpful later in this lesson when students recognize that every fraction can be written as the product of a whole number and a unit fraction.

Launch

  • “Count by 14\frac{1}{4}, starting at 0.”
Teacher Instructions
  • Record as students count.
  • Stop counting and recording at 114\frac{11}{4}.
  • Repeat with 18\frac{1}{8}.
  • Stop counting and recording at 158\frac{15}{8}.

Sample Response

  • Start recording 04\frac{0}{4}, 14\frac{1}{4}, 24\frac{2}{4}, 34\frac{3}{4}, 44\frac{4}{4}, . . . , and stop at 114\frac{11}{4}.
  • Start recording 08\frac{0}{8}, 18\frac{1}{8}, 28\frac{2}{8}, 38\frac{3}{8}, 48\frac{4}{8}, . . . , and stop at 158\frac{15}{8}.
Activity Synthesis (Teacher Notes)
  • “What patterns do you notice?” (In both counts, the numerators go up by 1, and the denominators stay the same.)
  • “How many groups of 14\frac{1}{4} do we have?” (11)
  • “Where do you see them?” (Each count represents a new group of 14\frac{1}{4}.)
  • “How might we represent 11 groups of 14\frac{1}{4}, with an expression?” (11×1411 \times \frac{1}{4})
  • “How many groups of 18\frac{1}{8} do we have?” (15)
  • “How might we represent 15 groups of 18\frac{1}{8}, with an expression?” (15×1815 \times \frac{1}{8})
  • “How would our count change if we counted by 24\frac{2}{4} or 28\frac{2}{8}?” (Each numerator would be a multiple of 2, or an even number.)
Standards
Addressing
  • 4.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
  • 4.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

15 min

20 min