Problem Solving with Perimeter and Area

10 min

Narrative

The purpose of this True or False is to elicit strategies and understandings students have for dividing within 100. It also prompts them to rely on properties of operations and familiar division facts to facilitate division.

When students think about how to decompose larger dividends using facts about 10 to make the division easier, they look for and make use of structure (MP7).

Launch

  • Display one statement.
  • “Give me a signal when you know whether the statement is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record answers and strategy.
  • Repeat with each statement.

Student Task

Decide if each statement is true or false. Be prepared to explain your reasoning.

  • 60÷6=1060 \div 6 = 10
  • 72÷6=(60÷6)+(12÷6)72 \div 6 = (60 \div 6) + (12 \div 6)
  • 78÷6=(60÷10)+(18÷6)78 \div 6 = (60 \div 10) + (18 \div 6)
  • 96÷8=(80÷8)−(16÷8)96 \div 8 = (80 \div 8)-(16 \div 8)

Sample Response

  • True: I just know it.
  • True: 72 is 60+1260 + 12, so I can divide in parts and add the quotients.
  • False: 78 is 60+1860 + 18, but we need to divide each part of the dividend by 6, not by 10.
  • False: 96 is 80+1680 + 16 and we can divide each part by 8, but then we need to add the parts together, not subtract.
Activity Synthesis (Teacher Notes)
  • “How can you explain your answer without finding the value of both sides?”
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

20 min