Estimate and Find Products

10 min

Narrative

The purpose of this Number Talk is to elicit the strategies and understandings students have for the multiplication of two- and three-digit numbers that are multiples of 10 and 100, respectively. These understandings help students develop fluency and will be helpful later in this lesson when students use multiplication to estimate products. This work also prepares them for the work of the standard algorithm for multiplication, in which each product is a product of single-digit multiples of powers of 10.

In this activity, students have an opportunity to look for and make use of structure (MP7) because the basic fact they are using is 5×6=305 \times 6 = 30, and each successive product is 10 times larger.

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 product mentally.

  • 50×650 \times 6
  • 50×6050 \times 60
  • 50×60050 \times 600
  • 600×500600 \times 500

Sample Response

  • 300: (5×6)×10=300(5 \times 6) \times 10 = 300
  • 3,000: (50×6)×10=3,000(50 \times 6) \times 10 = 3,000
  • 30,000: (50×60)×10=30,000(50 \times 60) \times 10 = 30,000
  • 300,000: (50×600)×10=300,000(50 \times 600) \times 10 = 300,000
Activity Synthesis (Teacher Notes)
  • “How can we use 5×65 \times 6 to find the value of each product?” (50×6=5×6×1050 \times 6 = 5 \times 6 \times 10, 50×60=5×6×10×1050 \times 60 = 5 \times 6 \times 10 \times 10, 50×600=5×6×10×10050 \times 600 = 5 \times 6 \times 10 \times 100, 600×500=6×5×100×100600 \times 500 = 6 \times 5 \times 100 \times 100)
  • “Why does each product in the Number Talk have one more 0 in it than the previous product?” (One of the factors has an additional 0.)
Standards
Building On
  • 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