Strategies for Dividing

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for using multiplication to help them divide. These understandings help students develop fluency and will be helpful later in this lesson when students need to find the value of quotients.

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.

  • 3×53 \times 5
  • 6×56 \times 5
  • 10×510 \times 5
  • 65÷565 \div 5
Solution Steps (4)
  1. 1
    Find 3×5 mentally
    →15 (known fact)
  2. 2
    Find 6×5 using doubling
    →30 (double 15, since 6=2×3)
  3. 3
    Find 10×5 mentally
    →50 (known fact)
  4. 4
    Find 65÷5 using multiplication facts
    →65=50+15, so 10 fives + 3 fives = 13 fives → 13

Sample Response

  • 15: I just know it.
  • 30: It’s double 15, since 6 is double 3.
  • 50: I just know it.
  • 13: I know that 65 is 50+1550 + 15. There are 10 groups of 5 in 50 since 5×10=505 \times 10 = 50 and 3 groups of 5 in 15 since 5×3=155 \times 3 = 15. That’s 13 groups of 5 in 65.
Activity Synthesis (Teacher Notes)
  • “How does thinking about multiplication help you divide?” (I can think about what number multiplied by 5 will be 65. I can break that into smaller products I know.)
  • Consider asking:
    • “Who can restate _____’s reasoning in a different way?”
    • “Did anyone use the same strategy but would explain it differently?”
    • “Did anyone approach the problem in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
Standards
Addressing
  • 3.OA.5·Apply properties of operations as strategies to multiply and divide.
  • 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.B.5·Apply properties of operations as strategies to multiply and divide.<span>Students need not use formal terms for these properties.</span> <span>Examples: If <span class="math">\(6 \times 4 = 24\)</span> is known, then <span class="math">\(4 \times 6 = 24\)</span> is also known. (Commutative property of multiplication.) <span class="math">\(3 \times 5 \times 2\)</span> can be found by <span class="math">\(3 \times 5 = 15\)</span>, then <span class="math">\(15 \times 2 = 30\)</span>, or by <span class="math">\(5 \times 2 = 10\)</span>, then <span class="math">\(3 \times 10 = 30\)</span>. (Associative property of multiplication.) Knowing that <span class="math">\(8 \times 5 = 40\)</span> and <span class="math">\(8 \times 2 = 16\)</span>, one can find <span class="math">\(8 \times 7\)</span> as <span class="math">\(8 \times (5 + 2) = (8 \times 5) + (8 \times 2) = 40 + 16 = 56\)</span>. (Distributive property.)</span>
  • 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.

15 min

15 min