Standard Algorithm: Multi-digit Numbers, with Composing

10 min

Narrative

The purpose of this Number Talk is to elicit the strategies and understandings students have for multiplying three factors, one of which is 10. These understandings help students develop fluency and will be helpful when they apply the standard algorithm to find the product of a three-digit and a two-digit number.

Students have an opportunity to look for and make use of structure (MP7) because they can use previous calculations and the distributive property to find a product.

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 product mentally.

  • (2×3)×10(2 \times 3) \times 10
  • (2×40)×10(2 \times 40) \times 10
  • (2×200)×10(2 \times 200) \times 10
  • (2×243)×10(2 \times 243) \times 10

Sample Response

  • 60: I know 2×3=62 \times 3 = 6 and 10 times as much is 60.
  • 800: I know 2×4=82 \times 4 =8 and 100 times as much is 800.
  • 4,000: I know 2×2=42 \times 2 = 4 and 1,000 times as much is 4,000.
  • 4,860: I added up the three numbers from the other calculations.
Activity Synthesis (Teacher Notes)
  • “How did multiplying all the products by 10 influence the result?” (It made the result ten times as big, so the digits all shift one place to the left and it has a zero at the end.)
  • “How are the products 2×2432 \times 243 and 20×24320 \times 243 related?” (The second one is ten times as big, so the digits shift one place to the left and it has a 0 at the end.)
  • “You can use this idea today when we apply the standard algorithm to find the products of a three-digit number and a two-digit number.”
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.

25 min

10 min