More Factors, More Problems

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplication by 10. These understandings help students develop fluency and will be helpful later in this lesson when students need to be able to represent and solve a problem involving groups of 10.

When students reason why the product increases by 10 as one factor increases by 1, they look for and express regularity in the expressions (MP8).

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 expression mentally.

  • 1×101\times10
  • 2×102\times10
  • 3×103\times10
  • 4×104\times10
Solution Steps (5)
  1. 1
    Find 1×10 mentally
    →1 group of 10 = 10
  2. 2
    Find 2×10 mentally
    →2 groups of 10 = 10+10 = 20 (or skip count: 10, 20)
  3. 3
    Find 3×10 mentally
    →3 groups of 10 = 10+10+10 = 30 (or skip count: 10, 20, 30)
  4. 4
    Find 4×10 mentally
    →4 groups of 10 = 40 (skip count: 10, 20, 30, 40)
  5. 5
    Notice the pattern
    →Product increases by 10 each time because we add one more group of 10

Sample Response

  • 10: It's only 1 group of 10.
  • 20: I added 10 more to the first answer.
  • 30: I added 10+10+1010+10+10.
  • 40: I counted by 10 four times.

Activity Synthesis (Teacher Notes)
  • "What pattern do you see as you look at the expressions and their values? Why is that happening?" (The factor that isn't 10 goes up by 1 each time. The value of the product increases by 10 each time because I have 1 more group of 10.)
  • As needed, record student thinking using equal-groups drawings or tape diagrams to help all students visualize the pattern.
  • Consider asking:
    • "Did anyone notice a different pattern?"
    • "Did anyone notice the same pattern but would explain it differently?"
Standards
Addressing
  • 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.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <em>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</em>
  • 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.
  • 3.OA.D.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <span>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</span>

15 min

20 min