Shipping Trash

10 min

Narrative

The purpose of this Number Talk is for students to mentally calculate a product, with which students will work in context in this lesson. The first two products students may know from memory but if not, the idea of doubling 8×48 \times 4 to find 8×88 \times 8 can be helpful both for finding the value of 8×88 \times 8 and for starting a pattern that continues with the next product, 8×8×28 \times 8 \times 2, which is double 8×88 \times 8. The factors 8, 8, and 20 turn out to be the side lengths, in feet, of a standard container used on cargo ships. Students will examine these containers and the ships that carry them throughout the lesson.

Launch

  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 8×48 \times 4
  • 8×88 \times 8
  • 8×8×28 \times 8 \times 2
  • 8×8×208 \times 8 \times 20

Sample Response

Sample responses
  • 32: I just knew it.
  • 64: I doubled 32.
  • 128: I doubled 60 to get 120, and then doubled 4 and added that to 120.
  • 1,280: I know that multiplying by 10 shifts all of the digits one place to the left.
Activity Synthesis (Teacher Notes)
  • “How did you find the value of 8×8×208 \times 8 \times 20?” (I multiplied 8×8×28 \times 8 \times 2 by 10 because 20 is 10×210 \times 2.)
Standards
Building Toward
  • 5.NBT.5·Fluently multiply multi-digit whole numbers using the standard algorithm.
  • 5.NBT.B.5·Fluently multiply multi-digit whole numbers using the standard algorithm.

15 min

20 min