Recording Partial Products: One-Digit and Three- or Four-Digit Factors

10 min

Narrative

This Warm-up prompts students to carefully analyze and compare four equivalent expressions. In making comparisons, students have a reason to attend closely to the features and the value of the expressions and to use language precisely (MP6). The activity also enables the teacher to gain insight into students’ understanding of properties of operations and how they talk about them.

Launch

  • Groups of 2
  • Display the expressions.
  • “Pick 3 that go together. Be ready to share why they go together.”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 2–3 minutes: partner discussion
  • Share and record responses.

Student Task

Which 3 go together?

A

7×507 \times 50

B

(3×50)+(4×50)(3 \times 50) + (4 \times 50)

C

(5×10)×7(5 \times 10) \times 7

D

50+50+50+50+50+50+5050 + 50 + 50 + 50 + 50 + 50 + 50

Sample Response

Sample responses:

  • A, B, and C go together because they have a multiplication symbol.
  • A, B, and D go together because they include 50.
  • A, C, and D go together because each has only one type of operation symbol.
  • B, C, and D go together because they have multiple operations.
Activity Synthesis (Teacher Notes)
  • “How are the expressions alike?” (They all have a value of 350.)
  • “Were there expressions that you knew right away had the same value? Which ones? How did you know?”
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.

20 min

15 min