The purpose of this Warm-up is to remind students of doubling as a strategy for multiplication where a factor in one product is twice a factor in another product. The reasoning that students do here with the factors 2, 4, 8, and 16 will support them as they reason about equivalent fractions and find multiples of numerators and denominators.
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 problems and work displayed.
Repeat with each expression.
Student Task
Find the value of each expression mentally.
2×12
4×12
8×12
16×12
Sample Response
24: I just know it.
48: 4 is twice 2, so 4×12 is twice 2×12. I doubled 24 to get 48.
96: 8 is twice 4, so 8×12 is twice 4×12. I doubled 48 to get 96.
192: 16 is twice 8, so 16×12 is twice 8×12. I doubled 96 to get 192.
Activity Synthesis (Teacher Notes)
“How did the first three expressions help you find the value of the last expression?”
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>
20 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Fractions on Number Lines
10 min
Narrative
The purpose of this Warm-up is to remind students of doubling as a strategy for multiplication where a factor in one product is twice a factor in another product. The reasoning that students do here with the factors 2, 4, 8, and 16 will support them as they reason about equivalent fractions and find multiples of numerators and denominators.
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 problems and work displayed.
Repeat with each expression.
Student Task
Find the value of each expression mentally.
2×12
4×12
8×12
16×12
Sample Response
24: I just know it.
48: 4 is twice 2, so 4×12 is twice 2×12. I doubled 24 to get 48.
96: 8 is twice 4, so 8×12 is twice 4×12. I doubled 48 to get 96.
192: 16 is twice 8, so 16×12 is twice 8×12. I doubled 96 to get 192.
Activity Synthesis (Teacher Notes)
“How did the first three expressions help you find the value of the last expression?”
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>