The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100. These understandings help students develop fluency and will be helpful later in this lesson when students find factor pairs of numbers.
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 for each expression.
Student Task
Find the value of each expression mentally.
12÷3
30÷3
60÷3
72÷3
Sample Response
4: I know 4 groups of 3 is 12.
10: I know that 10 groups of 3 is 30.
20: I know that 20×3=60.
24: 72 is 60 and 12 so that’s 20 and 4 groups or 24 groups of 3.
Activity Synthesis (Teacher Notes)
“How does knowing the first and third quotients help you find the last quotient?” (Since 12+60=72 , we can add the answers to those quotients to get the answer to the last problem.)
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.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
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Find Factors and Multiples
10 min
Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100. These understandings help students develop fluency and will be helpful later in this lesson when students find factor pairs of numbers.
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 for each expression.
Student Task
Find the value of each expression mentally.
12÷3
30÷3
60÷3
72÷3
Sample Response
4: I know 4 groups of 3 is 12.
10: I know that 10 groups of 3 is 30.
20: I know that 20×3=60.
24: 72 is 60 and 12 so that’s 20 and 4 groups or 24 groups of 3.
Activity Synthesis (Teacher Notes)
“How does knowing the first and third quotients help you find the last quotient?” (Since 12+60=72 , we can add the answers to those quotients to get the answer to the last problem.)
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.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.