Solve Area Problems

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying within 100. These understandings help students develop fluency and will be helpful later in this lesson when students multiply side lengths to find area. While recording students’ thinking, consider using equal groups or arrays, as in the images in the Warm-up of the previous lesson.

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 strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 5×25 \times 2
  • 6×26 \times 2
  • 5×65 \times 6
  • 6×66 \times 6
Solution Steps (4)
  1. 1
    Find 5 × 2
    →10 (count by 2s or known fact)
  2. 2
    Use 5×2 to find 6×2
    →6×2 = 5×2 + one more 2 = 10 + 2 = 12
  3. 3
    Find 5 × 6
    →30 (count by 6s or use 5 times any number ends in 0 or 5)
  4. 4
    Use 5×6 to find 6×6
    →6×6 = 5×6 + one more 6 = 30 + 6 = 36

Sample Response

  • 10: I counted by 2. I just knew 5 times 2 is 10.
  • 12: I knew that 5 groups of 2 is 10, so 1 group of 2 more would be 12. I knew 2 times 6 is 12, and that 6 times 2 is 12 because the factors were just in a different order. I just knew it.
  • 30: I counted by 10. I just knew 5 times 6 is 30.
  • 36: I knew that 5 groups of 6 is 30, so 1 group of 6 more would make 36.
Activity Synthesis (Teacher Notes)
  • “What do you notice happens when we increase one of the factors by 1?” (The product goes up by the amount of the other factor.)
  • “What makes this happen?” (The amount increases by 1 group of the other factor. Each group gets 1 more.)
  • As needed, record students' thinking, using drawings of equal groups or arrays 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
Building On
  • 3.OA.5·Apply properties of operations as strategies to multiply and divide.
  • 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>
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>

10 min

25 min