Standard Algorithm: Multi-digit Numbers, without Composing

10 min

Narrative

The purpose of this Number Talk is to elicit the strategies and understandings students have for mentally multiplying numbers that require composing a new unit. Students apply this understanding in the lesson when they compose a new unit, using the standard algorithm.

Launch

  • Display one problem.
  • “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 product mentally.

  • 20×320 \times 3
  • 24×324 \times 3
  • 120×3120 \times 3
  • 140×3140 \times 3

Sample Response

  • 60:  3×23 \times 2 is 6, and then I multiplied by 10.
  • 72:  4×34 \times 3 is 12, and then I added that to the 60. 
  • 360:  3×1003 \times 100 is 300 and 3×203 \times 20 is 60. 
  • 420:  3×1003 \times 100 is 300 and 3×403 \times 40 is 120, and then I added 300 and 120. 

Synthesis

  • “How do the tens in 20×320 \times 3 compare to the tens in 24 × 324 \times  3?” (There is 1 more ten in 24×324 \times 3 that came from 3×43 \times 4.)
  • “How do the hundreds in 120×3120 \times 3 compare to the hundreds in 140×3140 \times 3?” (There is 1 more hundred in 140×3140 \times 3 that came from 40 ×340 \times 3.)
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.

20 min

15 min