Factor Pairs

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying single-digit numbers. These understandings help students develop fluency and will be helpful later in this lesson when students find factor pairs of numbers.

As students use earlier problems to find the new products, they look for and make use of structure (MP7) and use repeated reasoning (MP8).

This is the first time students experience the Number Talk routine in IM Grade 4. Students are familiar with this routine from a previous grade. However, they may benefit from a brief review of the steps involved.

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.

  • 2×72\times7
  • 4×74\times7
  • 3×73\times7
  • 7×77\times7

Sample Response

  • 14: I just know it. It’s 2 groups of 7.
  • 28: Four is double 2, so 4×74\times7 is double 2×72\times7 or double 14, which is 28.
  • 21: It’s one less group of 7 than 4×74 \times7, or 7 less than 28.
  • 49: Seven is 4+34 + 3, so I could add the answers to the previous two problems: 28+21=4928 + 21 = 49.
Activity Synthesis (Teacher Notes)
  • “How did the first three expressions help you find 7×77 \times 7?” (The 7 breaks apart into 3 and 4, so I could multiply in parts and then add them.)
  • Consider asking:
    • “Who can restate _____’s reasoning in a different way?”
    • “Did anyone have the same strategy but would explain it differently?”
    • “Did anyone approach the expression in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
Standards
Building On
  • 3.OA.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
  • 3.OA.C.7·Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that <span class="math">\(8 \times 5 = 40\)</span>, one knows <span class="math">\(40 \div 5 = 8\)</span>) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

20 min

15 min