Factors as a Factor in Our Strategy Choice

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying multi-digit whole numbers. These understandings help students develop fluency and will be helpful later in this lesson when students need to choose a multiplication strategy and justify that choice.

The products in this Number Talk get increasingly more cumbersome to keep track of mentally. This progression helps students identify products that are more easily found mentally versus those that are easier to find using the standard algorithm, with pencil and paper.

Launch

  • Display the first 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.

  • 230×10230 \times 10
  • 230×12230 \times 12
  • 230×15230 \times 15
  • 232×15232 \times 15

Sample Response

  • 2,300: 230×10=2,300230 \times 10 = 2,300

  • 2,760: 230×10=2,300230 \times 10 = 2,300

    230×2=460230 \times 2 = 460

    2,300+460=2,7602,300 + 460 = 2,760

  • 3,450: 230×10=2,300230 \times 10 = 2,300

    230×5=1,150230 \times 5 = 1,150

    2,300+1,150=3,4502,300 + 1,150 = 3,450

  • 3,480: 3,450+30=3,4803,450 + 30 = 3,480
Activity Synthesis (Teacher Notes)
  • “Which expression was the most challenging to solve mentally? Why do you think so?” (230×12230\times12, 230×15230\times15, or 232×15232\times15, because there are different partial products to keep track of and add.)
Standards
Addressing
  • 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