Products Beyond 100

10 min

Narrative

This Number Talk encourages students to decompose factors and to rely on the distributive property to mentally solve. The strategies elicited in this routine will be helpful later in the lesson when students multiply up to four-digit numbers by one-digit numbers, and later in the section when they multiply 2 two-digit numbers by decomposing factors.

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 strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 8×308 \times 30
  • 5×305\times30
  • 10×3010\times30
  • 15×3015 \times 30

Sample Response

  • 240: 8×308 \times 30 is 8×3×108 \times 3 \times 10 or 24×1024 \times 10, which is 240.
  • 150: 5×3=155 \times 3 =15 so 5×30=1505 \times 30 = 150.
  • 300: 10×3010 \times 30 is 5×305 \times 30 doubled. 
  • 450: 15×3015 \times 30 is 15×3×1015 \times 3 \times 10 or 45×1045 \times 10, which is 450.
Activity Synthesis (Teacher Notes)
  • “How did the first three expressions help you find the value of 15×3015 \times 30?” (I know that (5×30)+(10×30)(5 \times 30) + (10 \times 30) is 15×3015 \times 30. I doubled the value of 8×308 \times 30 to get the value of 16×3016 \times 30 and then I subtracted 30 from it to get the value of 15×3015 \times 30.)
Standards
Addressing
  • 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

15 min

20 min